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http://theory.fnal.gov/people/kronfeld/TeX/mPole/ | ## The Perturbative Pole Mass in QCD
by Andreas S. Kronfeld.
Fermilab report FERMILAB-PUB-98/139-T
SPIRES entry
E-print archive hep-ph/9805215
### Some Background
Many physicists are probably astonished that a proof of the infrared finiteness and gauge independence of the pole mass in QCD is being written up in 1998. If you are one of them, please read the following before assuming that the results have long been known.
This paper grew out of Referee A's report on another paper of mine, hep-lat/9712024, written with Bart Mertens and Aida El-Khadra and submitted to (and published in) Physical Review D. The referee wrote
2) The authors assume that the pole mass of a quark is a well-defined concept order by order in perturbation theory. To the best of my knowledge this has not been shown in the literature. It has been demonstrated that the pole mass is infrared finite and gauge invariant to order $\alpha^2$~[C], and the corresponding finite part in the relation to the $\overline{\rm MS}$ mass has been worked out in ref.~[D].
It is quite possible that infrared problems prevent a definition of the quark's pole mass to all orders in perturbation theory....
[C] R. Tarrach, Nucl. Phys. B183 (1981) 384.
[D] N. Gray, D.J. Broadhurst, W. Grafe and K. Schilcher, Z. Phys. C 48, 673 (1990).
Let me add that other parts of the report revealed that Referee A is exceptionally well-informed on theoretical issues. It turns out, he/she also knows the literature better than most of us.
After considerable literature search I could not find a proof anywhere. During my search I found numerous authors who assert that the pole mass is, indeed, well-defined order by order in perturbation theory. Many papers cite Tarrach's paper for an all-orders proof, even though it sticks to two loops. Indeed, Tarrach is openly worried about the infrared. He writes [italics mine]
It may be evident to many theorists that the pole-mass is gauge-parameter independent in perturbative QCD, but it is less evident whether it is IR finite or not. Let us study these issues at the two loop level.
When Tarrach did his work, in 1981, there had been an effort to uncover a confining mechanism in the infrared divergences of QCD, so his concerns are a sign of the times.
In trying to trace the history of the QCD pole mass, I've noticed two folklores, which have evolved side-by-side. One, espoused by Referee A, holds that infrared divergences in QCD are so serious that nothing can be taken for granted. The other, which is nowadays probably more popular, takes for granted that the pole mass is infrared finite. (I have found no citation to a paper, even one on QED, that purports to study the problem to all orders; a remark in a footnote shows that Noboru Nakanishi knew what to do [Prog. Theor. Phys. 19 (1958) 159].)
I realize that some of you will have known the QED literature well enough to see that the generalization to QCD was straightforward. I would be happy to acknowledge unpublished work on the subject here: feel free to send me a copy of your notes. (Of course, it goes without saying that I would like to know of a detailed published reference.) At the same time, I hope that my paper serves as a useful reference, underpinning the (now publicly proven) fact that the pole mass in QCD is well defined at every order in perturbation theory.
During the time this paper was circulated as an e-print, several physicists from around the world alerted me to proofs of gauge independence of the pole mass, in QED and QCD, and of analogous quantities such as gluon damping rates at nonzero temperature. By and large, these papers do not pay close attention to infrared divergences. An exception is in Lowell Brown's text, Quantum Field Theory, which contains an elegant proof that infrared divergences and gauge dependence of the electron propagator (in QED) resides in the residue only, not the pole position. The proof is relegated to a problem and is, thus, easy to overlook. The proof assumes an Abelian gauge group, and I have not tried to generalize it.
Finally, I would also like to thank Referee A; without his/her strict report, I would not have tried to prove something that so many experts'' thought was done in 1981.
01 May 1998 --- Andreas Kronfeld ask@fnal.gov
Modified 29 July 1998 | 2014-04-24T10:57:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8596415519714355, "perplexity": 807.252566850113}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00568-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://pos.sissa.it/396/293/ | Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation
An update on QCD+QED simulations with C* boundary conditions
J. Luecke*, L. Bushnaq, I. Campos, M. Catillo, A. Cotellucci, M.E.B. Dale, P. Fritzsch, M.K. Marinkovic, A. Patella and N. Tantalo
Full text: pdf
Pre-published on: May 16, 2022
Published on:
Abstract
We present two novelties in our analysis of fully dynamical QCD+QED ensembles with C* boundary conditions. The first one is the explicit computation of the sign of the Pfaffian. We present an algorithm that provides a significant speedup compared to traditional methods. The second one is a reweighting of the mass in the context of the RHMC. We have tested the techniques on both pure QCD and QCD+QED ensembles with pions at $m_{\pi^\pm}\approx400$ MeV, a lattice spacing of $a\approx0.05$ fm, a fine-structure constant of $\alpha_{\mathrm{R}}=0$ and $0.04$.
DOI: https://doi.org/10.22323/1.396.0293
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2022-06-28T05:37:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.334401398897171, "perplexity": 1830.6569644033973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103355949.26/warc/CC-MAIN-20220628050721-20220628080721-00089.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Ahamkins.joel-david | # zbMATH — the first resource for mathematics
## Hamkins, Joel David
Compute Distance To:
Author ID: hamkins.joel-david Published as: Hamkins, Joel; Hamkins, Joel D.; Hamkins, Joel David Homepage: http://jdh.hamkins.org/ External Links: MGP · Wikidata · MathOverflow · ORCID · dblp
Documents Indexed: 88 Publications since 1994, including 2 Books
all top 5
#### Co-Authors
24 single-authored 7 Apter, Arthur W. 7 Gitman, Victoria 6 Fuchs, Gunter 6 Miller, Russell G. 5 Johnstone, Thomas A. 4 Reitz, Jonas 3 Coskey, Samuel 3 Löwe, Benedikt 3 Woodin, W. Hugh 2 Brendle, Jörg 2 Brian, William Rea 2 Cummings, James 2 Greenberg, Noam 2 Hirschfeldt, Denis Roman 2 Linetsky, David 2 Schindler, Ralf-Dieter 2 Seabold, Daniel Evan 1 Bagaria, Joan 1 Barton, Neil 1 Blair, D. Dakota 1 Blass, Andreas Raphael 1 Brumleve, Dan 1 Caicedo, Andrés Eduardo 1 Cheng, Yong 1 Cody, Brent M. 1 Daghighi, Ali Sadegh 1 Deolalikar, Vinay 1 Dorais, François Gilbert 1 Džamonja, Mirna 1 Enayat, Ali 1 Evans, C. D. A. 1 Friedman, Sy-David 1 Gitik, Moti 1 Godziszewski, Michał Tomasz 1 Golshani, Mohammad 1 Groszek, Marcia J. 1 Habič, Miha Emerik 1 Hardy, Michael 1 Jeřábek, Emil 1 Kikuchi, Makoto 1 Kirmayer, Greg 1 Klausner, Lukas Daniel 1 Larson, Paul B. 1 Leahy, Cole 1 Leibman, George 1 Lewis, Andrew D. 1 Lewis, Andy 1 Miller, Russel G. 1 Myasnikov, Alexei G. 1 O’Bryant, Kevin 1 Palumbo, Justin 1 Perlmutter, Norman Lewis 1 Schanker, Jason Aaron 1 Schlicht, Philipp 1 Shelah, Saharon 1 Thomas, Simon R. 1 Tsaprounis, Konstantinos 1 Usuba, Toshimichi 1 Verner, Jonathan L. 1 Warner, Steve 1 Welch, Philip D. 1 Williams, Kameryn J.
all top 5
#### Serials
14 The Journal of Symbolic Logic 9 Archive for Mathematical Logic 9 Mathematical Logic Quarterly (MLQ) 8 Annals of Pure and Applied Logic 7 Notre Dame Journal of Formal Logic 5 Proceedings of the American Mathematical Society 2 Israel Journal of Mathematics 2 Fundamenta Mathematicae 2 Transactions of the American Mathematical Society 2 Integers 1 Annals of the Japan Association for Philosophy of Science 1 Studia Logica 1 Kobe Journal of Mathematics 1 Journal of Logic and Computation 1 1 The Bulletin of Symbolic Logic 1 Journal of Mathematical Logic 1 Logic and Logical Philosophy 1 Central European Journal of Mathematics 1 Lecture Notes in Logic 1 The Review of Symbolic Logic 1 Computability
all top 5
#### Fields
85 Mathematical logic and foundations (03-XX) 7 Computer science (68-XX) 4 Group theory and generalizations (20-XX) 3 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Sequences, series, summability (40-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Number theory (11-XX)
#### Citations contained in zbMATH
72 Publications have been cited 648 times in 321 Documents Cited by Year
Infinite time Turing machines. Zbl 0963.03064
Hamkins, Joel David; Lewis, Andy
2000
Extensions with the approximation and cover properties have no new large cardinals. Zbl 1066.03052
Hamkins, Joel David
2003
The lottery preparation. Zbl 0949.03045
Hamkins, Joel David
2000
Gap forcing: Generalizing the Lévy-Solovay theorem. Zbl 0933.03067
Hamkins, Joel David
1999
Gap forcing. Zbl 1010.03042
Hamkins, Joel David
2001
Set-theoretic geology. Zbl 1348.03051
Fuchs, Gunter; Hamkins, Joel David; Reitz, Jonas
2015
What is the theory ZFC without power set? Zbl 1375.03059
Gitman, Victoria; Hamkins, Joel David; Johnstone, Thomas A.
2016
The set-theoretic multiverse. Zbl 1260.03103
Hamkins, Joel David
2012
The modal logic of forcing. Zbl 1139.03039
Hamkins, Joel David; Löwe, Benedikt
2008
The halting problem is decidable on a set of asymptotic probability one. Zbl 1137.03024
Hamkins, Joel David; Miasnikov, Alexei
2006
A simple maximality principle. Zbl 1056.03028
Hamkins, Joel David
2003
Small forcing creates neither strong nor Woodin cardinals. Zbl 0959.03040
Hamkins, Joel David; Woodin, W. Hugh
2000
Indestructibility and the level-by-level agreement between strong compactness and supercompactness. Zbl 1010.03043
Apter, Arthur W.; Hamkins, Joel David
2002
Fragile measurability. Zbl 0796.03054
Hamkins, Joel
1994
Resurrection axioms and uplifting cardinals. Zbl 1351.03043
Hamkins, Joel David; Johnstone, Thomas A.
2014
Destruction or preservation as you like it. Zbl 0949.03047
Hamkins, Joel David
1998
Small forcing makes any cardinal superdestructible. Zbl 0906.03051
Hamkins, Joel David
1998
Tall cardinals. Zbl 1165.03044
Hamkins, Joel D.
2009
Infinite time Turing machines. Zbl 1030.68036
Hamkins, Joel David
2002
Superstrong and other large cardinals are never Laver indestructible. Zbl 1402.03073
Bagaria, Joan; Hamkins, Joel David; Tsaprounis, Konstantinos; Usuba, Toshimichi
2016
Indestructible strong unfoldability. Zbl 1207.03057
Hamkins, Joel David; Johnstone, Thomas A.
2010
Generalizations of the Kunen inconsistency. Zbl 1270.03100
Hamkins, Joel David; Kirmayer, Greg; Perlmutter, Norman Lewis
2012
Diamond (on the regulars) can fail at any strongly unfoldable cardinal. Zbl 1110.03032
Džamonja, Mirna; Hamkins, Joel David
2006
Superdestructibility: A dual to Laver’s indestructibility. Zbl 0921.03051
Hamkins, Joel David; Shelah, Saharon
1998
The hierarchy of equivalence relations on the natural numbers under computable reducibility. Zbl 1325.03049
Coskey, Amuel; Hamkins, Joel David; Miller, Russell
2012
The ground axiom is consistent with $$V \neq \text{HOD}$$. Zbl 1145.03029
Hamkins, Joel David; Reitz, Jonas; Woodin, W. Hugh
2008
Large cardinals with few measures. Zbl 1115.03075
Apter, Arthur W.; Cummings, James; Hamkins, Joel David
2007
The Necessary Maximality Principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal. Zbl 1078.03042
Hamkins, Joel D.; Woodin, W. Hugh
2005
Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata. Zbl 0992.03064
Apter, Arthur W.; Hamkins, Joel David
2001
Universal indestructibility. Zbl 0953.03060
Apter, Arthur W.; Hamkins, Joel David
1999
Canonical seeds and Prikry trees. Zbl 0890.03024
Hamkins, Joel David
1997
The wholeness axioms and V=HOD. Zbl 0969.03063
Hamkins, Joel David
2001
A natural model of the multiverse axioms. Zbl 1214.03035
Gitman, Victoria; Hamkins, Joel David
2010
Post’s problem for supertasks has both positive and negative solutions. Zbl 1024.03043
Hamkins, Joel David; Lewis, Andrew
2002
Infinite time Turing machines with only one tape. Zbl 0990.03031
Hamkins, Joel David; Seabold, Daniel Evan
2001
Effective mathematics of the uncountable. Zbl 1297.03006
Greenberg, Noam (ed.); Hamkins, Joel David (ed.); Hirschfeldt, Denis (ed.); Miller, Russell (ed.)
2013
Degrees of rigidity for Souslin trees. Zbl 1179.03043
Fuchs, Gunter; Hamkins, Joel David
2009
Exactly controlling the non-supercompact strongly compact cardinals. Zbl 1056.03030
Apter, Arthur W.; Hamkins, Joel David
2003
Unfoldable cardinals and the GCH. Zbl 1025.03051
Hamkins, Joel David
2001
Strongly uplifting cardinals and the boldface resurrection axioms. Zbl 1417.03269
Hamkins, Joel David; Johnstone, Thomas A.
2017
Moving up and down in the generic multiverse. Zbl 1303.03078
Hamkins, Joel David; Löwe, Benedikt
2013
Infinite time decidable equivalence relation theory. Zbl 1233.03050
Coskey, Samuel; Hamkins, Joel David
2011
P$$\neq \text{NP}\cap$$co-NP for infinite time Turing machines. Zbl 1089.68043
Deolalikar, Vinay; Hamkins, Joel David; Schindler, Ralf
2005
Changing the heights of automorphism towers. Zbl 0944.03048
Hamkins, Joel David; Thomas, Simon
2000
Algebraicity and implicit definability in set theory. Zbl 1436.03264
Hamkins, Joel David; Leahy, Cole
2016
Structural connections between a forcing class and its modal logic. Zbl 1367.03095
Hamkins, Joel David; Leibman, George; Löwe, Benedikt
2015
The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $$\theta$$-supercompact. Zbl 1360.03082
Cody, Brent; Gitik, Moti; Hamkins, Joel David; Schanker, Jason A.
2015
Every countable model of set theory embeds into its own constructible universe. Zbl 1326.03046
Hamkins, Joel David
2013
Pointwise definable models of set theory. Zbl 1270.03101
Hamkins, Joel David; Linetsky, David; Reitz, Jonas
2013
Inner models with large cardinal features usually obtained by forcing. Zbl 1250.03104
Apter, Arthur W.; Gitman, Victoria; Hamkins, Joel David
2012
Some second order set theory. Zbl 1209.03045
Hamkins, Joel David
2009
Every group has a terminating transfinite automorphism tower. Zbl 0904.20027
Hamkins, Joel David
1998
A model of the generic Vopěnka principle in which the ordinals are not Mahlo. Zbl 07006136
Gitman, Victoria; Hamkins, Joel David
2019
A multiverse perspective on the axiom of constructibility. Zbl 1321.03061
Hamkins, Joel David
2014
Transfinite game values in infinite chess. Zbl 1369.03118
Evans, C. D. A.; Hamkins, Joel David
2014
The proper and semi-proper forcing axioms for forcing notions that preserve $$\aleph_2$$ or $$\aleph_3$$. Zbl 1166.03030
Hamkins, Joel David; Johnstone, Thomas A.
2009
Changing the heights of automorphism towers by forcing with Souslin trees over L. Zbl 1153.03026
Fuchs, Gunter; Hamkins, Joel David
2008
A survey of infinite time Turing machines. Zbl 1211.03060
Hamkins, Joel David
2007
Post’s problem for ordinal register machines. Zbl 1151.03339
Hamkins, Joel D.; Miller, Russell G.
2007
The rearrangement number. Zbl 07144584
Blass, Andreas; Brendle, Jörg; Brian, Will; Hamkins, Joel David; Hardy, Michael; Larson, Paul B.
2020
ZFC proves that the class of ordinals is not weakly compact for definable classes. Zbl 1447.03016
Enayat, Ali; Hamkins, Joel David
2018
Open determinacy for class games. Zbl 1423.03200
Gitman, Victoria; Hamkins, Joel David
2017
Large cardinals need not be large in HOD. Zbl 1373.03109
Cheng, Yong; Friedman, Sy-David; Hamkins, Joel David
2015
Is the dream solution of the continuum hypothesis attainable? Zbl 1331.03034
Hamkins, Joel David
2015
The rigid relation principle, a new weak choice principle. Zbl 1268.03067
Hamkins, Joel David; Palumbo, Justin
2012
The mate-in-$$n$$ problem of infinite chess is decidable. Zbl 1357.03042
Brumleve, Dan; Hamkins, Joel David; Schlicht, Philipp
2012
The set-theoretic multiverse: a natural context for set theory. Zbl 1274.03076
Hamkins, Joel David
2011
Post’s problem for ordinal register machines: an explicit approach. Zbl 1178.03060
Hamkins, Joel David; Miller, Russell G.
2009
The complexity of quickly ORM-decidable sets. Zbl 1150.03321
Hamkins, Joel D.; Linetsky, David; Miller, Russell
2007
Infinitary computability with infinite time Turing machines. Zbl 1113.68399
Hamkins, Joel David
2005
$$\text P^f\neq\text{NP}^{f}$$ for almost all $$f$$. Zbl 1043.03036
Hamkins, Joel David; Welch, Philip D.
2003
How tall is the automorphism tower of a group? Zbl 1012.20034
Hamkins, Joel David
2002
The rearrangement number. Zbl 07144584
Blass, Andreas; Brendle, Jörg; Brian, Will; Hamkins, Joel David; Hardy, Michael; Larson, Paul B.
2020
A model of the generic Vopěnka principle in which the ordinals are not Mahlo. Zbl 07006136
Gitman, Victoria; Hamkins, Joel David
2019
ZFC proves that the class of ordinals is not weakly compact for definable classes. Zbl 1447.03016
Enayat, Ali; Hamkins, Joel David
2018
Strongly uplifting cardinals and the boldface resurrection axioms. Zbl 1417.03269
Hamkins, Joel David; Johnstone, Thomas A.
2017
Open determinacy for class games. Zbl 1423.03200
Gitman, Victoria; Hamkins, Joel David
2017
What is the theory ZFC without power set? Zbl 1375.03059
Gitman, Victoria; Hamkins, Joel David; Johnstone, Thomas A.
2016
Superstrong and other large cardinals are never Laver indestructible. Zbl 1402.03073
Bagaria, Joan; Hamkins, Joel David; Tsaprounis, Konstantinos; Usuba, Toshimichi
2016
Algebraicity and implicit definability in set theory. Zbl 1436.03264
Hamkins, Joel David; Leahy, Cole
2016
Set-theoretic geology. Zbl 1348.03051
Fuchs, Gunter; Hamkins, Joel David; Reitz, Jonas
2015
Structural connections between a forcing class and its modal logic. Zbl 1367.03095
Hamkins, Joel David; Leibman, George; Löwe, Benedikt
2015
The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $$\theta$$-supercompact. Zbl 1360.03082
Cody, Brent; Gitik, Moti; Hamkins, Joel David; Schanker, Jason A.
2015
Large cardinals need not be large in HOD. Zbl 1373.03109
Cheng, Yong; Friedman, Sy-David; Hamkins, Joel David
2015
Is the dream solution of the continuum hypothesis attainable? Zbl 1331.03034
Hamkins, Joel David
2015
Resurrection axioms and uplifting cardinals. Zbl 1351.03043
Hamkins, Joel David; Johnstone, Thomas A.
2014
A multiverse perspective on the axiom of constructibility. Zbl 1321.03061
Hamkins, Joel David
2014
Transfinite game values in infinite chess. Zbl 1369.03118
Evans, C. D. A.; Hamkins, Joel David
2014
Effective mathematics of the uncountable. Zbl 1297.03006
Greenberg, Noam (ed.); Hamkins, Joel David (ed.); Hirschfeldt, Denis (ed.); Miller, Russell (ed.)
2013
Moving up and down in the generic multiverse. Zbl 1303.03078
Hamkins, Joel David; Löwe, Benedikt
2013
Every countable model of set theory embeds into its own constructible universe. Zbl 1326.03046
Hamkins, Joel David
2013
Pointwise definable models of set theory. Zbl 1270.03101
Hamkins, Joel David; Linetsky, David; Reitz, Jonas
2013
The set-theoretic multiverse. Zbl 1260.03103
Hamkins, Joel David
2012
Generalizations of the Kunen inconsistency. Zbl 1270.03100
Hamkins, Joel David; Kirmayer, Greg; Perlmutter, Norman Lewis
2012
The hierarchy of equivalence relations on the natural numbers under computable reducibility. Zbl 1325.03049
Coskey, Amuel; Hamkins, Joel David; Miller, Russell
2012
Inner models with large cardinal features usually obtained by forcing. Zbl 1250.03104
Apter, Arthur W.; Gitman, Victoria; Hamkins, Joel David
2012
The rigid relation principle, a new weak choice principle. Zbl 1268.03067
Hamkins, Joel David; Palumbo, Justin
2012
The mate-in-$$n$$ problem of infinite chess is decidable. Zbl 1357.03042
Brumleve, Dan; Hamkins, Joel David; Schlicht, Philipp
2012
Infinite time decidable equivalence relation theory. Zbl 1233.03050
Coskey, Samuel; Hamkins, Joel David
2011
The set-theoretic multiverse: a natural context for set theory. Zbl 1274.03076
Hamkins, Joel David
2011
Indestructible strong unfoldability. Zbl 1207.03057
Hamkins, Joel David; Johnstone, Thomas A.
2010
A natural model of the multiverse axioms. Zbl 1214.03035
Gitman, Victoria; Hamkins, Joel David
2010
Tall cardinals. Zbl 1165.03044
Hamkins, Joel D.
2009
Degrees of rigidity for Souslin trees. Zbl 1179.03043
Fuchs, Gunter; Hamkins, Joel David
2009
Some second order set theory. Zbl 1209.03045
Hamkins, Joel David
2009
The proper and semi-proper forcing axioms for forcing notions that preserve $$\aleph_2$$ or $$\aleph_3$$. Zbl 1166.03030
Hamkins, Joel David; Johnstone, Thomas A.
2009
Post’s problem for ordinal register machines: an explicit approach. Zbl 1178.03060
Hamkins, Joel David; Miller, Russell G.
2009
The modal logic of forcing. Zbl 1139.03039
Hamkins, Joel David; Löwe, Benedikt
2008
The ground axiom is consistent with $$V \neq \text{HOD}$$. Zbl 1145.03029
Hamkins, Joel David; Reitz, Jonas; Woodin, W. Hugh
2008
Changing the heights of automorphism towers by forcing with Souslin trees over L. Zbl 1153.03026
Fuchs, Gunter; Hamkins, Joel David
2008
Large cardinals with few measures. Zbl 1115.03075
Apter, Arthur W.; Cummings, James; Hamkins, Joel David
2007
A survey of infinite time Turing machines. Zbl 1211.03060
Hamkins, Joel David
2007
Post’s problem for ordinal register machines. Zbl 1151.03339
Hamkins, Joel D.; Miller, Russell G.
2007
The complexity of quickly ORM-decidable sets. Zbl 1150.03321
Hamkins, Joel D.; Linetsky, David; Miller, Russell
2007
The halting problem is decidable on a set of asymptotic probability one. Zbl 1137.03024
Hamkins, Joel David; Miasnikov, Alexei
2006
Diamond (on the regulars) can fail at any strongly unfoldable cardinal. Zbl 1110.03032
Džamonja, Mirna; Hamkins, Joel David
2006
The Necessary Maximality Principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal. Zbl 1078.03042
Hamkins, Joel D.; Woodin, W. Hugh
2005
P$$\neq \text{NP}\cap$$co-NP for infinite time Turing machines. Zbl 1089.68043
Deolalikar, Vinay; Hamkins, Joel David; Schindler, Ralf
2005
Infinitary computability with infinite time Turing machines. Zbl 1113.68399
Hamkins, Joel David
2005
Extensions with the approximation and cover properties have no new large cardinals. Zbl 1066.03052
Hamkins, Joel David
2003
A simple maximality principle. Zbl 1056.03028
Hamkins, Joel David
2003
Exactly controlling the non-supercompact strongly compact cardinals. Zbl 1056.03030
Apter, Arthur W.; Hamkins, Joel David
2003
$$\text P^f\neq\text{NP}^{f}$$ for almost all $$f$$. Zbl 1043.03036
Hamkins, Joel David; Welch, Philip D.
2003
Indestructibility and the level-by-level agreement between strong compactness and supercompactness. Zbl 1010.03043
Apter, Arthur W.; Hamkins, Joel David
2002
Infinite time Turing machines. Zbl 1030.68036
Hamkins, Joel David
2002
Post’s problem for supertasks has both positive and negative solutions. Zbl 1024.03043
Hamkins, Joel David; Lewis, Andrew
2002
How tall is the automorphism tower of a group? Zbl 1012.20034
Hamkins, Joel David
2002
Gap forcing. Zbl 1010.03042
Hamkins, Joel David
2001
Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata. Zbl 0992.03064
Apter, Arthur W.; Hamkins, Joel David
2001
The wholeness axioms and V=HOD. Zbl 0969.03063
Hamkins, Joel David
2001
Infinite time Turing machines with only one tape. Zbl 0990.03031
Hamkins, Joel David; Seabold, Daniel Evan
2001
Unfoldable cardinals and the GCH. Zbl 1025.03051
Hamkins, Joel David
2001
Infinite time Turing machines. Zbl 0963.03064
Hamkins, Joel David; Lewis, Andy
2000
The lottery preparation. Zbl 0949.03045
Hamkins, Joel David
2000
Small forcing creates neither strong nor Woodin cardinals. Zbl 0959.03040
Hamkins, Joel David; Woodin, W. Hugh
2000
Changing the heights of automorphism towers. Zbl 0944.03048
Hamkins, Joel David; Thomas, Simon
2000
Gap forcing: Generalizing the Lévy-Solovay theorem. Zbl 0933.03067
Hamkins, Joel David
1999
Universal indestructibility. Zbl 0953.03060
Apter, Arthur W.; Hamkins, Joel David
1999
Destruction or preservation as you like it. Zbl 0949.03047
Hamkins, Joel David
1998
Small forcing makes any cardinal superdestructible. Zbl 0906.03051
Hamkins, Joel David
1998
Superdestructibility: A dual to Laver’s indestructibility. Zbl 0921.03051
Hamkins, Joel David; Shelah, Saharon
1998
Every group has a terminating transfinite automorphism tower. Zbl 0904.20027
Hamkins, Joel David
1998
Canonical seeds and Prikry trees. Zbl 0890.03024
Hamkins, Joel David
1997
Fragile measurability. Zbl 0796.03054
Hamkins, Joel
1994
all top 5
#### Cited by 243 Authors
43 Apter, Arthur W. 37 Hamkins, Joel David 14 Fuchs, Gunter 13 Friedman, Sy-David 12 Carl, Merlin 9 Gitman, Victoria 8 Cody, Brent M. 8 Schlicht, Philipp 7 Lücke, Philipp Moritz 7 Rybalov, Aleksandr Nikolaevich 7 Sargsyan, Grigor 6 Honzik, Radek 6 Koepke, Peter 6 Tsaprounis, Konstantinos 6 Welch, Philip D. 5 Antos, Carolin 5 Johnstone, Thomas A. 5 Löwe, Benedikt 5 Schindler, Ralf-Dieter 4 Ben-Neria, Omer 4 Bringsjord, Selmer 4 Cheng, Yong 4 Corazza, Paul 4 Kanovei, Vladimir G. 4 Krueger, John 4 Myasnikov, Alexei G. 4 Perlmutter, Norman Lewis 4 Reitz, Jonas 4 Usuba, Toshimichi 4 Viale, Matteo 3 Barton, Neil 3 Cox, Sean D. 3 Cummings, James 3 Friedman, Shoshana 3 Gitik, Moti 3 Khoussainov, Bakhadyr M. 3 Lubarsky, Robert S. 3 Mitchell, William John 3 Monin, Benoît 3 Ng, KengMeng 3 Rin, Benjamin G. 3 Sorbi, Andrea 3 Wilson, Trevor Miles 3 Woodin, W. Hugh 2 Andrews, Uri 2 Bazhenov, Nikolaĭ Alekseevich 2 Brooke-Taylor, Andrew D. 2 Burgin, Mark 2 Calude, Cristian S. 2 Coskey, Samuel 2 d’Auriac, Paul-Elliot Anglès 2 Desfontaines, Damien 2 Dimonte, Vincenzo 2 Durand, Bruno 2 Govindarajulu, Naveen Sundar 2 Habič, Miha Emerik 2 Köllner, Peter 2 Lafitte, Grégory 2 Meadows, Toby 2 Miller, Russell G. 2 Osin, Denis V. 2 Potgieter, Petrus H. 2 Sakai, Hiroshi 2 Schanker, Jason Aaron 2 Schweber, Noah David 2 Shagrir, Oron 2 Shelah, Saharon 2 Siders, Ryan 2 Stephan, Frank 2 Ternullo, Claudio 2 Venturi, Giorgio 2 Welch, Peter D. 2 Wiedermann, Jiří 2 Williams, Kameryn J. 2 Ziegler, Martin 1 Ackerman, Nathanael Leedom 1 Akl, Selim G. 1 Arkoudas, Konstantine 1 Arrigoni, Tatiana 1 Asperó, David 1 Astor, Eric P. 1 Audrito, Giorgio 1 Badaev, Serikzhan A. 1 Bagaria, Joan 1 Bard, Vittorio 1 Bauer, Andrej 1 Baumes, Jeffrey 1 Bianchetti, Matteo 1 Bienvenu, Laurent 1 Boney, Will 1 Bruni, Riccardo 1 Button, Tim 1 Cabessa, Jérémie 1 Caicedo, Andrés Eduardo 1 Chan, William C. Y. 1 Clemens, John Daniel 1 Cockshott, Paul 1 Costa, José Félix 1 Cramer, Scott S. 1 Daghighi, Ali Sadegh ...and 143 more Authors
all top 5
#### Cited in 54 Serials
52 Archive for Mathematical Logic 47 The Journal of Symbolic Logic 36 Annals of Pure and Applied Logic 19 Mathematical Logic Quarterly (MLQ) 16 Theoretical Computer Science 12 Notre Dame Journal of Formal Logic 11 The Bulletin of Symbolic Logic 10 Israel Journal of Mathematics 6 Studia Logica 6 The Review of Symbolic Logic 5 Proceedings of the American Mathematical Society 4 Applied Mathematics and Computation 4 Journal of Mathematical Logic 4 Natural Computing 3 Algebra and Logic 3 Transactions of the American Mathematical Society 3 Bulletin of the Polish Academy of Sciences, Mathematics 3 Theory of Computing Systems 2 Advances in Mathematics 2 Fundamenta Mathematicae 2 Illinois Journal of Mathematics 2 Journal of Philosophical Logic 2 Siberian Mathematical Journal 2 Logical Methods in Computer Science 2 Computability 2 Bollettino dell’Unione Matematica Italiana 1 International Journal of Theoretical Physics 1 Information Processing Letters 1 Periodica Mathematica Hungarica 1 Journal of Algebra 1 Journal of Computer and System Sciences 1 Journal of Pure and Applied Algebra 1 Synthese 1 Topology and its Applications 1 Advances in Applied Mathematics 1 Bulletin of the Iranian Mathematical Society 1 Order 1 Journal of Complexity 1 Journal of Automated Reasoning 1 Journal of the American Mathematical Society 1 MSCS. Mathematical Structures in Computer Science 1 International Journal of Foundations of Computer Science 1 International Journal of Computer Mathematics 1 Indagationes Mathematicae. New Series 1 Erkenntnis 1 Foundations of Science 1 Lobachevskii Journal of Mathematics 1 Parallel Processing Letters 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Sarajevo Journal of Mathematics 1 International Journal of Parallel, Emergent and Distributed Systems 1 Logica Universalis 1 Groups, Complexity, Cryptology 1 Forum of Mathematics, Sigma
all top 5
#### Cited in 16 Fields
294 Mathematical logic and foundations (03-XX) 50 Computer science (68-XX) 11 General and overarching topics; collections (00-XX) 9 Group theory and generalizations (20-XX) 4 Combinatorics (05-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Category theory; homological algebra (18-XX) 3 Quantum theory (81-XX) 2 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Numerical analysis (65-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-01-23T12:31:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7504221796989441, "perplexity": 8453.603494930068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703537796.45/warc/CC-MAIN-20210123094754-20210123124754-00106.warc.gz"} |
https://pos.sissa.it/338/031/ | Volume 338 - High Energy Astrophysics in Southern Africa (HEASA2018) - HEASA 2018 Speakers
Spectral Variability Signatures of Relativistic Shocks in Blazars
M. Böttcher,* M. Baring
*corresponding author
Full text: pdf
Published on: July 29, 2019
Abstract
Mildly relativistic, oblique shocks are frequently invoked as possible sites of relativistic particle acceleration and production of strongly variable, polarized multi-wavelength emission from relativistic jet sources such as blazars, via diffusive shock acceleration (DSA). In recent work, we had self-consistently coupled DSA and radiation transfer simulations in blazar jets. These one-zone models determined that the observed spectral energy distributions (SEDs) of blazars strongly constrain the nature of the hydromagnetic turbulence responsible for pitch-angle scattering. In this paper, we expand our previous work by including full time dependence and treating two emission zones, one being the site of acceleration.
This modeling is applied to a multiwavelength flare of the flat spectrum radio quasar 3C~279, fitting snap-shot SEDs and light curves. We predict spectral hysteresis patterns in various energy bands as well as cross-band time lags with optical and GeV $\gamma$-rays as well as radio and X-rays tracing each other closely with zero time lag, but radio and X-rays lagging behind the optical and $\gamma$-ray variability by several hours.
DOI: https://doi.org/10.22323/1.338.0031
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-07-14T00:34:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3554486036300659, "perplexity": 7102.270627520973}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657147031.78/warc/CC-MAIN-20200713225620-20200714015620-00391.warc.gz"} |
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# 36th Annual International Symposium on Lattice Field Theory
22-28 July 2018
Kellogg Hotel and Conference Center
EST timezone
## Control of SU(3) symmetry breaking effects in calculations of B meson decay constant
Jul 25, 2018, 3:20 PM
20m
103 (Kellogg Hotel and Conference Center)
### 103
#### Kellogg Hotel and Conference Center
219 S Harrison Rd, East Lansing, MI 48824
Weak Decays and Matrix Elements
### Speaker
Sophie Hollitt (University of Adelaide)
### Description
Early B physics experiments have left us with a number of puzzles in heavy flavour physics. New lattice calculations and greater understanding of QCD effects in the Standard Model will be needed to support greater experimental precision in the coming years. In particular, the B meson decay constant is involved in calculations of CKM matrix elements and useful to measurements of the branching ratio B $\to \tau \nu$ expected at the Belle II Experiment. We extend the QCDSF studies of SU(3) breaking of light decay constants into the heavy-flavour regime to examine the effects of SU(3) breaking on $f_B$ and $f_{B_s}$. $b$-quarks are generated using an anisotropic clover-improved heavy-quark action. The decay constants $f_B$ and $f_{B_s}$ will be presented for a variety of light quark masses, from the SU(3) symmetric point toward the physical quark masses. In order to focus on the SU(3) symmetry breaking effects in our extrapolation to the physical point, we choose u,d,s quark masses in each simulation such that the average quark mass, $m = m_u + m_d + m_s$, is constant and equal to its physical value. Results will be presented at a number of different lattice spacings and volumes, toward calculations of $f_B$ and $f_{B_s}$ at the physical point.
### Primary author
Sophie Hollitt (University of Adelaide)
Slides | 2021-06-19T18:52:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4940197169780731, "perplexity": 1915.849861487991}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487649688.44/warc/CC-MAIN-20210619172612-20210619202612-00092.warc.gz"} |
https://covid19-data.nist.gov/pid/rest/local/paper/comix_comparing_mixing_patterns_in_the_belgian_population_during_and_after_lockdown | ## comix comparing mixing patterns in the belgian population during and after lockdown CORD-Papers-2022-06-02 (Version 1)
Title: CoMix: comparing mixing patterns in the Belgian population during and after lockdown The COVID-19 pandemic has shown how a newly emergent communicable disease can lay considerable burden on public health. To avoid system collapse governments have resorted to several social distancing measures. In Belgium this included a lockdown and a following period of phased re-opening. A representative sample of Belgian adults was asked about their contact behaviour from mid-April to the beginning of August during different stages of the intervention measures in Belgium. Use of personal protection equipment (face masks) and compliance to hygienic measures was also reported. We estimated the expected reproduction number computing the ratio of [Formula: see text] with respect to pre-pandemic data. During the first two waves (the first month) of the survey the reduction in the average number of contacts was around 80% and was quite consistent across all age-classes. The average number of contacts increased over time particularly for the younger age classes still remaining significantly lower than pre-pandemic values. From the end of May to the end of July the estimated reproduction number has a median value larger than one although with a wide dispersion. Estimated [Formula: see text] fell below one again at the beginning of August. We have shown how a rapidly deployed survey can measure compliance to social distancing and assess its impact on COVID-19 spread. Monitoring the effectiveness of social distancing recommendations is of paramount importance to avoid further waves of COVID-19. 2020-12-14 Sci Rep 10.1038/s41598-020-78540-7 http://doi.org/10.1038/s41598-020-78540-7 Coletti Pietro https://covid19-data.nist.gov/pid/rest/local/author/coletti_pietro Wambua James https://covid19-data.nist.gov/pid/rest/local/author/wambua_james Gimma Amy https://covid19-data.nist.gov/pid/rest/local/author/gimma_amy Willem Lander https://covid19-data.nist.gov/pid/rest/local/author/willem_lander Vercruysse Sarah https://covid19-data.nist.gov/pid/rest/local/author/vercruysse_sarah Vanhoutte Bieke https://covid19-data.nist.gov/pid/rest/local/author/vanhoutte_bieke Jarvis Christopher I https://covid19-data.nist.gov/pid/rest/local/author/jarvis_christopher_i Van Zandvoort Kevin https://covid19-data.nist.gov/pid/rest/local/author/van_zandvoort_kevin Edmunds John https://covid19-data.nist.gov/pid/rest/local/author/edmunds_john Beutels Philippe https://covid19-data.nist.gov/pid/rest/local/author/beutels_philippe Hens Niel https://covid19-data.nist.gov/pid/rest/local/author/hens_niel 3d35638e8ce7a35203afd21d4187048dcb8b299d cc-by https://creativecommons.org/licenses/by/4.0/ Medline; PMC https://www.medline.com/https://www.ncbi.nlm.nih.gov/pubmed/ 33318521 https://www.ncbi.nlm.nih.gov/pubmed/33318521 PMC7736856 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7736856 https://doi.org/10.1038/s41598-020-78540-7 https://www.ncbi.nlm.nih.gov/pubmed/33318521/ TRUE lockdown COVID-19 Shanghai 5 face-masks post-lockdown direct/ Zenodo 31 COVID-19 children line Brussels and Netherlands 7 EC UZA 20/13/147 lockdown globe contacts US 9 UK matrix Shanghai and participants 5-17 phone/tablet Face coronavirus UK 6 15,26 close-contact Wuhan households social contacts France S15 Wuhan 5 multi-wave SARS-CoV-2 www.nature.com/scientificreports/ supermarkets/shops contact matrix www.nature.com/scientificreports/ Figure 3 (= people children contacts SocialMixr age-values ses/by/4.0/. line Innovations Programme-Project EpiPose http://creat iveco mmons COVID-19's Public Health First 5000 Characters:The COVID-19 pandemic has shown how a newly emergent communicable disease can lay considerable burden on public health. To avoid system collapse, governments have resorted to several social distancing measures. In Belgium, this included a lockdown and a following period of phased re-opening. A representative sample of Belgian adults was asked about their contact behaviour from mid-April to the beginning of August, during different stages of the intervention measures in Belgium. Use of personal protection equipment (face masks) and compliance to hygienic measures was also reported. We estimated the expected reproduction number computing the ratio of R 0 with respect to pre-pandemic data. During the first two waves (the first month) of the survey, the reduction in the average number of contacts was around 80% and was quite consistent across all age-classes. The average number of contacts increased over time, particularly for the younger age classes, still remaining significantly lower than pre-pandemic values. From the end of May to the end of July , the estimated reproduction number has a median value larger than one, although with a wide dispersion. Estimated R 0 fell below one again at the beginning of August. We have shown how a rapidly deployed survey can measure compliance to social distancing and assess its impact on COVID-19 spread. Monitoring the effectiveness of social distancing recommendations is of paramount importance to avoid further waves of COVID-19. OPEN The COVID-19 pandemic due to the novel coronavirus (SARS-CoV-2) has shown how newly emerging infectious diseases can lay considerable burden on public health and social economic welfare of the society. Since its emergence, over million confirmed cases and deaths have been recorded as of 2020 1 . In the absence of established pharmaceutical interventions, many countries across the globe have resorted to non-pharmaceutical interventions, advocacy of proper hygienic measures (hand washing, sanitizing), as well as promotion of wide-spread usage of masks to help combat the spread of this disease. However, sustainability of some of the imposed measures is infeasible in the long term, due to an urgent need to returning back to normal social life as well as rekindling the economy. Thus governments have been prompted to lift some of the measures in a phased manner whilst enforcing new/existing rules such as wearing masks in designated places such as in public transport, hospitals, schools, workplaces and other places that attract large crowds and gatherings. As COVID-19 is primarily transmitted through close-contact interaction with infected individuals 2 , data on social contacts is indispensable in informing mathematical modeling studies being employed to explore the evolution of this disease. The last decade of research in infectious disease modeling has shown how quantifying contact patterns is crucial to capture disease dynamics 3 . However, social contact data capturing behavioral changes in the population during and across different stages of an epidemic is mostly lacking and mathematical models need to rely on various assumptions, which might be unverifiable. This raises validity concerns on their appropriateness in guiding decision making. Thus, as many governments are carefully monitoring the situation to avoid further waves of COVID-19, continual data collection is vitally important to closely monitor changes in social mixing. This can provide insights Scientific Reports | (2020) 10:21885 | https://doi.org/10.1038/s41598-020-78540-7 www.nature.com/scientificreports/ on the impact of different intervention measures as well as help in real-time management of the COVID-19 crisis, together with other insights from social and behavioral sciences 4 . Studies comparing social contact patterns before and during the COVID-19 pandemic have been reported for Wuhan and Shanghai 5 , the UK 6 , the Netherlands 7 , Luxembourg 8 , the US 9 and in multiple countries (Belgium, France, Germany, Italy, the Netherlands, Spain, the UK, and the US) 10 . The overall reduction in the total number of contacts made by individuals ranged from 48% to 85%, stressing once again the importance of quantifying the impact of social distancing separately for each country. Also, although little variations in the number of contacts over time were measured 10 up to mid-April, this may change as countries relieve stricter measures and social interactions need to adjust to the new post-lockdown reality 8 . In this paper, we present results from a longitudinal survey of the adult population in Belgium, representative by age, gender and region of residence. The survey involves multiple waves of data collection, and is part of a wider study to look at changes in contact patterns across European countries (see e.g. UK 6 ). Here, we present results for eight waves (= 16 weeks). We quantify the changes in social contact patterns comparing pre-pandemic, lockdown and post-lockdown period \documentclass[12pt]{minimal} UK SARS-CoV-2 sciences4 US)10 time25 initiative6 EC UZA 20/13/147 contact matrix Shanghai measured10 globe households people children21 adults19 S15 US9 lockdown \documentclass[12pt]{minimal children contacts mandatory23 multi-wave number15 place22 survey22 face-masks France phone/tablet contacts July14 Netherlands7 Zenodo31 bias3,24 Wuhan line children Wuhan5 's Brussels and reality8 Luxembourg8 close-contact participants age-values hypothesis"15,26 in29 19–65 individuals2 0.02813 SocialMixr matrix supermarkets/shops restaurants conversational contacts individuals UK6 Shanghai5 face Fig. 7 post-lockdown coronavirus COVID-19 First 5000 Characters:The COVID-19 pandemic due to the novel coronavirus (SARS-CoV-2) has shown how newly emerging infectious diseases can lay considerable burden on public health and social economic welfare of the society. Since its emergence, over million confirmed cases and deaths have been recorded as of 20201. In the absence of established pharmaceutical interventions, many countries across the globe have resorted to non-pharmaceutical interventions, advocacy of proper hygienic measures (hand washing, sanitizing), as well as promotion of wide-spread usage of masks to help combat the spread of this disease. However, sustainability of some of the imposed measures is infeasible in the long term, due to an urgent need to returning back to normal social life as well as rekindling the economy. Thus governments have been prompted to lift some of the measures in a phased manner whilst enforcing new/existing rules such as wearing masks in designated places such as in public transport, hospitals, schools, workplaces and other places that attract large crowds and gatherings. As COVID-19 is primarily transmitted through close-contact interaction with infected individuals2, data on social contacts is indispensable in informing mathematical modeling studies being employed to explore the evolution of this disease. The last decade of research in infectious disease modeling has shown how quantifying contact patterns is crucial to capture disease dynamics3. However, social contact data capturing behavioral changes in the population during and across different stages of an epidemic is mostly lacking and mathematical models need to rely on various assumptions, which might be unverifiable. This raises validity concerns on their appropriateness in guiding decision making. Thus, as many governments are carefully monitoring the situation to avoid further waves of COVID-19, continual data collection is vitally important to closely monitor changes in social mixing. This can provide insights on the impact of different intervention measures as well as help in real-time management of the COVID-19 crisis, together with other insights from social and behavioral sciences4. Studies comparing social contact patterns before and during the COVID-19 pandemic have been reported for Wuhan and Shanghai5, the UK6, the Netherlands7 , Luxembourg8, the US9 and in multiple countries (Belgium, France, Germany, Italy, the Netherlands, Spain, the UK, and the US)10. The overall reduction in the total number of contacts made by individuals ranged from 48% to 85%, stressing once again the importance of quantifying the impact of social distancing separately for each country. Also, although little variations in the number of contacts over time were measured10 up to mid-April, this may change as countries relieve stricter measures and social interactions need to adjust to the new post-lockdown reality8. In this paper, we present results from a longitudinal survey of the adult population in Belgium, representative by age, gender and region of residence. The survey involves multiple waves of data collection, and is part of a wider study to look at changes in contact patterns across European countries (see e.g. UK6). Here, we present results for eight waves (= 16 weeks). We quantify the changes in social contact patterns comparing pre-pandemic, lockdown and post-lockdown periods and its impact on the transmission dynamics of COVID-19 based on the changes in the basic reproduction number relying on the next generation principle. We use a published survey of the Flemish region (Belgium) conducted in 201011,12 as reference for the pre-pandemic social mixing. Also, we assess the uptake of face mask wearing and adherence to hygienic measures in the population over time. During the first wave, 1542 participants took part in the survey, divided among 732 males (47.5%) and 810 females (52.5%) (Table 1). Table S2 presents information on participation rates for each wave. The average participant's age was 48.4 years (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {standard deviation (sd)} =16.3\hbox { years}$$\end{document}standard deviation (sd)=16.3years), with a median age of 50 years, and an inter-quartile range (IQR) of [35–65]. The average household size was 2.8 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {sd} = 1.4$$\end{document}sd=1.4), IQR [2–4] with a maximum household size of 10. In total, data on 4290 household members, including the participants, was collected. Nearly half of the participants were living with children (51. document_parses/pdf_json/3d35638e8ce7a35203afd21d4187048dcb8b299d.json document_parses/pmc_json/PMC7736856.xml.json comix_comparing_mixing_patterns_in_the_belgian_population_during_and_after_lockdown | 2022-08-15T19:30:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4411126971244812, "perplexity": 4918.498042379544}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572198.93/warc/CC-MAIN-20220815175725-20220815205725-00485.warc.gz"} |
http://dergipark.gov.tr/ijot/issue/35770/316300 | | | | |
## Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel
#### Salman Abdu Ahmed [1] , Song Zhou [2] , Yuangqing Zhu [3]
##### 133 107
The demand for higher output efficiencies, greater specific power output, increased reliability, and ever reduced emissions has been rising. One promising alternative is the use of a gaseous fuel as partial supplement to liquid fuel. In this study, the effects of diesel-natural gas substitution ratios on the engine performance parameters like brake specific fuel consumption (BSFC), and gaseous emissions of nitrogen oxides (NOX), hydrocarbons (HC), carbon monoxide (CO) and carbon dioxide (CO2) were investigated for natural gas-diesel fuel operation and then compared with the original diesel operation. The engine was modeled with GT-Power computational simulation tool. The diesel fuel was injected into the cylinder while natural gas was injected in to air-intake pipe then compressed together with air. The simulation was carried out at constant engine speed of 1800rpm for four different natural gas fractions (15%, 25%, and 50% and 75%). NOX and CO2 emissions decreased sharply by more than 45% and 50% respectively in dual-fuel mode when compared to only diesel fuel mode. However an increase was observed in CO and HC emissions in dual fuel mode. The results also indicated that higher BSFC and lower brake thermal efficiency (BTE) in dual fuel mode when compared to those of the corresponding diesel engine.
Diesel, dual-fuel engine, natural gas, engine performance
• [1] H.Bayraktar, "An experimental study on the performance parameters of an experimental CI engine fueled with diesel–methanol–dodecanol blends," Fuel, vol. 87, pp. 158-164, 2008. [2] J. Liu, A. Yao, and C. Yao, "Effects of injection timing on performance and emissions of a HD diesel engine with DMCC," Fuel, vol. 134, pp. 107-113, 2014. [3] A. Broatch, J. Luján, S. Ruiz, and P. Olmeda, "Measurement of hydrocarbon and carbon monoxide emissions during the starting of automotive DI diesel engines," International Journal of Automotive Technology, vol. 9, pp. 129-140, 2008. [4] MARPOL Annex IV, Regulations 13 I. M. Organization, 2014. [5] B. Sahoo, N. Sahoo, and U. Saha, "Effect of engine parameters and type of gaseous fuel on the performance of dual-fuel gas diesel engines—A critical review," Renewable and Sustainable Energy Reviews, vol. 13, pp. 1151-1184, 2009. [6] O. Badr, G. Karim, and B. Liu, "An examination of the flame spread limits in a dual fuel engine," Applied Thermal Engineering, vol. 19, pp. 1071-1080, 1999. [7] J. Kusaka, T. Okamoto, Y. Daisho, R. Kihara, and T. Saito, "Combustion and exhaust gas emission characteristics of a diesel engine dual-fueled with natural gas," JSAE review, vol. 21, pp. 489-496, 2000. [8] G. A. Alla, H. Soliman, O. Badr, and M. A. Rabbo, "Effect of pilot fuel quantity on the performance of a dual fuel engine," Energy Conversion and Management, vol. 41, pp. 559-572, 2000. [9] Y. Karagöz, T. Sandalcı, U. O. Koylu, A. S. Dalkılıç, and S. Wongwises, "Effect of the use of natural gas–diesel fuel mixture on performance, emissions, and combustion characteristics of a compression ignition engine," Advances in Mechanical Engineering, vol. 8, p. 1687814016643228, 2016. [10]R. Papagiannakis and D. Hountalas, "Combustion and exhaust emission characteristics of a dual fuel compression ignition engine operated with pilot diesel fuel and natural gas," Energy conversion and management, vol. 45, pp. 2971-2987, 2004. [11]J. Egúsquiza, S. Braga, and C. Braga, "Performance and gaseous emissions characteristics of a natural gas/diesel dual fuel turbocharged and aftercooled engine," Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 31, pp. 142-150, 2009. [12]V. K. Gaba and P. Nashine, "Shubhankar. Bhowmick,” Combustion Modeling of Diesel Engine Using Bio-Diesel as Secondary Fuel," in International Conference on Mechanical and Robotics Engineering (ICMRE'2012) May, 2012, pp. 26-27. [13]V. Ayhan, A. Parlak, I. Cesur, B. Boru, and A. Kolip, "Performance and exhaust emission characteristics of a diesel engine running with LPG," International Journal of Physical Sciences, vol. 6, pp. 1905-1914, 2011. [14]A. Kumaraswamy and B. D. Prasad, "Performance analysis of a dual fuel engine using LPG and diesel with EGR system," Procedia Engineering, vol. 38, pp. 2784-2792, 2012. [15] G. Theotokatos, S. Stoumpos, Y. Ding, L. Xiang, and G. Livanos, "COMPUTATIONAL INVESTIGATION OF A LARGE DUAL FUEL MARINE ENGINE." [16]K. D. Bob-Manuel and R. J. Crookes, "Performance and Emission Evaluation in Dual-Fuel Engine Using Renewable Fuels for Pilot Injection," SAE Technical Paper 0148-7191, 2007. [17]S. Randive and D. Thombare, "Modelling and Simulation of Methanol and Diesel Fuelled HCCI Engine for Improved Performance and Emission Characteristics." [18]R. Singh and S. Maji, "Performance and exhaust gas emissions analysis of direct injection cng-diesel dual fuel engine," Research Scholar, PhD Candidate, University of Delhi, Delhi, INDIA, 2012. [19]P. L. Mtui, "Performance And Emissions Modeling Of Natural Gas Dual Fuelling Of Large Diesel Engines," International Journal of Scientific & Technology Research, vol. 2, pp. 317-323, 2013. [20] C. R. Ferguson and A. T. Kirkpatrick, Internal combustion engines: applied thermosciences: John Wiley & Sons, 2015. [21] G. A. Karim, Dual-fuel diesel engines: CRC Press, 2015. [22] H. Köse and M. Ciniviz, "An experimental investigation of effect on diesel engine performance and exhaust emissions of addition at dual fuel mode of hydrogen," Fuel processing technology, vol. 114, pp. 26-34, 2013. [23] B. John, "Heywood internal combustion engine fndament als," ed: Mc Graw-Hill Book Company, 1988. [24] W. A. Majewski and M. K. Khair, "Diesel emissions and their control," SAE Technical Paper2006. [25] K. Cheenkachorn, C. Poompipatpong, and C. G. Ho, "Performance and emissions of a heavy-duty diesel engine fuelled with diesel and LNG (liquid natural gas)," Energy, vol. 53, pp. 52-57, 2013. [26] G. A. Karim, "A review of combustion processes in the dual fuel engine—the gas diesel engine," Progress in Energy and Combustion Science, vol. 6, pp. 277-285, 1980. [27] D. Kouremenos, D. Hountalas, and A. Kouremenos, "Experimental investigation of the effect of fuel composition on the formation of pollutants in direct injection diesel engines," SAE Technical Paper 0148-7191, 1999.
Birincil Dil en Mühendislik Regular Original Research Article Yazar: Salman Abdu AhmedKurum: Harbin Engineering UniversityÜlke: China Yazar: Song ZhouKurum: Harbin Engineering UniversityÜlke: China Yazar: Yuangqing ZhuKurum: Harbin Engineering UniversityÜlke: China
Bibtex @araştırma makalesi { ijot316300, journal = {International Journal of Thermodynamics}, issn = {1301-9724}, eissn = {2146-1511}, address = {Yaşar DEMİREL}, year = {2018}, volume = {21}, pages = {16 - 25}, doi = {10.5541/ijot.316300}, title = {Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel}, key = {cite}, author = {Ahmed, Salman Abdu and Zhou, Song and Zhu, Yuangqing} } APA Ahmed, S , Zhou, S , Zhu, Y . (2018). Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel. International Journal of Thermodynamics, 21 (1), 16-25. DOI: 10.5541/ijot.316300 MLA Ahmed, S , Zhou, S , Zhu, Y . "Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel". International Journal of Thermodynamics 21 (2018): 16-25 Chicago Ahmed, S , Zhou, S , Zhu, Y . "Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel". International Journal of Thermodynamics 21 (2018): 16-25 RIS TY - JOUR T1 - Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel AU - Salman Abdu Ahmed , Song Zhou , Yuangqing Zhu Y1 - 2018 PY - 2018 N1 - doi: 10.5541/ijot.316300 DO - 10.5541/ijot.316300 T2 - International Journal of Thermodynamics JF - Journal JO - JOR SP - 16 EP - 25 VL - 21 IS - 1 SN - 1301-9724-2146-1511 M3 - doi: 10.5541/ijot.316300 UR - http://dx.doi.org/10.5541/ijot.316300 Y2 - 2018 ER - EndNote %0 International Journal of Thermodynamics Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel %A Salman Abdu Ahmed , Song Zhou , Yuangqing Zhu %T Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel %D 2018 %J International Journal of Thermodynamics %P 1301-9724-2146-1511 %V 21 %N 1 %R doi: 10.5541/ijot.316300 %U 10.5541/ijot.316300 ISNAD Ahmed, Salman Abdu , Zhou, Song , Zhu, Yuangqing . "Performance and Emission Characteristics Analysis of Dual Fuel Compression Ignition Engine Using Natural Gas and Diesel". International Journal of Thermodynamics 21 / 1 (Mart 2018): 16-25. http://dx.doi.org/10.5541/ijot.316300 | 2019-03-25T17:56:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.48056116700172424, "perplexity": 12877.136849759152}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204086.87/warc/CC-MAIN-20190325174034-20190325200034-00492.warc.gz"} |
https://par.nsf.gov/biblio/10312146-first-principles-study-dense-metallic-nitric-sulfur-hydrides | First principles study of dense and metallic nitric sulfur hydrides
Abstract Studies of molecular mixtures containing hydrogen sulfide (H 2 S) could open up new routes towards hydrogen-rich high-temperature superconductors under pressure. H 2 S and ammonia (NH 3 ) form hydrogen-bonded molecular mixtures at ambient conditions, but their phase behavior and propensity towards mixing under pressure is not well understood. Here, we show stable phases in the H 2 S–NH 3 system under extreme pressure conditions to 4 Mbar from first-principles crystal structure prediction methods. We identify four stable compositions, two of which, (H 2 S) (NH 3 ) and (H 2 S) (NH 3 ) 4 , are stable in a sequence of structures to the Mbar regime. A re-entrant stabilization of (H 2 S) (NH 3 ) 4 above 300 GPa is driven by a marked reversal of sulfur-hydrogen chemistry. Several stable phases exhibit metallic character. Electron–phonon coupling calculations predict superconducting temperatures up to 50 K, in the Cmma phase of (H 2 S) (NH 3 ) at 150 GPa. The present findings shed light on how sulfur hydride bonding and superconductivity are affected in molecular mixtures. They also suggest a reservoir for hydrogen sulfide in the upper mantle regions of icy planets in a potentially metallic mixture, which could more »
Authors:
; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10312146
Journal Name:
Communications Chemistry
Volume:
4
Issue:
1
ISSN:
2399-3669
5. Sub-Neptunes are common among the discovered exoplanets. However, lack of knowledge on the state of matter in$H2$O-rich setting at high pressures and temperatures ($P−T$) places important limitations on our understanding of this planet type. We have conducted experiments for reactions between$SiO2$and$H2$O as archetypal materials for rock and ice, respectively, at high$P−T$. We found anomalously expanded volumes of dense silica (up to 4%) recovered from hydrothermal synthesis above ∼24 GPa where the$CaCl2$-type (Ct) structure appears at lower pressures than in the anhydrous system. Infrared spectroscopy identified strong OH modes from the dense silica samples. Both previous experiments and our density functional theory calculations support up to 0.48 hydrogen atoms per formula unit of ($Si1−xH4x$)$O2 (x=0.12)$. At pressures above 60 GPa,$H2$O further changes the structural behavior of silica, stabilizing a niccolite-type structure, which is unquenchable. From unit-cell volume and phase equilibrium considerations, we infer that the niccolite-type phase may contain H with an amount at least comparable with or higher than that of the Ct phase. Our results suggest that the phases containing both hydrogen and lithophile elements could bemore » | 2023-03-28T23:39:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 9, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6460606455802917, "perplexity": 4982.946990479523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948900.50/warc/CC-MAIN-20230328232645-20230329022645-00775.warc.gz"} |
https://www.usgs.gov/center-news/continued-rumblings-2006-kiholo-bay-earthquake | # Continued Rumblings of the 2006 Kiholo Bay Earthquake
Release Date:
This past weekend, Kohala's famed Mauna Kea Beach Hotel celebrated a "soft reopening" following repairs and renovations in the aftermath of the October 15, 2006 Kiholo Bay earthquake. A formal "grand reopening" is scheduled to follow this Spring.
Plume of brown water at the base of the pali between Kaaha and Halape, on Kīlauea's south flank, marks the location of rock slides triggered by the earthquake. Halape is visible in the background.
(Public domain.)
Residents of and visitors to the island of Hawaii are reminded of the earthquake in this and other ways. Some, like the replacement bridge on the Mamalahoa Highway (Route 19) in Paauilo are quite visible.
For the most part, the October 2006 earthquake experiences are memories. We were fortunate that our community was not forced to endure more widespread and more devastating consequence due to the earthquake.
At the same time, as residents of an earthquake-prone region, we know that future large earthquakes are expected. The principal means of mitigating the effects of large earthquakes include developing and adopting appropriate building codes and use of appropriate earthquake-resistant design and building practice, as well as establishing community and personal earthquake response plans.
While current scientific capabilities do not afford the means to precisely predict the time, location, and magnitude of future large earthquakes, we are able to forecast the effects of future large earthquakes as the probabilities of strong earthquake shaking. The U. S. Geological Survey (USGS) features this information online, with explanations, as probabilistic seismic hazards maps at http://earthquake.usgs.gov/research/hazmaps/.
As is the case for any large earthquake, the 2006 Kiholo Bay earthquake sequence (including main and after shocks) provided important observations and data that will fuel research toward a better understanding of earthquakes and their effects. For Kiholo Bay, such data were recorded by a set of instruments installed and maintained by the USGS National Strong Motion Project (NSMP). Beginning in the year 2000 and only now recently completed, the NSMP has upgraded all of its strong motion instrumentation, some of which recorded on film in 2006, to current operational (digital) standards.
The NSMP instruments are referred to as "strong motion accelerographs" that record the strongest shaking expected from earthquakes without exceeding the maximum working range of the instruments. There are two-dozen NSMP instruments on the island of Hawaii, and a few more on Oahu and in Maui County.
The maximum shaking from the October 15 M6.7 mainshock was not recorded by the NSMP instrument nearest the earthquake epicenter as expected. Instead, the strongest shaking was recorded at the Waimea Fire Station (more than 32 km or 20 miles away), and the overall pattern of strong motion data suggested significant variations in response due to soil and geological conditions beneath the individual instrument locations.
Data collected from the NSMP sites since 2006 have been compiled into a new map of strong motion site conditions for the Big Island that was presented earlier this month at the Fall 2008 Meeting of the American Geophysical Union (AGU). While an earlier version of the map showed much of the island to be classified as "rock" sites, the recent work suggests that much of Hawaii Island should be considered soft rock or very dense soil. Shaking at soft rock or very dense soil sites would be amplified over shaking at hard rock sites. The differences must be incorporated into updated seismic hazard maps of Hawaii to properly estimate future strong earthquake shaking.
Also presented at the AGU meeting was an HVO study of the rupture process of the Kiholo Bay M6.7 mainshock. This study also used NSMP recordings from the Kiholo Bay sequence, including the M5.0 aftershock that occurred on Thanksgiving Day, 2006.
The October 15, 2006 M6.7 Kiholo Bay earthquake occurred on a deep fault, approximately 39 km (24 miles) below sea level. The slippage that caused the earthquake started at its hypocenter and continued over an area of the fault roughly 30 km X 20 km (18 miles X 12 miles) in size, in a westward direction away from the island at a speed of 3.5 km/s (2.2 miles/s or 7.900 miles/hr). Maximum slippage was more than 1 m (3.3 ft).
Such studies will contribute to a better understanding of large earthquakes and how their effects are distributed across Hawaii.
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### Volcano Activity Update
Kīlauea Volcano continues to be active. A vent in Halemaumau Crater is erupting elevated amounts of sulfur dioxide gas and very small amounts of ash. Resulting high concentrations of sulfur dioxide in downwind air have closed the south part of Kīlauea caldera and produced occasional air quality alerts in more distant areas, such as Pahala and communities adjacent to Hawaii Volcanoes National Park, during kona wind periods.
Puu Ōō continues to produce sulfur dioxide at even higher rates than the vent in Halemaumau Crater. Trade winds tend to pool these emissions along the West Hawaii coast, while Kona winds blow these emissions into communities to the north, such as Mountain View, Volcano, and Hilo.
Lava erupting from the Thanksgiving Eve Breakout (TEB) vent at the eastern base of Puu Ōō continues to flow to the ocean at Waikupanaha through a well-established lava tube. Breakouts from the lava tube were active in the abandoned Royal Gardens subdivision and on the coastal plain in the past week. Active portions of the flow on the coastal plain were within 100 yards of the National Park boundary, as they have been during the last several weeks. Ocean entry activity has fluctuated in the past week, due to a deflation-inflation cycle that began on Sunday, Dec. 21. These cycles normally cause changes in lava supply to the flow field that can last a few days.
Be aware that active lava deltas can collapse at any time, potentially generating large explosions. This may be especially true during times of rapidly changing lava supply conditions. The Waikupanaha delta has collapsed many times over the last several months, with three of the collapses resulting in rock blasts that tossed television-sized rocks up onto the sea-cliff and threw fist-sized rocks more than 200 yards inland.
Do not approach the ocean entry or venture onto the lava deltas. Even the intervening beaches are susceptible to large waves generated during delta collapse; avoid these beaches. In addition, steam plumes rising from ocean entries are highly acidic and laced with glass particles. Call Hawaii County Civil Defense at 961-8093 for viewing hours.
Mauna Loa is not erupting. Two earthquakes were located beneath the summit this past week. Continuing extension between locations spanning the summit indicates slow inflation of the volcano, combined with slow eastward slippage of its east flank.
No earthquakes beneath Hawaii Island were reported felt within the past week.
The staff of the Hawaiian Volcano Observatory wishes you a Happy Holiday Season. Visit our Web site for daily Kīlauea eruption updates, a summary of volcanic events over the past year, and nearly real-time Hawaii earthquake information. Kīlauea daily update summaries are also available by phone at (808) 967-8862. Questions can be emailed to askHVO@usgs.gov. skip past bottom navigational bar | 2020-01-25T01:37:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20035870373249054, "perplexity": 3727.0248187707284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250628549.43/warc/CC-MAIN-20200125011232-20200125040232-00470.warc.gz"} |
http://legisquebec.gouv.qc.ca/en/showversion/cs/I-8.1?code=se:103_4&pointInTime=20210906 | ### I-8.1 - Act respecting offences relating to alcoholic beverages
103.4. In proceedings for contravention of section 103.1 or 103.2, the permit holder shall incur no penalty if he proves that he used reasonable diligence to ascertain the age of the person and that he had reasonable ground for believing that that person was of full age or if he proves that he had reasonable ground for believing that it was a case contemplated in the second paragraph of section 103.2.
1979, c. 71, s. 128. | 2021-10-25T08:46:39 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8366407155990601, "perplexity": 2790.266276743814}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587655.10/warc/CC-MAIN-20211025061300-20211025091300-00139.warc.gz"} |
https://www.zbmath.org/authors/?q=ai%3Akim.jeong-han | # zbMATH — the first resource for mathematics
## Kim, Jeong Han
Compute Distance To:
Author ID: kim.jeong-han Published as: Kim, Jeong Han; Kim, J. H.; Kim, Jeong-Han; Kim, J.; Kim, Jeong H. Homepage: https://www.mathnet.or.kr/people_list/view/4242 External Links: MGP · Wikidata
Documents Indexed: 59 Publications since 1993
all top 5
#### Co-Authors
10 single-authored 10 Vu, Van H. 4 Choi, Sung-Soon 4 Peres, Yuval 4 Tetali, Prasad 3 Alon, Noga M. 3 Bollobás, Béla 3 Wormald, Nicholas Charles 2 Bayati, Mohsen Fathollah 2 Ding, Jian 2 Fishburn, Peter Clingerman 2 Greenhill, Catherine S. 2 Jung, Kyomin 2 Lee, Choongbum 2 Lee, Joonkyung 2 Lee, Sangjune 2 Lubetzky, Eyal 2 Mandjes, Michel Robertus Hendrikus 2 Montenegro, Ravi 2 Pittel, Boris G. 2 Saberi, Amin 2 Spencer, Joel H. 2 Sudakov, Benny 2 Verstraëte, Jacques 1 Achlioptas, Dimitris 1 Armero, Francisco 1 Bohman, Tom 1 Borgs, Christian 1 Chayes, Jennifer Tour 1 Chen, Bob 1 Conlon, David 1 Hajiaghayi, Mohammad Taghi 1 Jang, Lee-Chae 1 Janson, Svante 1 Jo, Gwanghyun 1 Kahn, Jeff D. 1 Kim, Taekyun 1 Krivelevich, Michael 1 Lagarias, Jeffrey C. 1 Lee, Sungchul 1 Leighton Tom 1 Matoušek, Jiří 1 Na, Joohan 1 Park, Dal-Won 1 Pikhurko, Oleg 1 Racke, Harald 1 Roche, James R. 1 Tait, Michael 1 Verbitsky, Oleg 1 Wilson, David Bruce 1 Wright, Paul E.
all top 5
#### Serials
11 Random Structures & Algorithms 4 Combinatorica 3 Journal of Combinatorial Theory. Series A 3 Journal of Combinatorial Theory. Series B 3 Journal of Computer and System Sciences 3 Combinatorics, Probability and Computing 2 Artificial Intelligence 2 Discrete Mathematics 2 SIAM Journal on Discrete Mathematics 1 Advances in Applied Probability 1 Computer Methods in Applied Mechanics and Engineering 1 Discrete Applied Mathematics 1 Israel Journal of Mathematics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Advances in Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Graph Theory 1 Journal of the London Mathematical Society. Second Series 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 Statistics & Probability Letters 1 Algorithmica 1 Queueing Systems 1 The Annals of Applied Probability 1 Far East Journal of Mathematical Sciences 1 Journal of Applied Mathematics 1 Annals of Fuzzy Mathematics and Informatics
all top 5
#### Fields
43 Combinatorics (05-XX) 14 Probability theory and stochastic processes (60-XX) 11 Computer science (68-XX) 4 Operations research, mathematical programming (90-XX) 4 Information and communication theory, circuits (94-XX) 3 Number theory (11-XX) 2 Numerical analysis (65-XX) 2 Mechanics of deformable solids (74-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Partial differential equations (35-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Biology and other natural sciences (92-XX)
#### Citations contained in zbMATH Open
49 Publications have been cited 578 times in 503 Documents Cited by Year
The Ramsey number $$R(3,t)$$ has order of magnitude $$t^ 2 /\log t$$. Zbl 0832.05084
Kim, Jeong Han
1995
Concentration of multivariate polynomials and its applications. Zbl 0969.60013
Kim, Jeong Han; Vu, Van H.
2000
The scaling window of the 2-SAT transition. Zbl 0979.68053
Bollobás, Béla; Borgs, Christian; Chayes, Jennifer T.; Kim, Jeong Han; Wilson, David B.
2001
On Brooks’ theorem for sparse graphs. Zbl 0833.05030
Kim, Jeong Han
1995
Nearly perfect matchings in regular simple hypergraphs. Zbl 0882.05107
Alon, Noga; Kim, Jeong-Han; Spencer, Joel
1997
Divide and conquer martingales and the number of triangles in a random graph. Zbl 1041.60042
Kim, J. H.; Vu, V. H.
2004
Small complete arcs in projective planes. Zbl 1027.05015
Kim, J. H.; Vu, V. H.
2003
On the asymmetry of random regular graphs and random graphs. Zbl 1012.05143
Kim, Jeong Han; Sudakov, Benny; Vu, Van H.
2002
Sandwiching random graphs: universality between random graph models. Zbl 1050.05111
Kim, J. H.; Vu, V. H.
2004
Diameters in supercritical random graphs via first passage percolation. Zbl 1260.05048
Ding, Jian; Kim, Jeong Han; Lubetzky, Eyal; Peres, Yuval
2010
Two approaches to Sidorenko’s conjecture. Zbl 1331.05220
Kim, Jeong Han; Lee, Choongbum; Lee, Joonkyung
2016
A sequential algorithm for generating random graphs. Zbl 1198.05138
Bayati, Mohsen; Kim, Jeong Han; Saberi, Amin
2010
How complex are random graphs in first order logic? Zbl 1060.05085
Kim, Jeong Han; Pikhurko, Oleg; Spencer, Joel H.; Verbitsky, Oleg
2005
Poisson cloning model for random graphs. Zbl 1100.05093
Kim, Jeong Han
2006
Two-coloring random hypergraphs. Zbl 1001.05059
Achlioptas, Dimitris; Kim, Jeong Han; Krivelevich, Michael; Tetali, Prasad
2002
Random matchings which induce Hamilton cycles and Hamiltonian decompositions of random regular graphs. Zbl 1030.05107
Kim, Jeong Han; Wormald, Nicholas C.
2001
Optimal query complexity bounds for finding graphs. Zbl 1231.68150
Choi, Sung-Soon; Kim, Jeong Han
2008
Anatomy of a Young giant component in the random graph. Zbl 1230.05260
Ding, Jian; Kim, Jeong Han; Lubetzky, Eyal; Peres, Yuval
2011
Entropy and sorting. Zbl 1294.68069
Kahn, Jeff; Kim, Jeong Han
1995
Generating random regular graphs. Zbl 1121.05110
Kim, J. H.; Vu, V. H.
2006
Generating random regular graphs. Zbl 1192.05146
Kim, Jeong Han; Vu, Van H.
2003
Small subgraphs of random regular graphs. Zbl 1118.05088
Kim, Jeong Han; Sudakov, Benny; Vu, Van
2007
On increasing subsequences of random permutations. Zbl 0859.05002
Kim, Jeong Han
1996
A phase transition for avoiding a giant component. Zbl 1092.05061
Bohman, Tom; Kim, Jeong Han
2006
On coupon colorings of graphs. Zbl 1317.05052
Chen, Bob; Kim, Jeong Han; Tait, Michael; Verstraete, Jacques
2015
Some advances on Sidorenko’s conjecture. Zbl 1433.05166
Conlon, David; Kim, Jeong Han; Lee, Choongbum; Lee, Joonkyung
2018
Regular subgraphs of random graphs. Zbl 1101.05061
Bollobás, Béla; Kim, Jeong Han; Verstraëte, Jacques
2006
Large deviations for Small buffers: An insensitivity result. Zbl 1017.90023
Mandjes, Michel; Kim, Jeong Han
2001
Permutation pseudographs and contiguity. Zbl 1006.05056
Greenhill, Catherine; Janson, Svante; Kim, Jeong Han; Wormald, Nicholas C.
2002
On the degree, size, and chromatic index of a uniform hypergraph. Zbl 0868.05037
Alon, Noga; Kim, Jeong Han
1997
Perfect matchings in random uniform hypergraphs. Zbl 1028.05088
Kim, Jeong Han
2003
Universality of random graphs for graphs of maximum degree two. Zbl 1305.05209
Kim, Jeong Han; Lee, Sang June
2014
Hamiltonian decompositions of random bipartite regular graphs. Zbl 1033.05082
Greenhill, Catherine; Kim, Jeong Han; Wormald, Nicholas C.
2004
Discrepancy after adding a single set. Zbl 1092.05069
Kim, Jeong Han; Matoušek, Jiří; Vu, Van H.
2005
A birthday paradox for Markov chains with an optimal bound for collision in the Pollard rho algorithm for discrete logarithm. Zbl 1195.60096
Kim, Jeong Han; Montenegro, Ravi; Peres, Yuval; Tetali, Prasad
2010
Optimal query complexity bounds for finding graphs. Zbl 1206.68228
Choi, Sung-Soon; Kim, Jeong Han
2010
A birthday paradox for Markov chains, with an optimal bound for collision in the Pollard rho algorithm for discrete logarithm. Zbl 1205.11135
Kim, Jeong Han; Montenegro, Ravi; Peres, Yuval; Tetali, Prasad
2008
A sequential algorithm for generating random graphs. Zbl 1171.05423
Bayati, Mohsen; Kim, Jeong Han; Saberi, Amin
2007
Confirming the Kleitman-Winston conjecture on the largest coefficient in a $$q$$-Catalan number. Zbl 0968.05037
Kim, Jeong Han; Pittel, Boris
2000
On tail distribution of interpost distance. Zbl 1029.05138
Kim, Jeong Han; Pittel, Boris
2000
Almost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions. Zbl 1234.68148
Choi, Sung-Soon; Jung, Kyomin; Kim, Jeong Han
2011
Score certificates for tournaments. Zbl 0865.05044
Kim, Jeong Han; Tetali, Prasad; Fishburn, Peter
1997
Interference-minimizing colorings of regular graphs. Zbl 0912.05036
Fishburn, P. C.; Kim, J. H.; Lagarias, J. C.; Wright, P. E.
1998
Analysis of a phase transition phenomenon in packet networks. Zbl 0979.60081
Mandjes, Michel; Kim, Jeong-Han
2001
Nearly optimal partial Steiner systems. Zbl 0981.05017
Kim, Jeong Han
2001
Economical covers with geometric applications. Zbl 1029.05109
Alon, Noga; Bollobás, Béla; Kim, Jeong Han; Vu, Van H.
2003
Oblivious routing in directed graphs with random demands. Zbl 1192.90229
Hajiaghayi, Mohammad Taghi; Kim, Jeong Han; Leighton Tom; Räcke, Harald
2005
Covering cubes by random half cubes, with applications to binary neural networks. Zbl 0948.68163
Kim, Jeong Han; Roche, James R.
1998
On the total variation distance between the binomial random graph and the random intersection graph. Zbl 1441.05203
Kim, Jeong Han; Lee, Sang June; Na, Joohan
2018
Some advances on Sidorenko’s conjecture. Zbl 1433.05166
Conlon, David; Kim, Jeong Han; Lee, Choongbum; Lee, Joonkyung
2018
On the total variation distance between the binomial random graph and the random intersection graph. Zbl 1441.05203
Kim, Jeong Han; Lee, Sang June; Na, Joohan
2018
Two approaches to Sidorenko’s conjecture. Zbl 1331.05220
Kim, Jeong Han; Lee, Choongbum; Lee, Joonkyung
2016
On coupon colorings of graphs. Zbl 1317.05052
Chen, Bob; Kim, Jeong Han; Tait, Michael; Verstraete, Jacques
2015
Universality of random graphs for graphs of maximum degree two. Zbl 1305.05209
Kim, Jeong Han; Lee, Sang June
2014
Anatomy of a Young giant component in the random graph. Zbl 1230.05260
Ding, Jian; Kim, Jeong Han; Lubetzky, Eyal; Peres, Yuval
2011
Almost tight upper bound for finding Fourier coefficients of bounded pseudo-Boolean functions. Zbl 1234.68148
Choi, Sung-Soon; Jung, Kyomin; Kim, Jeong Han
2011
Diameters in supercritical random graphs via first passage percolation. Zbl 1260.05048
Ding, Jian; Kim, Jeong Han; Lubetzky, Eyal; Peres, Yuval
2010
A sequential algorithm for generating random graphs. Zbl 1198.05138
Bayati, Mohsen; Kim, Jeong Han; Saberi, Amin
2010
A birthday paradox for Markov chains with an optimal bound for collision in the Pollard rho algorithm for discrete logarithm. Zbl 1195.60096
Kim, Jeong Han; Montenegro, Ravi; Peres, Yuval; Tetali, Prasad
2010
Optimal query complexity bounds for finding graphs. Zbl 1206.68228
Choi, Sung-Soon; Kim, Jeong Han
2010
Optimal query complexity bounds for finding graphs. Zbl 1231.68150
Choi, Sung-Soon; Kim, Jeong Han
2008
A birthday paradox for Markov chains, with an optimal bound for collision in the Pollard rho algorithm for discrete logarithm. Zbl 1205.11135
Kim, Jeong Han; Montenegro, Ravi; Peres, Yuval; Tetali, Prasad
2008
Small subgraphs of random regular graphs. Zbl 1118.05088
Kim, Jeong Han; Sudakov, Benny; Vu, Van
2007
A sequential algorithm for generating random graphs. Zbl 1171.05423
Bayati, Mohsen; Kim, Jeong Han; Saberi, Amin
2007
Poisson cloning model for random graphs. Zbl 1100.05093
Kim, Jeong Han
2006
Generating random regular graphs. Zbl 1121.05110
Kim, J. H.; Vu, V. H.
2006
A phase transition for avoiding a giant component. Zbl 1092.05061
Bohman, Tom; Kim, Jeong Han
2006
Regular subgraphs of random graphs. Zbl 1101.05061
Bollobás, Béla; Kim, Jeong Han; Verstraëte, Jacques
2006
How complex are random graphs in first order logic? Zbl 1060.05085
Kim, Jeong Han; Pikhurko, Oleg; Spencer, Joel H.; Verbitsky, Oleg
2005
Discrepancy after adding a single set. Zbl 1092.05069
Kim, Jeong Han; Matoušek, Jiří; Vu, Van H.
2005
Oblivious routing in directed graphs with random demands. Zbl 1192.90229
Hajiaghayi, Mohammad Taghi; Kim, Jeong Han; Leighton Tom; Räcke, Harald
2005
Divide and conquer martingales and the number of triangles in a random graph. Zbl 1041.60042
Kim, J. H.; Vu, V. H.
2004
Sandwiching random graphs: universality between random graph models. Zbl 1050.05111
Kim, J. H.; Vu, V. H.
2004
Hamiltonian decompositions of random bipartite regular graphs. Zbl 1033.05082
Greenhill, Catherine; Kim, Jeong Han; Wormald, Nicholas C.
2004
Small complete arcs in projective planes. Zbl 1027.05015
Kim, J. H.; Vu, V. H.
2003
Generating random regular graphs. Zbl 1192.05146
Kim, Jeong Han; Vu, Van H.
2003
Perfect matchings in random uniform hypergraphs. Zbl 1028.05088
Kim, Jeong Han
2003
Economical covers with geometric applications. Zbl 1029.05109
Alon, Noga; Bollobás, Béla; Kim, Jeong Han; Vu, Van H.
2003
On the asymmetry of random regular graphs and random graphs. Zbl 1012.05143
Kim, Jeong Han; Sudakov, Benny; Vu, Van H.
2002
Two-coloring random hypergraphs. Zbl 1001.05059
Achlioptas, Dimitris; Kim, Jeong Han; Krivelevich, Michael; Tetali, Prasad
2002
Permutation pseudographs and contiguity. Zbl 1006.05056
Greenhill, Catherine; Janson, Svante; Kim, Jeong Han; Wormald, Nicholas C.
2002
The scaling window of the 2-SAT transition. Zbl 0979.68053
Bollobás, Béla; Borgs, Christian; Chayes, Jennifer T.; Kim, Jeong Han; Wilson, David B.
2001
Random matchings which induce Hamilton cycles and Hamiltonian decompositions of random regular graphs. Zbl 1030.05107
Kim, Jeong Han; Wormald, Nicholas C.
2001
Large deviations for Small buffers: An insensitivity result. Zbl 1017.90023
Mandjes, Michel; Kim, Jeong Han
2001
Analysis of a phase transition phenomenon in packet networks. Zbl 0979.60081
Mandjes, Michel; Kim, Jeong-Han
2001
Nearly optimal partial Steiner systems. Zbl 0981.05017
Kim, Jeong Han
2001
Concentration of multivariate polynomials and its applications. Zbl 0969.60013
Kim, Jeong Han; Vu, Van H.
2000
Confirming the Kleitman-Winston conjecture on the largest coefficient in a $$q$$-Catalan number. Zbl 0968.05037
Kim, Jeong Han; Pittel, Boris
2000
On tail distribution of interpost distance. Zbl 1029.05138
Kim, Jeong Han; Pittel, Boris
2000
Interference-minimizing colorings of regular graphs. Zbl 0912.05036
Fishburn, P. C.; Kim, J. H.; Lagarias, J. C.; Wright, P. E.
1998
Covering cubes by random half cubes, with applications to binary neural networks. Zbl 0948.68163
Kim, Jeong Han; Roche, James R.
1998
Nearly perfect matchings in regular simple hypergraphs. Zbl 0882.05107
Alon, Noga; Kim, Jeong-Han; Spencer, Joel
1997
On the degree, size, and chromatic index of a uniform hypergraph. Zbl 0868.05037
Alon, Noga; Kim, Jeong Han
1997
Score certificates for tournaments. Zbl 0865.05044
Kim, Jeong Han; Tetali, Prasad; Fishburn, Peter
1997
On increasing subsequences of random permutations. Zbl 0859.05002
Kim, Jeong Han
1996
The Ramsey number $$R(3,t)$$ has order of magnitude $$t^ 2 /\log t$$. Zbl 0832.05084
Kim, Jeong Han
1995
On Brooks’ theorem for sparse graphs. Zbl 0833.05030
Kim, Jeong Han
1995
Entropy and sorting. Zbl 1294.68069
Kahn, Jeff; Kim, Jeong Han
1995
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#### Cited by 729 Authors
16 Sudakov, Benny 13 Mubayi, Dhruv 12 Frieze, Alan Michael 12 Kim, Jeong Han 10 Bartoli, Daniele 10 Bohman, Tom 10 Marcugini, Stefano 10 Pambianco, Fernanda 10 Warnke, Lutz 9 Davydov, Alexander A. 9 Janson, Svante 9 Lubetzky, Eyal 9 Pikhurko, Oleg 8 Conlon, David 8 Faina, Giorgio 8 Krivelevich, Michael 8 Rodl, Vojtech 8 Shabanov, Dmitry A. 8 Vu, Van H. 7 Dudek, Andrzej 7 Fox, Jacob 7 Greenhill, Catherine S. 7 Osthus, Deryk 7 Spencer, Joel H. 6 Bshouty, Nader H. 6 Chatterjee, Sourav 6 Ding, Jian 6 Henning, Michael Anthony 6 Kühn, Daniela 5 Alon, Noga M. 5 Ferber, Asaf 5 Gao, Pu 5 Kang, Mihyun 5 Lee, Choongbum 5 Mandjes, Michel Robertus Hendrikus 5 Peres, Yuval 5 Prałat, Paweł 5 Ruciński, Andrzej 5 Verbitsky, Oleg 5 Verstraëte, Jacques 5 Zhao, Yufei 4 Bhamidi, Shankar 4 Coja-Oghlan, Amin 4 Cooper, Jeff 4 Fiorini, Samuel 4 Foucaud, Florent 4 Gyárfás, András 4 Kahn, Jeff D. 4 Kohayakawa, Yoshiharu 4 Kostochka, Aleksandr Vasil’evich 4 Mazzawi, Hanna 4 Perkins, Will 4 Person, Yury Aleksandrovic 4 Ravelomanana, Vlady 4 Schiermeyer, Ingo 4 Sly, Allan 4 Suk, Andrew 4 Wormald, Nicholas Charles 3 Bennett, Patrick 3 Brightwell, Graham R. 3 Cardinal, Jean 3 Choi, Sung-Soon 3 Chudnovsky, Maria 3 Dembo, Amir 3 Giulietti, Massimo 3 Haxell, Penny E. 3 Joos, Felix Claudius 3 Joret, Gwenaël 3 Kreshchuk, Alexey A. 3 Li, Yusheng 3 Lin, Qizhong 3 Liu, Hong 3 Loh, Po-Shen 3 Markström, Klas 3 Mertzios, George B. 3 Montanari, Andrea 3 Nagy, Zoltán Lóránt 3 Naserasr, Reza 3 Nenadov, Rajko 3 Parreau, Aline 3 Pastor, Lucas 3 Picollelli, Michael E. 3 Pittel, Boris G. 3 Pontiveros, Gonzalo Fiz 3 Rossignol, Raphaël 3 Samotij, Wojciech 3 Schudy, Warren 3 Seppäläinen, Timo 3 Šileikis, Matas 3 Sun, Nike 3 Sviridenko, Maxim I. 3 Thomassé, Stéphan 3 Trotignon, Nicolas 3 Valicov, Petru 3 van der Hofstad, Remco W. 3 Vigoda, Eric 3 Yeo, Anders 3 Yuster, Raphael 2 Achlioptas, Dimitris 2 Addario-Berry, Louigi ...and 629 more Authors
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#### Cited in 115 Serials
61 Random Structures & Algorithms 28 Journal of Combinatorial Theory. Series B 27 Combinatorics, Probability and Computing 26 Discrete Mathematics 20 Theoretical Computer Science 20 European Journal of Combinatorics 15 Discrete Applied Mathematics 15 SIAM Journal on Discrete Mathematics 12 The Annals of Probability 12 Graphs and Combinatorics 11 The Electronic Journal of Combinatorics 9 The Annals of Applied Probability 8 Israel Journal of Mathematics 8 Advances in Mathematics 8 Journal of Graph Theory 7 Journal of Applied Probability 7 Combinatorica 7 Algorithmica 7 Journal of Combinatorial Designs 6 Proceedings of the American Mathematical Society 6 Journal of Combinatorial Optimization 5 Journal of Combinatorial Theory. Series A 5 Journal of Computer and System Sciences 5 Probability Theory and Related Fields 4 Artificial Intelligence 4 Information Processing Letters 4 Journal of Geometry 4 SIAM Journal on Computing 4 Transactions of the American Mathematical Society 4 Order 3 Inventiones Mathematicae 3 Statistics & Probability Letters 3 Annals of Pure and Applied Logic 3 Discrete & Computational Geometry 3 Designs, Codes and Cryptography 3 Bulletin of the American Mathematical Society. New Series 3 Journal of Discrete Algorithms 3 Forum of Mathematics, Sigma 3 Computer Science Review 2 Advances in Applied Probability 2 Journal of Statistical Physics 2 Russian Mathematical Surveys 2 Applied Mathematics and Computation 2 Duke Mathematical Journal 2 Journal of the London Mathematical Society. Second Series 2 Memoirs of the American Mathematical Society 2 Networks 2 Applied Mathematics Letters 2 Discrete Mathematics and Applications 2 Mathematical Programming. Series A. Series B 2 Journal of Mathematical Sciences (New York) 2 Annals of Combinatorics 2 Stochastic Models 1 Communications in Mathematical Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Biology 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Problems of Information Transmission 1 Theory of Probability and its Applications 1 Acta Mathematica 1 The Annals of Statistics 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Functiones et Approximatio. Commentarii Mathematici 1 Journal of the American Statistical Association 1 Journal of Number Theory 1 Mathematics of Operations Research 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Operations Research 1 Proceedings of the London Mathematical Society. Third Series 1 Studies in Applied Mathematics 1 Advances in Applied Mathematics 1 Operations Research Letters 1 Optimization 1 Statistical Science 1 Information and Computation 1 Journal of the American Mathematical Society 1 Journal of Cryptology 1 Journal of Parallel and Distributed Computing 1 International Journal of Computer Mathematics 1 SIAM Review 1 Stochastic Processes and their Applications 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 The Australasian Journal of Combinatorics 1 Journal of Algebraic Combinatorics 1 Discussiones Mathematicae. Graph Theory 1 Electronic Journal of Probability 1 INFORMS Journal on Computing 1 Doklady Mathematics 1 Journal of Graph Algorithms and Applications 1 Chaos 1 Discrete Dynamics in Nature and Society 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 RAIRO. Theoretical Informatics and Applications 1 Journal of Systems Science and Complexity 1 Journal of Applied Mathematics ...and 15 more Serials
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#### Cited in 28 Fields
397 Combinatorics (05-XX) 104 Probability theory and stochastic processes (60-XX) 94 Computer science (68-XX) 31 Operations research, mathematical programming (90-XX) 20 Geometry (51-XX) 17 Number theory (11-XX) 17 Information and communication theory, circuits (94-XX) 14 Statistical mechanics, structure of matter (82-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Mathematical logic and foundations (03-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 10 Statistics (62-XX) 6 Numerical analysis (65-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Convex and discrete geometry (52-XX) 4 Biology and other natural sciences (92-XX) 3 Measure and integration (28-XX) 2 Algebraic geometry (14-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Functional analysis (46-XX) 2 Manifolds and cell complexes (57-XX) 1 General algebraic systems (08-XX) 1 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Partial differential equations (35-XX) 1 Mechanics of deformable solids (74-XX)
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http://trilinos.sandia.gov/packages/docs/r11.2/packages/ifpack2/doc/html/classIfpack2_1_1Details_1_1Chebyshev.html | Ifpack2 Templated Preconditioning Package Version 1.0
Ifpack2::Details::Chebyshev< ScalarType, MV, MAT > Class Template Reference
Left-scaled Chebyshev iteration. More...
#include <Ifpack2_Details_Chebyshev_decl.hpp>
List of all members.
## Public Member Functions
Chebyshev (Teuchos::RCP< const MAT > A)
Chebyshev (Teuchos::RCP< const MAT > A, Teuchos::ParameterList ¶ms)
void setParameters (Teuchos::ParameterList &plist)
Set (or reset) parameters.
void compute ()
(Re)compute the left scaling, and (if applicable) estimate max and min eigenvalues of D_inv * A.
MT apply (const MV &B, MV &X)
Teuchos::RCP< const MAT > getMatrix () const
Get the matrix given to the constructor.
bool hasTransposeApply () const
Whether it's possible to apply the transpose of this operator.
void print (std::ostream &out)
Print instance data to the given output stream.
## Detailed Description
### template<class ScalarType, class MV, class MAT> class Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >
Left-scaled Chebyshev iteration.
Template Parameters:
ScalarType The type of entries in the matrix and vectors. MV Specialization of Tpetra::MultiVector. MAT Corresponding specialization of Tpetra::RowMatrix.
This class implements two variants of Chebyshev iteration: 1. A direct imitation of Ifpack's implementation 2. A textbook version of the algorithm
All implemented variants use the diagonal of the matrix to precondition the linear system on the left. Diagonal entries less than machine precision are replaced with machine precision.
The first version imitates Ifpack::Chebyshev, both in how it sets parameters and in the actual iteration (ApplyInverse()). The "textbook" in variant #2 above is "Templates for the Solution of Linear Systems," 2nd edition. Experiments show that the Ifpack imitation is much less sensitive to the eigenvalue bounds than the textbook version, so users should prefer it. (In fact, it is the default.)
We require that the matrix A be real valued and symmetric positive definite. If users could provide the ellipse parameters ("d" and "c" in the literature, where d is the real-valued center of the ellipse, and d-c and d+c the two foci), the iteration itself would work fine with nonsymmetric real-valued A, as long as the eigenvalues of A can be bounded in an ellipse that is entirely to the right of the origin.
There is also dead code for imitating ML's Chebyshev implementation (ML_Cheby(), in packages/ml/src/Smoother/ml_smoother.c). I couldn't get it to converge in time to be useful for testing, so it is disabled.
## Constructor & Destructor Documentation
template<class ScalarType , class MV , class MAT>
Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >::Chebyshev ( Teuchos::RCP< const MAT > A )
Constructor that takes a sparse matrix and sets default parameters.
Parameters:
A [in] The matrix A in the linear system to solve. A must be real-valued and symmetric positive definite.
template<class ScalarType , class MV , class MAT>
Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >::Chebyshev ( Teuchos::RCP< const MAT > A, Teuchos::ParameterList & params )
Constructor that takes a sparse matrix and sets the user's parameters.
Parameters:
A [in] The matrix A in the linear system to solve. A must be real-valued and symmetric positive definite. params [in/out] On input: the parameters. On output: filled with the current parameter settings.
## Member Function Documentation
template<class ScalarType , class MV , class MAT >
void Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >::setParameters ( Teuchos::ParameterList & plist )
Set (or reset) parameters.
This method fills in the input ParameterList with missing parameters set to their default values. You may call this method as many times as you want. On each call, the input ParameterList is treated as a complete list of the desired parameters, not as a "delta" or change list from the current set of parameters. (That is, if you remove parameters from the list that were there in the last call to setParameters() and call setParameters() again with the revised list, this method will use default values for the removed parameters, rather than letting the current settings remain.) However, since the method fills in missing parameters, you may keep calling it with the ParameterList used in the previous call in order to get the same behavior as before.
Parameters that govern spectral bounds of the matrix:
• "chebyshev: max eigenvalue" (ScalarType): lambdaMax, an upper bound of the bounding ellipse of the eigenvalues of the matrix A. If you do not set this parameter, we will compute an approximation. See "Parameters that govern eigenvalue analysis" to control this approximation process.
• "chebyshev: ratio eigenvalue" (ScalarType): eigRatio, the ratio of lambdaMax to the lower bound of the bounding ellipse of the eigenvalues of A. We use lambdaMax and eigRatio to determine the Chebyshev iteration coefficients. This parameter is optional and defaults to 30.
• "chebyshev: min eigenvalue" (ScalarType): lambdaMin, a lower bound of real part of bounding ellipse of eigenvalues of the matrix A. This parameter is optional and only used for a quick check if the matrix is the identity matrix (if lambdaMax == lambdaMin == 1).
Parameters that govern the number of Chebyshev iterations:
• "chebyshev: degree" (int): numIters, the number of iterations. This overrides "relaxation: sweeps" and "smoother: sweeps" (see below).
• "relaxation: sweeps" (int): numIters, the number of iterations. We include this for compatibility with Ifpack. This overrides "smoother: sweeps" (see below).
• "smoother: sweeps" (int): numIters, as above. We include this for compatibility with ML.
Parameters that govern eigenvalue analysis:
• "chebyshev: eigenvalue max iterations" (int): eigMaxIters, the number of power method iterations used to compute the maximum eigenvalue. This overrides "eigen-analysis: iterations" (see below).
• "eigen-analysis: iterations" (int): eigMaxIters, as above. We include this parameter for compatibility with ML.
• "eigen-analysis: type" (std::string): The algorithm to use for estimating the max eigenvalue. This parameter is optional. Currently, we only support "power-method" (or "power method"), which is what Ifpack::Chebyshev uses for eigenanalysis. We include this parameter for compatibility with ML.
Parameters that govern other algorithmic details:
• "chebyshev: operator inv diagonal" (RCP<const V> or const V*): If nonnull, we will use a deep copy of this vector for left scaling as the inverse diagonal of the matrix A, instead of computing the inverse diagonal ourselves. We will make a copy every time you call setParameters(). If you ever call setParameters() without this parameter, we will clear our copy and compute the inverse diagonal ourselves again. You are responsible for updating this if the matrix has changed.
• "chebyshev: min diagonal value" (ST): minDiagVal. If any entry of the diagonal of the matrix is less than this in magnitude, it will be replaced with this value in the inverse diagonal used for left scaling.
• "chebyshev: zero starting solution" (bool): If true, then always use the zero vector(s) as the initial guess(es). If false, then apply() will use X on input as the initial guess(es).
Parameters that govern backwards compatibility:
• "chebyshev: textbook algorithm" (bool): If true, use the textbook version of Chebyshev iteration. We recommend against this, since the default algorithm is less sensitive to the quality of the eigenvalue bounds.
• "chebyshev: compute max residual norm" (bool): If true, apply() will compute and return the max (absolute) residual norm. Otherwise, apply() returns 0. This defaults to false.
Precondition:
lambdaMin, lambdaMax, and eigRatio are real
0 < lambdaMin <= lambdaMax
numIters >= 0
eigMaxIters >= 0
Default settings for parameters relating to spectral bounds come from Ifpack.
template<class ScalarType , class MV , class MAT >
void Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >::compute ( )
(Re)compute the left scaling, and (if applicable) estimate max and min eigenvalues of D_inv * A.
You must call this method before calling apply(),
• if you have not yet called this method,
• if the matrix (either its values or its structure) has changed, or
• any time after you call setParameters().
Advanced users may omit calling compute() after calling setParameters(), as long as none of the changed parameters affect either computation of the inverse diagonal, or estimation of the max or min eigenvalues.
If estimation of the eigenvalues is required, this method may take as long as several Chebyshev iterations.
template<class ScalarType , class MV, class MAT >
Chebyshev< ScalarType, MV, MAT >::MT Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >::apply ( const MV & B, MV & X )
Solve Ax=b for x with Chebyshev iteration with left diagonal scaling.
Parameters:
B [in] Right-hand side(s) in the linear system to solve. X [in] Initial guess(es) for the linear system to solve.
If the "chebyshev: compute max residual norm" parameter is true (not the default), then this method returns the maximum (over all columns) absolute residual 2-norm after iterating. Otherwise, it returns zero.
Warning:
If you did not set the "chebyshev: zero starting solution" parameter to true, then this method will use X as the starting guess for Chebyshev iteration. If you did not initialize X before calling this method, then the resulting solution will be undefined, since it will be computed using uninitialized data.
template<class ScalarType , class MV , class MAT >
Teuchos::RCP< const MAT > Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >::getMatrix ( ) const
Get the matrix given to the constructor.
template<class ScalarType , class MV , class MAT >
bool Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >::hasTransposeApply ( ) const
Whether it's possible to apply the transpose of this operator.
template<class ScalarType , class MV , class MAT >
void Ifpack2::Details::Chebyshev< ScalarType, MV, MAT >::print ( std::ostream & out )
Print instance data to the given output stream.
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https://pos.sissa.it/358/434/ | Volume 358 - 36th International Cosmic Ray Conference (ICRC2019) - CRI - Cosmic Ray Indirect
Analysis of Data from Surface Detector Stations of the AugerPrime Upgrade
A. Taboada* on behalf of the Pierre Auger Collaboration
Full text: pdf
Pre-published on: July 22, 2019
Published on: July 02, 2021
Abstract
Measuring the different components of extensive air showers is of key importance in reconstructing the mass composition of ultra-high energy cosmic rays. AugerPrime, the upgrade of the Pierre Auger Observatory, aims to enhance the sensitivity of its surface detector to the masses of cosmic rays by installing a $3.8~\mathrm{m^2}$ plastic scintillator detector on top of each of the 1660 Water-Cherenkov Detectors (WCDs). This Scintillator Surface Detector (SSD) provides a complementary measurement which allows for disentanglement of the electromagnetic and muonic shower components. Another important improvement of AugerPrime are the surface-detector electronics. The new electronics will process signals from the WCD and the SSD with higher sampling frequency and enhanced resolution in signal amplitude. Furthermore, a smaller photomultiplier tube will be added to each WCD, thus increasing its dynamic range. Twelve upgraded surface detector stations have been operating since September 2016. Additionally, seventy-seven SSDs have been deployed and are taking data since March 2019. In this work, the analysis of the data from these detectors is presented.
DOI: https://doi.org/10.22323/1.358.0434
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
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https://www.zbmath.org/authors/?q=rv%3A163 | ## Boffi, Vinicio C.
Compute Distance To:
Author ID: boffi.vinicio-c Published as: Boffi, V. C.; Boffi, Vinicio; Boffi, Vinicio C.; Boffi, V. more...less External Links: Wikidata · IdRef
Documents Indexed: 53 Publications since 1960 5 Contributions as Editor Reviewing Activity: 219 Reviews Biographic References: 2 Publications Co-Authors: 30 Co-Authors with 48 Joint Publications 471 Co-Co-Authors
all top 5
### Co-Authors
8 single-authored 22 Spiga, Giampiero 4 Molinari, Vincenzo G. 4 Rossani, Alberto 3 Ganapol, Barry D. 3 Nonnenmacher, Theo F. 2 Dukek, Günter 2 Knoke, F. 2 Magnavacca, A. 2 Neunzert, Helmut 2 Santarelli, F. 2 Stramigioli, C. 2 Toscani, Giuseppe 1 Azmy, Yousry Y. 1 Bampi, Franco 1 Bowden, Robert L. 1 Caraffini, Gian Luca 1 Cercignani, Carlo 1 de Socio, Luciano M. 1 Franceschini, Valter 1 Gaffuri, Giovanni 1 Malvagi, F. 1 Mandrekas, J. 1 Menon, S. V. G. 1 Pescatore, Claudio 1 Pomraning, Gerald C. 1 Premuda, Francesco 1 Protopopescu, Vladimir A. 1 Rionero, Salvatore 1 Thomas, J. R. jun. 1 Torrisi, Mariano
all top 5
### Serials
9 Transport Theory and Statistical Physics 9 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Meccanica 6 Journal of Mathematical Physics 3 International Journal of Engineering Science 2 Physics of Fluids 2 Annals of Physics 2 Il Nuovo Cimento, X. Series 1 International Journal of Heat and Mass Transfer 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Atti del Seminario Matematico e Fisico dell’Università di Modena 1 Il Nuovo Cimento, Supplemento, X. Series 1 Lecture Notes in Mathematics 1 Series on Advances in Mathematics for Applied Sciences 1 Il Nuovo Cimento, X. Series, B
all top 5
### Fields
33 Fluid mechanics (76-XX) 29 Statistical mechanics, structure of matter (82-XX) 22 Integral equations (45-XX) 6 Partial differential equations (35-XX) 6 Numerical analysis (65-XX) 5 General and overarching topics; collections (00-XX) 2 Integral transforms, operational calculus (44-XX) 2 Astronomy and astrophysics (85-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX)
### Citations contained in zbMATH Open
33 Publications have been cited 122 times in 72 Documents Cited by Year
An equation of Hammerstein type arising in particle transport theory. Zbl 0526.45009
Boffi, V. C.; Spiga, G.
1983
On the solutions to a class of nonlinear integral equations arising in transport theory. Zbl 0567.45008
Spiga, G.; Bowden, R. L.; Boffi, V. C.
1984
Nonlinear removal effects in time-dependent particle transport theory. Zbl 0528.76082
Boffi, V. C.; Spiga, G.
1983
Dynamics of a gas mixture in an extended kinetic theory. Zbl 0586.76137
Boffi, V. C.; Franceschini, V.; Spiga, G.
1985
Extended kinetic theory for gas mixtures in the presence of removal and regeneration effects. Zbl 0587.76130
Boffi, V. C.; Spiga, G.
1986
Rigorous iterated solutions to a nonlinear integral evolution problem in particle transport theory. Zbl 0502.76090
Boffi, V. C.; Spiga, G.
1982
Global solution to a nonlinear integral evolution problem in particle transport theory. Zbl 0507.70011
Boffi, V. C.; Spiga, G.
1982
Linear integral transformations generated by the three-dimensional neutron transport kernel. Zbl 0272.44004
Boffi, V. C.; Spiga, G.
1973
Evaluation of the electrical conductivity via the time-dependent integral Boltzmann equation. Zbl 0488.76082
Ganapol, B. D.; Boffi, V. C.
1981
Nonlinear diffusion of test particles in the presence of an external conservative force. Zbl 0501.76066
Boffi, V. C.; Spiga, G.
1982
Solution to the Boltzmann equation for monoenergetic neutrons in a slab. Zbl 0206.41502
Boffi, V. C.; Molinari, V. G.
1970
Convergence in the mean of solutions to the neutron integral Boltzmann equation in three-dimensional systems. Zbl 0254.45017
Boffi, V. C.; Premuda, F.; Spiga, G.
1973
Rigorous constructive solution to monodimensional Poiseuille and thermal creep flows. Zbl 0398.76061
Boffi, Vinicio; De Socio, Luciano; Gaffuri, Giovanni; Pescatore, Claudio
1976
The multiple collision method in solving the Boltzmann equation for time- dependent test particle transport. Zbl 0492.76078
Ganapol, B. D.; Boffi, V. C.
1980
On the slowing down of neutrons in an homogeneous infinite medium. Zbl 0105.43303
Boffi, Vinicio C.
1960
A Riemann-Hilbert boundary value problem in neutron transport theory. Zbl 0183.10203
Boffi, V. C.; Molinari, V. G.
1969
Exact time-dependent solutions to the nonlinear Boltzmann equation. Zbl 0613.76082
Boffi, V. C.; Spiga, G.
1986
Exact and asymptotic solution of the energy-dependent Boltzmann equation in the study of the neutron slowing down. Zbl 0128.23502
Boffi, V. C.; Knoke, F.; Molinari, V. G.; Scozzafava, R.
1964
The constant collision frequency model for electrical conductivity. Zbl 0528.76108
Ganapol, B. D.; Boffi, V. C.
1982
Integral transport theory for test particles in the presence of a time- dependent conservative force. Zbl 0577.76085
Boffi, V. C.; Nonnenmacher, T.
1984
Solution of a nonlinear integral equation arising in particle transport theory. Zbl 0579.65145
Boffi, V. C.; Spiga, G.; Thomas, J. R. jun.
1985
Solution methods for discrete-state Markovian initial value problems. Zbl 0709.65124
Boffi, V. C.; Malvagi, F.; Pomraning, G. C.
1990
On the Boltzmann system for a mixture of reacting gases. Zbl 0699.76087
Boffi, V. C.; Rossani, A.
1990
Solution to the monoenergetic neutron Boltzmann equation for a finite parallelepiped. Zbl 0289.45019
Boffi, V. C.; Molinari, V. G.
1971
Calculation of the number densities in an extended kinetic theory of gas mixtures. Zbl 0622.76081
Boffi, V. C.; Spiga, G.
1987
Lie group analysis for a multispecies, spatially inhomogeneous, mutually interacting gas mixture. Zbl 0756.76065
Azmy, Y. Y.; Boffi, V. C.; Mandrekas, J.; Protopopescu, V.
1992
On the exact theory of the slowing-down of neutrons in an infinite homogeneous medium. Zbl 0113.46504
Boffi, V.
1961
Slowing-down of neutrons by mixtures. Zbl 0125.25105
Boffi, V. C.; Knoke, F.
1965
Anisotropy of the scattering in space-time neutron transport theory. Zbl 0144.48305
Boffi, V. C.; Trombetti, T.
1967
A first-order linear differential-difference equation with N delays. Zbl 0189.40102
Boffi, V.; Scozzafava, R.
1967
Methods of similarity analysis in the study of nonlinear dynamics of a gas mixture. Zbl 0716.35066
Boffi, Vinicio C.; Torrisi, Mariano
1990
Similarity solutions to a nonlinear model for the nuclear breeding process. Zbl 0783.35032
Boffi, V. C.; Caraffini, G. L.
1993
Transients of current density in linear particle transport theory. Zbl 0636.76078
Boffi, V. C.; Rossani, A.
1986
Similarity solutions to a nonlinear model for the nuclear breeding process. Zbl 0783.35032
Boffi, V. C.; Caraffini, G. L.
1993
Lie group analysis for a multispecies, spatially inhomogeneous, mutually interacting gas mixture. Zbl 0756.76065
Azmy, Y. Y.; Boffi, V. C.; Mandrekas, J.; Protopopescu, V.
1992
Solution methods for discrete-state Markovian initial value problems. Zbl 0709.65124
Boffi, V. C.; Malvagi, F.; Pomraning, G. C.
1990
On the Boltzmann system for a mixture of reacting gases. Zbl 0699.76087
Boffi, V. C.; Rossani, A.
1990
Methods of similarity analysis in the study of nonlinear dynamics of a gas mixture. Zbl 0716.35066
Boffi, Vinicio C.; Torrisi, Mariano
1990
Calculation of the number densities in an extended kinetic theory of gas mixtures. Zbl 0622.76081
Boffi, V. C.; Spiga, G.
1987
Extended kinetic theory for gas mixtures in the presence of removal and regeneration effects. Zbl 0587.76130
Boffi, V. C.; Spiga, G.
1986
Exact time-dependent solutions to the nonlinear Boltzmann equation. Zbl 0613.76082
Boffi, V. C.; Spiga, G.
1986
Transients of current density in linear particle transport theory. Zbl 0636.76078
Boffi, V. C.; Rossani, A.
1986
Dynamics of a gas mixture in an extended kinetic theory. Zbl 0586.76137
Boffi, V. C.; Franceschini, V.; Spiga, G.
1985
Solution of a nonlinear integral equation arising in particle transport theory. Zbl 0579.65145
Boffi, V. C.; Spiga, G.; Thomas, J. R. jun.
1985
On the solutions to a class of nonlinear integral equations arising in transport theory. Zbl 0567.45008
Spiga, G.; Bowden, R. L.; Boffi, V. C.
1984
Integral transport theory for test particles in the presence of a time- dependent conservative force. Zbl 0577.76085
Boffi, V. C.; Nonnenmacher, T.
1984
An equation of Hammerstein type arising in particle transport theory. Zbl 0526.45009
Boffi, V. C.; Spiga, G.
1983
Nonlinear removal effects in time-dependent particle transport theory. Zbl 0528.76082
Boffi, V. C.; Spiga, G.
1983
Rigorous iterated solutions to a nonlinear integral evolution problem in particle transport theory. Zbl 0502.76090
Boffi, V. C.; Spiga, G.
1982
Global solution to a nonlinear integral evolution problem in particle transport theory. Zbl 0507.70011
Boffi, V. C.; Spiga, G.
1982
Nonlinear diffusion of test particles in the presence of an external conservative force. Zbl 0501.76066
Boffi, V. C.; Spiga, G.
1982
The constant collision frequency model for electrical conductivity. Zbl 0528.76108
Ganapol, B. D.; Boffi, V. C.
1982
Evaluation of the electrical conductivity via the time-dependent integral Boltzmann equation. Zbl 0488.76082
Ganapol, B. D.; Boffi, V. C.
1981
The multiple collision method in solving the Boltzmann equation for time- dependent test particle transport. Zbl 0492.76078
Ganapol, B. D.; Boffi, V. C.
1980
Rigorous constructive solution to monodimensional Poiseuille and thermal creep flows. Zbl 0398.76061
Boffi, Vinicio; De Socio, Luciano; Gaffuri, Giovanni; Pescatore, Claudio
1976
Linear integral transformations generated by the three-dimensional neutron transport kernel. Zbl 0272.44004
Boffi, V. C.; Spiga, G.
1973
Convergence in the mean of solutions to the neutron integral Boltzmann equation in three-dimensional systems. Zbl 0254.45017
Boffi, V. C.; Premuda, F.; Spiga, G.
1973
Solution to the monoenergetic neutron Boltzmann equation for a finite parallelepiped. Zbl 0289.45019
Boffi, V. C.; Molinari, V. G.
1971
Solution to the Boltzmann equation for monoenergetic neutrons in a slab. Zbl 0206.41502
Boffi, V. C.; Molinari, V. G.
1970
A Riemann-Hilbert boundary value problem in neutron transport theory. Zbl 0183.10203
Boffi, V. C.; Molinari, V. G.
1969
Anisotropy of the scattering in space-time neutron transport theory. Zbl 0144.48305
Boffi, V. C.; Trombetti, T.
1967
A first-order linear differential-difference equation with N delays. Zbl 0189.40102
Boffi, V.; Scozzafava, R.
1967
Slowing-down of neutrons by mixtures. Zbl 0125.25105
Boffi, V. C.; Knoke, F.
1965
Exact and asymptotic solution of the energy-dependent Boltzmann equation in the study of the neutron slowing down. Zbl 0128.23502
Boffi, V. C.; Knoke, F.; Molinari, V. G.; Scozzafava, R.
1964
On the exact theory of the slowing-down of neutrons in an infinite homogeneous medium. Zbl 0113.46504
Boffi, V.
1961
On the slowing down of neutrons in an homogeneous infinite medium. Zbl 0105.43303
Boffi, Vinicio C.
1960
all top 5
### Cited by 94 Authors
21 Boffi, Vinicio C. 16 Spiga, Giampiero 6 Darwish, Mohamed Abdalla 3 Pomraning, Gerald C. 3 Rossani, Alberto 3 Vianello, Marco 2 Gaffuri, Giovanni 2 Ganapol, Barry D. 2 Garcia, Roberto D. M. 2 Meleshko, Sergey V. 2 Nonnenmacher, Theo F. 2 Premuda, Francesco 2 Schürrer, Ferdinand 2 Sommariva, Alvise 2 Suriyawichitseranee, Amornrat 1 Afonso, Suzete Maria 1 Ali, Javid 1 Alyami, Maryam Ahmed 1 Azevedo, Juarez S. 1 Bobylev, Alexandre Vasiljévitch 1 Bowden, Robert L. 1 Busoni, Giorgio 1 Caballero, Josefa 1 Caraffini, Gian Luca 1 Cardinali, Tiziana 1 Cercignani, Carlo 1 Cornille, Henri 1 da Silva, Mariana P. G. 1 Das, Anupam 1 De Florio, Mario 1 de Socio, Luciano M. 1 Dehesa, Jesús S. 1 Dogbé, Christian 1 Dorning, John J. 1 Dukek, Günter 1 Elabsy, A. M. 1 Espesset, Aude 1 Fotros, Forough 1 Frosali, Giovanni 1 Furfaro, Roberto 1 Gardini, Laura 1 Germano, Bruna 1 Grandjean, Philippe 1 Griehsnig, P. 1 Grigor’ev, Yu. N. 1 Guerriero, Gabriele 1 Hadj Amor, Sana 1 Haque, Inzamamul 1 Hazarika, Bipan 1 Henderson, Johnny Lee 1 Holloway, James Paul 1 İnönü, Erdal 1 Khchine, Abdelmjid 1 Knoke, F. 1 Küchler, Uwe 1 Kügerl, Georg 1 Lampis, Maria 1 Li, Gang 1 Lupini, Renzo 1 Madkour, M. A. 1 Magnavacca, A. 1 Majorana, Armando 1 Malvagi, F. 1 Mangiarotti, Luigi 1 Maniar, Lahcen 1 Marano, Salvatore Angelo 1 Marinescu, Dorin 1 Mensch, Beatrice 1 Messia, Maria Grazia 1 Molinari, Vincenzo G. 1 Ntouyas, Sotiris K. 1 Oliveira, Saulo Pomponet 1 Panda, Sumati Kumari 1 Prelati, G. P. 1 Prinja, Anil K. 1 Ricci, Paolo Emilio 1 Richman, Mark W. 1 Rionero, Salvatore 1 Rubbioni, Paola 1 Rupp, Daniela 1 Rzepka, Beata 1 Sadarangani, Kishin B. 1 Schaler, M. 1 Schiassi, Enrico 1 Sgarra, Carlo 1 Shahsavaran, Ahmad 1 Siewert, Charles E. 1 Spiga, Marco 1 Taoudi, Mohamed Aziz 1 Traiki, Abdelhak 1 Trombetti, Tullio 1 Yáñez, Rafael J. 1 Zarzo, Alejandro 1 Zhu, Tao
all top 5
### Cited in 28 Serials
12 ZAMP. Zeitschrift für angewandte Mathematik und Physik 11 Meccanica 8 Transport Theory and Statistical Physics 7 Journal of Mathematical Physics 4 Journal of Integral Equations and Applications 3 Journal of Statistical Physics 2 Computers & Mathematics with Applications 2 Journal of Mathematical Analysis and Applications 2 Il Nuovo Cimento, X. Series 2 Journal of Function Spaces 1 Applicable Analysis 1 Astrophysics and Space Science 1 Journal of Mathematical Biology 1 Rocky Mountain Journal of Mathematics 1 Physics of Fluids, A 1 Chaos, Solitons and Fractals 1 Applied Mathematics and Computation 1 Journal of Computational and Applied Mathematics 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Stochastics and Stochastics Reports 1 Computational and Applied Mathematics 1 Journal of Applied Mechanics and Technical Physics 1 Communications in Nonlinear Science and Numerical Simulation 1 Mathematical Modelling and Analysis 1 Fixed Point Theory and Applications 1 Discrete and Continuous Dynamical Systems. Series S 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
all top 5
### Cited in 20 Fields
36 Integral equations (45-XX) 27 Fluid mechanics (76-XX) 27 Statistical mechanics, structure of matter (82-XX) 15 Operator theory (47-XX) 9 Numerical analysis (65-XX) 5 Real functions (26-XX) 5 Partial differential equations (35-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Integral transforms, operational calculus (44-XX) 3 Probability theory and stochastic processes (60-XX) 3 Astronomy and astrophysics (85-XX) 2 Special functions (33-XX) 2 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Biology and other natural sciences (92-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-07-07T14:19:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7299346923828125, "perplexity": 12208.806322481629}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104692018.96/warc/CC-MAIN-20220707124050-20220707154050-00225.warc.gz"} |
https://wlresources.dpi.wi.gov/authoring/1762-check-your-work/view | Overview / Description:
This lesson will help students understand why it is important to check their work after they complete a math problem. They will be searching other students work to find a mistake in the work they completed.
Learning goals/objectives:
After completing this activity, students should be able to . . .
• check their work.
• explain their work.
• understand the importance of checking their work for mistakes.
Content Standards:
Wisconsin Standards for Mathematics
Mathematical Practices
Make sense of problems and persevere in solving them.
Construct viable arguments and critique the reasoning of others.
Attend to precision.
Algebra: Reasoning with Equations and Inequalities
CCSS.MATH.CONTENT.HSA.REI.A.1
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Educational Frameworks
B-LS 1. Demonstrate critical-thinking skills to make informed decisions
B-LS 9. Gather evidence and consider multiple perspectives to make informed decisions
Materials:
This can be used with any type of solving unit. I will be using this in my Tech Math class in our solving equations unit.
The teacher should have enough problems for one for each student. Multiple students could solve the same question.
Assessment:
Teacher will collect the papers that have been completed and check over what the students completed.
Exit Slip: List two ways you will pay attention to the quality of your work in the next week.
Wrap-Up:
Class discussion why checking your work is important.
Extension Activity (for intervention or enrichment):
Students could video their response and where they found the mistakes.
Differentiation - students could work in pairs to create an incorrect problem and to correct the problem in another pair's work. | 2022-05-29T09:39:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4957549273967743, "perplexity": 1613.1233002747422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663048462.97/warc/CC-MAIN-20220529072915-20220529102915-00451.warc.gz"} |
https://webarchive.nationalarchives.gov.uk/20110810103412/http:/teachingandlearningresources.org.uk/node/24878 | # Step 1
Recognise unit fractions such as $\frac{1}{2}$, $\frac{1}{3}$, $\frac{1}{4}$, $\frac{1}{5}$, $\frac{1}{10}$ … and use them to find fractions of shapes and numbers
### Probing questions
• What numbers are easy to find a third/quarter/fifth/tenth of? Why?
• If I cut a cake into four pieces will each piece be a quarter?
### What if pupils find this a barrier?
Use a counting stick to discuss halves and tenths. Some pupils think if there are two parts each must be a half – emphasise that the parts need to be equal.
Mathematics ITP: Fractions (SWF-18 KB) Attachments can provide a useful visual image for pupils. | 2019-06-19T03:41:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5267435908317566, "perplexity": 2217.8877345218375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998882.88/warc/CC-MAIN-20190619023613-20190619045613-00080.warc.gz"} |
http://www-spires.fnal.gov/spires/find/books/www?keyword=Functions+of+real+variables | Fermilab Core Computing Division
Library Home | Ask a Librarian library@fnal.gov | Book Catalog | Library Journals | Requests | SPIRES | Fermilab Documents |
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SPIRES-BOOKS: FIND KEYWORD FUNCTIONS OF REAL VARIABLES *END*INIT* use /tmp/qspiwww.webspi1/8403.22 QRY 131.225.70.96 . find keyword functions of real variables ( in books using www
Call number: SPRINGER-2011-9781441998132:ONLINE Show nearby items on shelf Title: Nonelliptic Partial Differential Equations [electronic resource] : Analytic Hypoellipticity and the Courage to Localize High Powers of T Author(s): David S Tartakoff Date: 2011 Publisher: New York, NY : Springer New York Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book fills a real gap in the analytical literature. After many years and many results of analytic regularity for partial differential equations, the only access to the technique known as $(T^p)_\phi$ has remained embedded inthe research papers t hemselves, making it difficult for a graduate student or a mature mathematician in another discipline to master the technique and use it to advantage. This monograph takes a particularly non-specialist approach,one might even say gentle, to smoothly bring the reader into the heart of the technique and its power, and ultimately to show many of the results it has been instrumental in proving. Another technique developed simultaneously by F.Treves is developed and compared and contrasted to ours. The techni ques developed here are tailored to proving real analytic regularity to solutions of sums of squares of vector fields with symplectic characteristic variety andothers, real and complex. The motivation came from the field of several complex variables and t he seminal work of J. J. Kohn. It has found application in non-degenerate (strictly pseudo-convex) and degenerate situations alike, linearand non-linear, partial and pseudo-differential equations, real and complex analysis. The technique is utterly elemen tary, involving powers of vector fields and carefully chosen localizing functions. No knowledge of advancedtechniques, such as the FBI transform or the theory of hyperfunctions is required. In fact analyticity is proved using only $C^\infty$ techniques. The book is intended for mathematicians from graduate students up, whether inanalysis or not, who are curious which non-elliptic partial differential operators have the property that all solutions must be real analytic. Enough background is provided to pr epare the reader with it for a clear understanding of thetext, although this is not, and does not need to be, very extensive. In fact, it is very nearly true that if the reader is willing to accept Note: Springer eBooks Contents: 1. What this book is and is not 2. Brief Introduction 3.Overview of Proofs 4. Full Proof for the Heisenberg Group 5. Coefficients 6. Pseudo differential Problems 7. Sums of Squares and Real Vector Fields 8. \bar{\partial} Neumann and the Boundary Laplacian 9. Symmetric Degeneracies 10. Details of the Previous Chapter 11. Non symplectic Strategem ahe 12.Operators of Kohn Type Which Lose Derivatives 13. Non linear Problems 14. Treves' Approach 15. Appendix Bibliography ISBN: 9781441998132 Series: e-books Series: SpringerLink (Online service) Series: Developments in Mathematics, 1389-2177 : v22 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Global analysis (Mathematics) , Differential equations, partial Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2010-9788847017849:ONLINE Show nearby items on shelf Title: Mathematical Analysis II [electronic resource] Author(s): Claudio Canuto Anita Tabacco Date: 2010 Publisher: Milano : Springer Milan Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical secondlecture course in Calcu lus as offered in most Italian universities. While the subject matter known as Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on Calculus 2'can varya lot, resulting in a bigger flexibility. Fo r these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is notcomparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book.On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested read er may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. TheAuthors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the studentput his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined Note: Springer eBooks ISBN: 9788847017849 Series: e-books Series: SpringerLink (Online service) Series: Universitext Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Differential Equations , Differential equations, partial Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE | 2019-04-18T18:16:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4531647264957428, "perplexity": 2836.785028747845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578526228.27/warc/CC-MAIN-20190418181435-20190418202402-00025.warc.gz"} |
https://large-numbers.fandom.com/wiki/Templates | ## FANDOM
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Community content is available under CC-BY-SA unless otherwise noted. | 2019-12-14T08:34:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.254748672246933, "perplexity": 2625.5000603436974}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540585566.60/warc/CC-MAIN-20191214070158-20191214094158-00401.warc.gz"} |
https://pbn.nauka.gov.pl/pbn-report-web/pages/publication/id/5ab108ebd5defde9ca77942c | Thermodynamic analysis of power generation cycles with high-temperature gas-cooled nuclear reactor and additional coolant heating up to $1600 ^{\circ}$C
PBN-AR
Instytucja
Wydział Energetyki i Paliw (Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie)
##### Informacje podstawowe
Główny język publikacji
EN
Czasopismo
Journal of Energy Resources Technology-Transactions of the ASME (25pkt w roku publikacji)
ISSN
0195-0738
EISSN
1528-8994
Wydawca
The Americal Society of Mechanical Engineers ASME
DOI
Rok publikacji
2018
Numer zeszytu
2, art. no. 020906
Strony od-do
020906-1--020906-7
Numer tomu
140
Identyfikator DOI
Liczba arkuszy
0.5
##### Autorzy
(liczba autorów: 4)
Pozostali autorzy
+ 1
##### Słowa kluczowe
EN
high-temperature goas-cooled nuclear reactor (HTGR)
##### Streszczenia
Język
EN
Treść
Nuclear energy is one of the possibilities ensuring energy security, environmental protection, and high energy efficiency. Among many newest solutions, special attention is paid to the medium size high-temperature gas-cooled reactors (HTGR) with wide possible applications in electric energy production and district heating systems. Actual progress can be observed in the literature and especially in new projects. The maximum outlet temperature of helium as the reactor cooling gas is about 1000 °C which results in the relatively low energy efficiency of the cycle not greater than 40–45% in comparison to 55–60% of modern conventional power plants fueled by natural gas or coal. A significant increase of energy efficiency of HTGR cycles can be achieved with the increase of helium temperature from the nuclear reactor using additional coolant heating even up to 1600 °C in heat exchanger/gas burner located before gas turbine. In this paper, new solution with additional coolant heating is presented. Thermodynamic analysis of the proposed solution with a comparison to the classical HTGR cycle will be presented showing a significant increase of energy efficiency up to about 66%.
original article
peer-reviewed
##### Inne
System-identifier
idp:112160
Crossref
###### Cytowania
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###### Referencje
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Brak danych | 2019-12-13T10:06:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27357685565948486, "perplexity": 9484.940212286523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540553486.23/warc/CC-MAIN-20191213094833-20191213122833-00060.warc.gz"} |
https://www.usgs.gov/publications/effects-agricultural-land-use-changes-and-rainfall-ground-water-recharge-central-and | # Effects of Agricultural Land-Use Changes and Rainfall on Ground-Water Recharge in Central and West Maui, Hawaii, 1926-2004
September 22, 2007
Concern surrounding declines in ground-water levels and an increase in the chloride concentration of water pumped from wells in the Iao aquifer system on the Island of Maui has prompted an investigation into the long-term sustainability of current (2006) and future ground-water withdrawals. As part of this investigation, a water budget for central and west Maui was calculated from which (1) ground-water recharge was estimated for the period 1926-2004 and (2) the effects of agricultural land-use changes and drought were analyzed.
Estimated mean ground-water recharge decreased 44 percent from 1979 to 2004 in central and west Maui. Reduction in agricultural irrigation, resulting from more efficient irrigation methods and a reduction in the acreage used for agriculture, is largely responsible for the declining recharge. Recently, periods of lower-than-average rainfall have further reduced recharge. During the period 1926-79, ground-water recharge averaged 693 Mgal/d, irrigation averaged 437 Mgal/d, and rainfall averaged 897 Mgal/d. During the period 2000-04, ground-water recharge averaged 391 Mgal/d, irrigation averaged 237 Mgal/d, and rainfall averaged 796 Mgal/d.
Simulations of hypothetical future conditions indicate that a cessation of agriculture in central and west Maui would reduce mean ground-water recharge by 18 percent in comparison with current conditions, assuming that current climatic conditions are the same as the long-term-average conditions during the period 1926-2004. A period of drought identical to that of 1998-2002 would reduce mean recharge by 27 percent. Mean recharge would decrease by 46 percent if this drought were to occur after a cessation of agriculture in central and western Maui. Whereas droughts are transient phenomena, a reduction in agricultural irrigation is likely a permanent condition.
## Citation Information
Publication Year 2007 Effects of Agricultural Land-Use Changes and Rainfall on Ground-Water Recharge in Central and West Maui, Hawaii, 1926-2004 10.3133/sir20075103 John A. Engott, Thomas T. Vana Report USGS Numbered Series Scientific Investigations Report 2007-5103 sir20075103 USGS Publications Warehouse Pacific Islands Water Science Center | 2023-02-03T11:38:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3435148000717163, "perplexity": 12262.224043972523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500044.66/warc/CC-MAIN-20230203091020-20230203121020-00086.warc.gz"} |
https://pos.sissa.it/363/013/ | Volume 363 - 37th International Symposium on Lattice Field Theory (LATTICE2019) - Main session
Interglueball potential in SU(N$_c$) lattice gauge theory
N. Yamanaka,* H. Iida, A. Nakamura, M. Wakayama
*corresponding author
Full text: pdf
Pre-published on: January 03, 2020
Published on:
Abstract
We report on our calculation of the interglueball potentials in $SU(2)$, $SU(3)$, and $SU(4)$ lattice Yang-Mills theories using the indirect (so-called HAL QCD) method. We use the cluster decomposition error reduction technique to improve the statistical accuracy of the glueball correlators. After calculating the glueball scattering cross section in $SU(2)$ Yang-Mills theory and combining with the observational data of the dark matter mass distributions, we derive the lower limit on the scale parameter.
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-08-15T05:40:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2831364572048187, "perplexity": 2602.24650816146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439740679.96/warc/CC-MAIN-20200815035250-20200815065250-00171.warc.gz"} |
https://flyingcoloursmaths.co.uk/why-sohcahtoa-is-stupid-and-what-you-can-do-instead/ | My dad tells me that, above the blackboard in his 1960s Scottish high school, was a banner with the letters ‘SOH CAH TOA’ written out on it. Any questions about the banner were brushed off with a smile and ‘you’re not old enough to learn about SOH CAH TOA yet.”
Which, I have to concede, is a great way to pique kids’ interest in the topic. I’ve often wondered about the idea of telling students they’re not old enough to know about maths yet, it’s for over-16s only - and then let them get on with finding out the details on the sly.
### However, SOH CAH TOA is stupid - there, I said it
There are - if you count the SOH CAH TOA way - 11 types of right-angled triangle questions. (Finding the hypotenuse or a leg ((a short side’)) given the other two sides; three versions of finding the angle given the other two sides; and six versions of finding one side given an angle and another side.) If you ask me - and I suggest you do - that’s silly.
I say there are only two kinds of right-angled triangle problem: finding an angle if you know all the sides and finding a side if you know all the angles and a side. And all you need to know in order to solve all of these things: Pythagoras and the sine rule.
### Pythagoras
Now, you know Pythagoras. The square on the hypotenuse is equal to the sum of the squares on the other two sides - or, if you prefer, $opp^2 + adj^2 = hyp^2$. (I prefer this to $a^2 + b^2 = c^2$ because it tells you which side is which.) That means:
• if you know the two short sides, you square them, add them up and square root the answer to get the hypotenuse;
• if you know the hypotenuse and a leg, you square them, take them away (bigger minus smallest, of course) and square root the answer to get the other leg.
That’s straightforward. If you’re solving triangles the Table of Joy way, it usually makes sense to find the last side, just in case you need it.
### The other angle
Oh! If you have two angles of a triangle, it’s easy to find the third, isn’t it? Especially if one of them happens to be a right angle. You simply work out $\frac{\pi}{2}$ minus the other angle.
What’s that?
Oh, fine. If you MUST use degrees (radians are much better), it’s 90 minus the other angle.
### The Sine Rule
At GCSE, you get given the sine rule on the front of the paper. At A-level, nope, you have to remember it. It’s not exactly difficult, though:
$\\frac{a}{\\sin(A)} = \\frac{b}{\\sin(B)} = \\frac{c}{\\sin(C)}$
What you do once you have either all three sides (and the right angle, don’t forget) or all three angles (and a side), is label the corners of the triangle like the picture, with each angle (a big letter) opposite its corresponding little letter.
Also, write out the sine rule, and put a circle around all of the information you have, and a square around the thing you don’t know. If there’s a fraction with one of its numbers unshaped, that’s fine - just cross it out. Neatly.
### The Sine Rule with the Table of Joy
Here comes the clever bit! You can even do this without drawing the whole table - but if you’re curious, you can buy Basic Maths For Dummies and/or Numeracy Tests For Dummies to see exactly how the Table of Joy works.
Here’s what you do:
1. Rewrite your fractions with numbers in the appropriate places and a question mark in the missing space.
2. Find the number diagonally opposite the question mark and write it on the bottom of a big fraction.
3. Take the other two numbers and write them out on top of the fraction with a times between them.
4. Work out the fraction you’ve just written down.
5. If you were looking for a side, you’re done. Hooray.
6. If you’re after an angle, do $\sin^{-1}(Ans)$ and that’ll give you the answer.
### Example: finding an angle
With this one, we don’t really need the bottom (adjacent) side, but let’s find it anyway: $16.8^2 - 9.8^2 = 186.2$, so the bottom side is the square root of that - 13.64 units (to 2dp). The Table of Joy would have 9.8 and 16.8 on the top, and $\sin(x)$ next to $\sin(\frac{\pi}{2})$ on the bottom. You’d work out $9.8 \times \sin(\frac{\pi}{2}) \div 16.8 = 0.583$; since we want an angle, we do inverse sine of that using the answer button to get 0.623 radians (38.69°, if you must).
### Finding a side
This one gives an angle in degrees, tut tut. We can find the other angle by working out 90° - 33° = 57° and then work out the Table of Joy: you’ve got 8.7 and x on top, and $\sin(57^\circ)$ next to $\sin(90^\circ)$ on the bottom. The sum is $8.7 \times \sin(90^\circ) \div \sin(57^\circ) = 10.37$ units (2dp)
So there you go. A simple, easy way to solve any right-angled triangle without having to mess around with tan and cosine.
### Why is this better?
Oh yeah, why is this a better approach than slavishly learning all 11 possible right-angled triangle types? Because this method also works for non-right-angled triangles - although you also need the cosine rule instead of Pythagoras for some of those. It seems daft to me to learn a dozen different ways of doing special cases when you can learn a handful of general cases and be done with it. So there!
(Image by fdecomite used under a Creative Commons by licence)
* Edited 16/12/2013 for formatting. | 2021-06-16T11:04:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7157379984855652, "perplexity": 614.6043098186658}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487623596.16/warc/CC-MAIN-20210616093937-20210616123937-00368.warc.gz"} |
https://bison.inl.gov/Documentation/source/materials/ComputeStrainIncrementBasedStress.aspx | Compute Strain Increment Based Stress
Compute stress after subtracting inelastic strain increments
Description
This stress calculator finds the value of the stress as a function of the elastic strain increment when a series of inelastic strains are specified in the input file. The stress is calculated as (1) where is the stress and is the elasticity tensor of the material. The elastic strain increment, is found by subtracting the sum of the inelastic strains from the mechanical strain: (2) where is the mechanical strain and is the inelastic strain. In the tensor mechanics module mechanical strain is defined as the sum of the elastic and inelastic (e.g. creep and/or plasticity) strains.
Example Input File
[./stress]
type = ComputeStrainIncrementBasedStress
[../]
(moose/modules/tensor_mechanics/test/tests/plane_stress/weak_plane_stress_incremental.i)
Input Parameters
• store_stress_oldFalseParameter which indicates whether the old stress state, required for the HHT time integration scheme and Rayleigh damping, needs to be stored
Default:False
C++ Type:bool
Description:Parameter which indicates whether the old stress state, required for the HHT time integration scheme and Rayleigh damping, needs to be stored
• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.
Default:True
C++ Type:bool
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.
• base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
• inelastic_strain_namesNames of inelastic strain properties
C++ Type:std::vector
Description:Names of inelastic strain properties
• boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Description:The list of boundary IDs from the mesh where this boundary condition applies
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Description:The list of block ids (SubdomainID) that this object will be applied
Optional Parameters
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Description:Adds user-defined labels for accessing object parameters via control logic.
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Description:The seed for the master random number generator
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Description:Determines whether this object is calculated using an implicit or explicit form
• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object | 2020-11-27T08:36:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3517933189868927, "perplexity": 3932.7986531212605}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141191511.46/warc/CC-MAIN-20201127073750-20201127103750-00251.warc.gz"} |
https://gssc.esa.int/navipedia/index.php/Bancroft_Method | If you wish to contribute or participate in the discussions about articles you are invited to join Navipedia as a registered user
# Bancroft Method
Fundamentals
Title Bancroft Method
Author(s) J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain.
Year of Publication 2011
The Bancroft method allows obtaining a direct solution of the receiver position and the clock offset, without requesting any "a priori" knowledge for the receiver location.
## Raising and resolution
Let $PR^j$ the prefit-residual of satellite-$j$, computed from equation (1)
$R^j=\rho^j+c(\delta t-\delta t^j)+T^j+\hat{\alpha}\, I^j+TGD^j+\mathcal{M}^j+{\boldsymbol \varepsilon}^j \qquad \mbox{(1)}$
after removing all model terms not needing the a priory knowledge of the receiver position:[footnotes 1]
$PR^j\equiv R^j +c\,\delta t^j-TGD^j \qquad \mbox{(2)}$
Thence, neglecting the tropospheric and ionospheric terms, as well as the multipath and receiver noise, the equation (3)
$\begin{array}{r} R^j-D^j\simeq \sqrt{(x^j-x)^2+(y^j-y)^2+(z^j-z)^2}+c\,\delta t\\[0.3cm] j=1,2,...,n~~~~ (n \geq 4)\\ \end{array} \qquad \mbox{(3)}$
can be written as:
$PR^j = \sqrt{(x^j-x)^2+(y^j-y)^2+(z^j-z)^2}+c \, \delta t \qquad \mbox{(4)}$
Developing the previous equation (4), it follows:
$\left[{x^j}^2+{y^j}^2+{z^j}^2-{PR^j}^2 \right]-2 \left[x^j x+y^j y+z^j z-{PR^jc\,\delta t} \; \right] + \left[x^2+y^2+z^2-(c\,\delta t)^2 \right]=0 \qquad \mbox{(5)}$
Then, calling ${\mathbf r}=[x,y,z]^T$ and considering the inner product of Lorentz [footnotes 2] the previous equation (5) can be expressed in a more compact way as:
$\frac{1}{2} \left \langle \left[ \begin{array}{c} {\mathbf r}^j\\ PR^j\\ \end{array} \right], \left[ \begin{array}{c} {\mathbf r}^j\\ PR^j\\ \end{array} \right] \right \rangle - \left \langle \left[ \begin{array}{c} {\mathbf r}^j\\ PR^j\\ \end{array} \right], \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] \right \rangle + \frac{1}{2} \left \langle \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right], \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] \right \rangle =0 \qquad \mbox{(6)}$
The former equation can be raised for every satellite (or prefit-residual $PR^j$).
If four measurements are available, thence, the following matrix can be written, containing all the available information on satellite coordinates and pseudoranges (every row corresponds to a satellite):
${\mathbf B}= \left( \begin{array}{cccc} x^1&y^1&z^1&PR^1\\ x^2&y^2&z^2&PR^2\\ x^3&y^3&z^3&PR^3\\ x^4&y^4&z^4&PR^4\\ \end{array} \right) \qquad \mbox{(7)}$
Then, calling:
$\Lambda= \frac{1}{2} \left \langle \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right], \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] \right \rangle \; , \; {\mathbf 1}= \left[ \begin{array}{c} 1\\ 1\\ 1\\ 1\\ \end{array} \right] \; , \; {\mathbf a}= \left[ \begin{array}{c} a_1\\ a_2\\ a_3\\ a_4\\ \end{array} \right] \; \mbox{being} \; \; a_j= \frac{1}{2} \left \langle \left[ \begin{array}{c} {\mathbf r}^j\\ PR^j\\ \end{array} \right], \left[ \begin{array}{c} {\mathbf r}^j\\ PR^j\\ \end{array} \right] \right \rangle \qquad \mbox{(8)}$
The four equations for pseudorange can be expressed as:
${\mathbf a} -{\mathbf B}\,{\mathbf M} \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] +\Lambda \; {\mathbf 1}=0\;\;,\;\;\;\; \mbox{being} \;\;\;\;\;\; {\mathbf M}=\left( \begin{array}{cccc} 1&0&0&0\\ 0&1&0&0\\ 0&0&1&0\\ 0&0&0&-1\\ \end{array} \right) \qquad \mbox{(9)}$
from where:
$\left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] ={\mathbf M} {\mathbf B}^{-1} (\Lambda \; {\mathbf 1} + {\mathbf a}) \qquad \mbox{(10)}$
Then, taking into account the following equality
$\langle {\mathbf M}{\mathbf g},{\mathbf M}{\mathbf h} \rangle=\langle {\mathbf g},{\mathbf h} \rangle \qquad \mbox{(11)}$,
and that
$\Lambda= \frac{1}{2} \left \langle \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right], \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] \right \rangle \qquad \mbox{(12)}$,
from the former expression (10), one obtains:
$\left \langle {\mathbf B}^{-1} {\mathbf 1}, {\mathbf B}^{-1} {\mathbf 1} \right \rangle \Lambda^2+ 2\left [ \left \langle {\mathbf B}^{-1} {\mathbf 1}, {\mathbf B}^{-1} {\mathbf a} \right \rangle -1 \right ] \Lambda + \left \langle {\mathbf B}^{-1} {\mathbf a}, {\mathbf B}^{-1} {\mathbf a} \right \rangle =0 \qquad \mbox{(13)}$
The previous expression (13) is a quadratic equation in $\Lambda$ (note that matrix ${\mathbf B}$ and the vector $\mathbf a$ are also known) and provides two solutions, that introduced in expression (10) provides the searched solution:
$\left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] \qquad \mbox{(14)}$.
The other solution is far from the earth surface.
## Generalisation to the case of $n$-measurements:
If more than four observations are available, the matrix ${\mathbf B}$ is not square. However, multiplying by ${\mathbf B}^T$, one obtains (Least Squares solution):
${\mathbf B}^T{\mathbf a} -{\mathbf B}^T {\mathbf B}\,{\mathbf M} \left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] +\Lambda \; {\mathbf B}^T {\mathbf 1}=0 \qquad \mbox{(15)}$
where:
$\left[ \begin{array}{c} {\mathbf r}\\ c\,\delta t\\ \end{array} \right] ={\mathbf M} ({\mathbf B}^T {\mathbf B})^{-1}{\mathbf B}^T(\Lambda \; {\mathbf 1} + {\mathbf a}) \qquad \mbox{(16)}$
and then:
$\begin{array}{r} \left \langle ({\mathbf B}^T {\mathbf B})^{-1} {\mathbf B}^T{\mathbf 1}, ({\mathbf B}^T {\mathbf B})^{-1} {\mathbf B}^T{\mathbf 1} \right \rangle \Lambda^2+ 2\left [ \left \langle ({\mathbf B}^T {\mathbf B})^{-1} {\mathbf B}^T{\mathbf 1}, ({\mathbf B}^T {\mathbf B})^{-1} {\mathbf B}^T{\mathbf a} \right \rangle -1 \right ] \Lambda +\\[0.3cm] + \left \langle ({\mathbf B}^T {\mathbf B})^{-1} {\mathbf B}^T{\mathbf a}, ({\mathbf B}^T {\mathbf B})^{-1} {\mathbf B}^T{\mathbf a} \right \rangle =0 \end{array} \qquad \mbox{(17)}$
## Notes
1. ^ The tropospheric and ionospheric terms, $T^j$ and $\hat{\alpha} \,I^j$, can not be included, because the need to consider the satellite-receiver ray. Off course, after an initial computation of the receiver coordinates, the method could be iterated using the ionospheric and tropospheric corrections to improve the solution.
2. ^ $\left \langle{\mathbf a},{\mathbf b}\right \rangle={\mathbf a}^{t} \; {\mathbf M} \; {\mathbf b}= \left[ \begin{array}{c} a_1,a_2,a_3,a_4 \end{array} \right] \left( \begin{array}{cccc} 1&0&0&0\\ 0&1&0&0\\ 0&0&1&0\\ 0&0&0&-1\\ \end{array} \right) \left[ \begin{array}{c} b_1\\ b_2\\ b_3\\ b_4 \end{array} \right]$ | 2019-02-23T15:58:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5141576528549194, "perplexity": 2194.428341303163}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550249504746.91/warc/CC-MAIN-20190223142639-20190223164639-00611.warc.gz"} |
https://bison.inl.gov/Documentation/source/kernels/HydrogenDiffusion.aspx | # Hydrogen Diffusion in the Cladding
Calculates the diffusion of hydrogen in solid solution due to Fick's law and the Soret effect
## Description
Hydrogen in solid solution in zirconium will precipitate to form zirconium hydrides as the temperature of the sample is decreased. If the sample is then re-heated, dissolution will begin at a higher temperature than was required for precipitation. This hysteresis effect is due to a volumetric strain caused by mismatch of the density of the hydrides and the surrounding alloy. Thus, there are two terminal solid solubility (TSS) curves, denoted for precipitation and for dissolution. Bison uses the Arrhenius fits from McMinn et al. (2000) for and (1) Hydrogen in solid solution in zirconium diffuses under the influence of mass and temperature gradients by Fick's Law and the Soret effect, respectively. The mass flux is (2) where is the concentration of hydrogen in solid solution, is the mass diffusivity, and is the heat of transport for hydrogen in zirconium.
Bison uses and from Kammenzind et al. (1996): (3) Note that since the stoichiometry of the hydride phase is fixed, there is little or no driving force for diffusion of hydrogen in the hydrides. In addition, the diffusivity of hydrogen in hydrides has been measured to be at least 3 times smaller than the diffusivity of hydrogen in zirconium. Thus, we do not account for diffusion of hydrogen in the hydride phase in Bison.
## Example Input Syntax
[./hdiffusion] # diffusion of hydrogen by OC
type = HydrogenDiffusion
variable = Css
temp = temp
[../]
(test/tests/hydrogen/hydrogen.i)
## Input Parameters
• variableThe name of the variable that this Kernel operates on
C++ Type:NonlinearVariableName
Description:The name of the variable that this Kernel operates on
• tempCoupled Temperature
C++ Type:std::vector
Description:Coupled Temperature
### Required Parameters
• soret_scale1Soret effect scaling factor, 1 is default.
Default:1
C++ Type:double
Description:Soret effect scaling factor, 1 is default.
• soret1Soret effect switch, 1 is on (default).
Default:1
C++ Type:int
Description:Soret effect switch, 1 is on (default).
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Description:The list of block ids (SubdomainID) that this object will be applied
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
• save_inThe name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Description:The name of auxiliary variables to save this Kernel's residual contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Description:The seed for the master random number generator
• diag_save_inThe name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
C++ Type:std::vector
Description:The name of auxiliary variables to save this Kernel's diagonal Jacobian contributions to. Everything about that variable must match everything about this variable (the type, what blocks it's on, etc.)
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Description:Determines whether this object is calculated using an implicit or explicit form
• vector_tagsnontimeThe tag for the vectors this Kernel should fill
Default:nontime
C++ Type:MultiMooseEnum
Description:The tag for the vectors this Kernel should fill
• extra_vector_tagsThe extra tags for the vectors this Kernel should fill
C++ Type:std::vector
Description:The extra tags for the vectors this Kernel should fill
• matrix_tagssystemThe tag for the matrices this Kernel should fill
Default:system
C++ Type:MultiMooseEnum
Description:The tag for the matrices this Kernel should fill
• extra_matrix_tagsThe extra tags for the matrices this Kernel should fill
C++ Type:std::vector
Description:The extra tags for the matrices this Kernel should fill | 2020-11-26T22:20:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2302519828081131, "perplexity": 4396.279810697193}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141188947.19/warc/CC-MAIN-20201126200910-20201126230910-00336.warc.gz"} |
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Call number: SPRINGER-2012-9783642294044:ONLINE Show nearby items on shelf Title: Ten Physical Applications of Spectral Zeta Functions [electronic resource] Author(s): Emilio Elizalde Date: 2012 Edition: 2nd ed. 2012 Publisher: Springer Berlin Heidelberg Size: 1 online resource Note: Monograph Note: Springer 2012 Physics and Astronomy eBook collection Note: Springer e-book platform ISBN: 9783642294044 Series: Lecture Notes in Physics Series: e-books Keywords: Mathematical Methods in Physics , Mathematical Physics , Quantum Field Theories, String Theory , Mathematical Applications in the Physical Sciences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
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Call number: SPRINGER-2012-9783642276903:ONLINE Show nearby items on shelf Title: On Gauge Fixing Aspects of the Infrared Behavior of Yang-Mills Green Functions [electronic resource] Author(s): Markus Q. Huber Date: 2012 Publisher: Springer Berlin Heidelberg Size: 1 online resource Note: Monograph Note: Springer 2012 Physics and Astronomy eBook collection Note: Springer e-book platform ISBN: 9783642276903 Series: Springer Theses Series: e-books Keywords: Elementary Particles, Quantum Field Theory , Theoretical, Mathematical and Computational Physics , Mathematical Physics , Mathematical Applications in the Physical Sciences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9783642259463:ONLINE Show nearby items on shelf Title: Strings and Fundamental Physics [electronic resource] Author(s): Marco Baumgartl Ilka Brunner Michael Haack Date: 2012 Publisher: Springer Berlin Heidelberg Size: 1 online resource Note: Monograph Note: Springer 2012 Physics and Astronomy eBook collection Note: Springer e-book platform ISBN: 9783642259463 Series: Lecture Notes in Physics Series: e-books Keywords: Quantum Field Theories, String Theory , Mathematical Physics , Mathematical Applications in the Physical Sciences , Mathematical Methods in Physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9783642244391:ONLINE Show nearby items on shelf Title: Quantum Triangulations [electronic resource] Author(s): Mauro Carfora Annalisa Marzuoli Date: 2012 Publisher: Springer Berlin Heidelberg Size: 1 online resource Note: Monograph Note: Springer 2012 Physics and Astronomy eBook collection Note: Springer e-book platform ISBN: 9783642244391 Series: Lecture Notes in Physics Series: e-books Keywords: Physics, general , Mathematical Physics , Quantum Physics , Manifolds and Cell Complexes (incl. Diff.Topology) , Classical and Quantum Gravitation, Relativity Theory , Mathematical Applications in the Physical Sciences Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-1962-9783642856273:ONLINE Show nearby items on shelf Title: Antiplane Elastic Systems Author(s): L. M Milne-Thomson Date: 1962 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg Size: 1 online resource (266 p.) Note: 10.1007/978-3-642-85627-3 Contents: I. The Law of Elasticity -- 1.1. Continued dyadic products -- 1.2. The stress tensor -- 1.3. The deformation tensor -- 1.4. The equation of motion -- 1.5. Internal energy -- 1.6. Elastic deformation -- 1.7. Hooke’s law -- 1.8. Anisotropy -- 1.9. E lastic symmetry -- Examples I -- II. Stress functions and complex stresses -- 2.0. Introductory notions -- 2.1. Stress functions and fundamental stress combinations -- 2.3. The displacement -- 2.4. The strain-energy function -- 2.5. The elimination of the displacements -- 2.6. The complex stresses -- 2.7. Expression of the fundamental stress combinations in terms of the complex stresses -- 2.8. Effective stress functions -- 2.9. The shear function -- Examples II -- III. Isotropic beams -- 3.1. The boundar y conditions for a prismatic beam -- 3.2. The isotropic beam -- 3.3. Classification of certain antiplane problems -- 3.4. The equations which give the displacement in pure antiplane stress -- 3.5. The boundary condition for the pure antiplane problem for isotropic beams -- 3.6. Simple extension -- 3.7. Bending by terminal couples -- 3.8. Circular cylinder pushed into a hole -- Examples III -- IV. The torsion of isotropic beams -- 4.1. The torsion problem -- 4.2. Lines of shearing stress -- 4.3. The twisting moment -- 4.4. Solution by conformal mapping -- 4.5. The $$z\bar z$$method -- 4.6. Boundary conditions -- 4.7. A uniqueness theorem -- 4.8. The principle of virtual stresses -- 4.9. Torsion of a compound bar of isotropic materials - - Examples IV -- V. The flexure of isotropic beams -- 5.1. The flexure problem -- 5.2. The centre of flexure -- 5.3. Half-sections -- 5.4. Shear stress functions -- 5.5. de St. Venant’s flexure function -- Examples V -- VI. Antiplane of elastic symmetry -- 6.1. Bending by couples -- 6.2. Boundary conditions -- 6.3. A device for transforming integrals -- 6.4. Simplifying assumptions -- 6.5. Antiplane of elastic symmetry -- 6.6. The striess component zz -- 6.7. Orthotropic material -- 6.8. Methods of approximation -- Examples VI -- VII. General linear and cylindrical anisotropy -- 7.1. Generalized plane deformation -- 7.2. Line force applied to an elastic half-plane -- 7.3. Induced mappings for the region exterior to an ellipse -- 7.4 . Bending of a cantilever by a transverse force at the free end -- 7.5. Cylindrical anisotropy -- 7.6. Equations satisfied by the stress functions -- 7.7. Circular tube under pressure -- Examples VII -- References ISBN: 9783642856273 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Ergebnisse der Angewandten Mathematik, Unter Mitwirkung der Schriftleitung des „Zentralblatt für Mathematik“ : 8 Keywords: Mathematics , Mathematical physics , Continuum physics , Mechanics , Mechanics, Applied , Mathematics , Mathematical Applications in the Physical Sciences , Classical Continuum Physics , Theoretical and Applied Mechanics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE | 2019-03-26T12:33:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38351377844810486, "perplexity": 8565.802767625339}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912205163.72/warc/CC-MAIN-20190326115319-20190326141319-00397.warc.gz"} |
http://lammps.sandia.gov/doc/accelerate_gpu.html | # 5.3.1. GPU package
The GPU package was developed by Mike Brown at ORNL and his collaborators, particularly Trung Nguyen (ORNL). It provides GPU versions of many pair styles, including the 3-body Stillinger-Weber pair style, and for kspace_style pppm for long-range Coulombics. It has the following general features:
• It is designed to exploit common GPU hardware configurations where one or more GPUs are coupled to many cores of one or more multi-core CPUs, e.g. within a node of a parallel machine.
• Atom-based data (e.g. coordinates, forces) moves back-and-forth between the CPU(s) and GPU every timestep.
• Neighbor lists can be built on the CPU or on the GPU
• The charge assignment and force interpolation portions of PPPM can be run on the GPU. The FFT portion, which requires MPI communication between processors, runs on the CPU.
• Asynchronous force computations can be performed simultaneously on the CPU(s) and GPU.
• It allows for GPU computations to be performed in single or double precision, or in mixed-mode precision, where pairwise forces are computed in single precision, but accumulated into double-precision force vectors.
• LAMMPS-specific code is in the GPU package. It makes calls to a generic GPU library in the lib/gpu directory. This library provides NVIDIA support as well as more general OpenCL support, so that the same functionality can eventually be supported on a variety of GPU hardware.
Here is a quick overview of how to enable and use the GPU package:
• build the library in lib/gpu for your GPU hardware with the desired precision settings
• install the GPU package and build LAMMPS as usual
• use the mpirun command to set the number of MPI tasks/node which determines the number of MPI tasks/GPU
• specify the # of GPUs per node
• use GPU styles in your input script
The latter two steps can be done using the “-pk gpu” and “-sf gpu” command-line switches respectively. Or the effect of the “-pk” or “-sf” switches can be duplicated by adding the package gpu or suffix gpu commands respectively to your input script.
Required hardware/software:
To use this package, you currently need to have an NVIDIA GPU and install the NVIDIA CUDA software on your system:
• Check if you have an NVIDIA GPU: cat /proc/driver/nvidia/gpus/0/information
• Go to http://www.nvidia.com/object/cuda_get.html
• Install a driver and toolkit appropriate for your system (SDK is not necessary)
• Run lammps/lib/gpu/nvc_get_devices (after building the GPU library, see below) to list supported devices and properties
Building LAMMPS with the GPU package:
This requires two steps (a,b): build the GPU library, then build LAMMPS with the GPU package.
You can do both these steps in one line as described in Section 4 of the manual.
Or you can follow these two (a,b) steps:
1. Build the GPU library
The GPU library is in lammps/lib/gpu. Select a Makefile.machine (in lib/gpu) appropriate for your system. You should pay special attention to 3 settings in this makefile.
• CUDA_HOME = needs to be where NVIDIA CUDA software is installed on your system
• CUDA_ARCH = needs to be appropriate to your GPUs
• CUDA_PREC = precision (double, mixed, single) you desire
See lib/gpu/Makefile.linux.double for examples of the ARCH settings for different GPU choices, e.g. Fermi vs Kepler. It also lists the possible precision settings:
CUDA_PREC = -D_SINGLE_SINGLE # single precision for all calculations
CUDA_PREC = -D_DOUBLE_DOUBLE # double precision for all calculations
CUDA_PREC = -D_SINGLE_DOUBLE # accumulation of forces, etc, in double
The last setting is the mixed mode referred to above. Note that your GPU must support double precision to use either the 2nd or 3rd of these settings.
To build the library, type:
make -f Makefile.machine
If successful, it will produce the files libgpu.a and Makefile.lammps.
The latter file has 3 settings that need to be appropriate for the paths and settings for the CUDA system software on your machine. Makefile.lammps is a copy of the file specified by the EXTRAMAKE setting in Makefile.machine. You can change EXTRAMAKE or create your own Makefile.lammps.machine if needed.
Note that to change the precision of the GPU library, you need to re-build the entire library. Do a “clean” first, e.g. “make -f Makefile.linux clean”, followed by the make command above.
1. Build LAMMPS with the GPU package
cd lammps/src
make yes-gpu
make machine
Note that if you change the GPU library precision (discussed above) and rebuild the GPU library, then you also need to re-install the GPU package and re-build LAMMPS, so that all affected files are re-compiled and linked to the new GPU library.
Run with the GPU package from the command line:
The mpirun or mpiexec command sets the total number of MPI tasks used by LAMMPS (one or multiple per compute node) and the number of MPI tasks used per node. E.g. the mpirun command in MPICH does this via its -np and -ppn switches. Ditto for OpenMPI via -np and -npernode.
When using the GPU package, you cannot assign more than one GPU to a single MPI task. However multiple MPI tasks can share the same GPU, and in many cases it will be more efficient to run this way. Likewise it may be more efficient to use less MPI tasks/node than the available # of CPU cores. Assignment of multiple MPI tasks to a GPU will happen automatically if you create more MPI tasks/node than there are GPUs/mode. E.g. with 8 MPI tasks/node and 2 GPUs, each GPU will be shared by 4 MPI tasks.
Use the “-sf gpu” command-line switch, which will automatically append “gpu” to styles that support it. Use the “-pk gpu Ng” command-line switch to set Ng = # of GPUs/node to use.
lmp_machine -sf gpu -pk gpu 1 -in in.script # 1 MPI task uses 1 GPU
mpirun -np 12 lmp_machine -sf gpu -pk gpu 2 -in in.script # 12 MPI tasks share 2 GPUs on a single 16-core (or whatever) node
mpirun -np 48 -ppn 12 lmp_machine -sf gpu -pk gpu 2 -in in.script # ditto on 4 16-core nodes
Note that if the “-sf gpu” switch is used, it also issues a default package gpu 1 command, which sets the number of GPUs/node to 1.
Using the “-pk” switch explicitly allows for setting of the number of GPUs/node to use and additional options. Its syntax is the same as same as the “package gpu” command. See the package command doc page for details, including the default values used for all its options if it is not specified.
Note that the default for the package gpu command is to set the Newton flag to “off” pairwise interactions. It does not affect the setting for bonded interactions (LAMMPS default is “on”). The “off” setting for pairwise interaction is currently required for GPU package pair styles.
Or run with the GPU package by editing an input script:
The discussion above for the mpirun/mpiexec command, MPI tasks/node, and use of multiple MPI tasks/GPU is the same.
Use the suffix gpu command, or you can explicitly add an “gpu” suffix to individual styles in your input script, e.g.
pair_style lj/cut/gpu 2.5
You must also use the package gpu command to enable the GPU package, unless the “-sf gpu” or “-pk gpu” command-line switches were used. It specifies the number of GPUs/node to use, as well as other options.
Speed-ups to expect:
The performance of a GPU versus a multi-core CPU is a function of your hardware, which pair style is used, the number of atoms/GPU, and the precision used on the GPU (double, single, mixed).
See the Benchmark page of the LAMMPS web site for performance of the GPU package on various hardware, including the Titan HPC platform at ORNL.
You should also experiment with how many MPI tasks per GPU to use to give the best performance for your problem and machine. This is also a function of the problem size and the pair style being using. Likewise, you should experiment with the precision setting for the GPU library to see if single or mixed precision will give accurate results, since they will typically be faster.
Guidelines for best performance:
• Using multiple MPI tasks per GPU will often give the best performance, as allowed my most multi-core CPU/GPU configurations.
• If the number of particles per MPI task is small (e.g. 100s of particles), it can be more efficient to run with fewer MPI tasks per GPU, even if you do not use all the cores on the compute node.
• The package gpu command has several options for tuning performance. Neighbor lists can be built on the GPU or CPU. Force calculations can be dynamically balanced across the CPU cores and GPUs. GPU-specific settings can be made which can be optimized for different hardware. See the packakge command doc page for details.
• As described by the package gpu command, GPU accelerated pair styles can perform computations asynchronously with CPU computations. The “Pair” time reported by LAMMPS will be the maximum of the time required to complete the CPU pair style computations and the time required to complete the GPU pair style computations. Any time spent for GPU-enabled pair styles for computations that run simultaneously with bond, angle, dihedral, improper, and long-range calculations will not be included in the “Pair” time.
• When the mode setting for the package gpu command is force/neigh, the time for neighbor list calculations on the GPU will be added into the “Pair” time, not the “Neigh” time. An additional breakdown of the times required for various tasks on the GPU (data copy, neighbor calculations, force computations, etc) are output only with the LAMMPS screen output (not in the log file) at the end of each run. These timings represent total time spent on the GPU for each routine, regardless of asynchronous CPU calculations.
• The output section “GPU Time Info (average)” reports “Max Mem / Proc”. This is the maximum memory used at one time on the GPU for data storage by a single MPI process.
None. | 2017-10-17T03:52:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23659038543701172, "perplexity": 3850.9368247800157}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187820700.4/warc/CC-MAIN-20171017033641-20171017053641-00250.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=M196M&home=MXXX040 | # ${{\boldsymbol D}_{{s1}}^{*}{(2860)}^{+}}$ MASS INSPIRE search
VALUE (MeV) EVTS DOCUMENT ID TECN COMMENT
$2859$ $\pm12$ $\pm24$ 1
2014 AW
LHCB ${{\mathit B}^{0}_{{s}}}$ $\rightarrow$ ${{\overline{\mathit D}}^{0}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2866.1$ $\pm1.0$ $\pm6.3$ 36k 2, 3
2012 AU
LHCB ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ( ${{\mathit D}}{{\mathit K}}){}^{+}{{\mathit X}}$ at 7 TeV
$2862$ $\pm2$ ${}^{+5}_{-2}$ 3122 4, 3
2009 AR
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}^{(*)}}{{\mathit K}}{{\mathit X}}$
$2856.6$ $\pm1.5$ $\pm5.0$ 5
2006 E
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}}{{\mathit X}}$
1 Separated from the spin-3 component ${{\mathit D}_{{s3}}^{*}{(2860)}^{-}}$ by a fit of the helicity angle of the ${{\overline{\mathit D}}^{0}}{{\mathit K}^{-}}$ system, with a statistical significance of the spin-3 and spin-1 components in excess of 10 $\sigma$.
2 From the combined fit of the ${{\mathit D}^{+}}{{\mathit K}_S^0}$ and ${{\mathit D}^{0}}{{\mathit K}^{+}}$ modes in the model including the ${{\mathit D}_{{s2}}^{*}{(2573)}^{+}}$, ${{\mathit D}_{{s1}}^{*}{(2700)}^{+}}$ and spin-0 ${{\mathit D}_{{sJ}}^{*}{(2860)}^{+}}$.
3 Possible contribution from the ${{\mathit D}_{{s3}}^{*}{(2860)}}$ state.
4 From simultaneous fits to the two ${{\mathit D}}{{\mathit K}}$ mass spectra and to the total ${{\mathit D}^{*}}{{\mathit K}}$ mass spectrum.
5 Superseded by AUBERT 2009AR.
References:
AAIJ 2014AW
PRL 113 162001 Observation of Overlapping spin-1 and spin-3 ${{\overline{\mathit D}}^{0}}{{\mathit K}^{-}}$ Resonances at Mass 2.86 GeV/$\mathit c{}^{2}$
AAIJ 2012AU
JHEP 1210 151 Study of ${{\mathit D}_{{sJ}}}$ decays to ${{\mathit D}^{+}}{{\mathit K}_S^0}$ and ${{\mathit D}^{0}}{{\mathit K}^{+}}$ Final States in ${{\mathit p}}{{\mathit p}}$ Collisions
AUBERT 2009AR
PR D80 092003 Study of ${{\mathit D}_{{sJ}}}$ Decays to ${{\mathit D}^{*}}{{\mathit K}}$ in Inclusive ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Interactions
AUBERT,BE 2006E
PRL 97 222001 Observation of a New ${{\mathit D}_{{s}}}$ Meson Decaying to $\mathit DK$ at a Mass of 2.86 GeV/$\mathit c{}^{2}$ | 2020-01-26T14:23:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9159494042396545, "perplexity": 2473.9886302329073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251689924.62/warc/CC-MAIN-20200126135207-20200126165207-00195.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aji.lizhen | # zbMATH — the first resource for mathematics
## Ji, Lizhen
Compute Distance To:
Author ID: ji.lizhen Published as: Ji, L.; Ji, Lizhen Homepage: http://www.math.lsa.umich.edu/~lji/ External Links: MGP · Wikidata
Documents Indexed: 146 Publications since 1992, including 42 Books Reviewing Activity: 94 Reviews
all top 5
#### Co-Authors
61 single-authored 34 Yau, Shing-Tung 13 Papadopoulos, Athanase 9 Liu, Kefeng 7 Yang, Lo 5 A’Campo, Norbert 5 Borel, Armand 5 Poon, Yat Sun 5 Weber, Andreas 4 Li, Peter 3 Anker, Jean-Philippe 3 Cheng, Shiu-Yuen 3 Schoen, Richard Melvin 3 Simon, Leon Melvin 2 Guivarc’h, Yves 2 Leuzinger, Enrico 2 Mazzeo, Rafe R. 2 Oort, Frans 2 Taylor, John C. 2 Wolpert, Scott A. 2 Xu, Hao 2 Zworski, Maciej 1 A’Campo-Neuen, Annette 1 Atiyah, Michael Francis 1 Chiou, Wen-Lin 1 Cohen, Daniel C. 1 do Carmo, Manfredo Perdigão 1 Farb, Benson 1 Goresky, Robert Mark 1 Greene, Robert Everist 1 Hirzebruch, Friedrich 1 Huang, Jie (Jenny) 1 Huang, Wenling 1 Ivanov, Nikolai V. 1 Jost, Jürgen 1 Kuh, Ernest Shiu-jen 1 Kunstmann, Peer Christian 1 Li, Jian-Shu 1 Li, Jun 1 Lin, Zongzhu 1 Looijenga, Eduard J. N. 1 Lu, Jiang-Hua 1 Lyubich, Mikhail Yur’evich 1 MacPherson, Robert Duncan 1 McMullen, Curtis Tracy 1 Müller, Werner G. 1 Müller, Werner 1 Murty, Vijaya Kumar 1 Reich, Karin 1 Saper, Leslie 1 Scherk, John 1 Schilling, Anna-Sofie 1 Sesum, Natasa 1 Shen, Y. Ron 1 Singer, Isadore M. 1 Van der Geer, Gerard 1 Vasy, András 1 Wang, Chang 1 Wang, Jiaping 1 Wang, Liping 1 Weinstein, Alan David 1 Wentworth, Richard A. 1 Wolf, Joseph Albert 1 Wu, Baosen 1 Xiao, Jie 1 Xu, Huawei 1 Yamada, Sumio 1 Yang, Xiao-Kui 1 Zelditch, Steve 1 Zhang, Shou-Wu 1 Zheng, Zhujun 1 Zucker, Steven Mark
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#### Serials
24 Advanced Lectures in Mathematics (ALM) 9 Pure and Applied Mathematics Quarterly 7 Journal of Differential Geometry 6 ICCM Notices 5 AMS/IP Studies in Advanced Mathematics 3 Geometric and Functional Analysis. GAFA 3 L’Enseignement Mathématique. 2e Série 3 Mathematical Research Letters 3 The Asian Journal of Mathematics 2 Archive for History of Exact Sciences 2 Journal of Functional Analysis 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Ergodic Theory and Dynamical Systems 2 Notices of the American Mathematical Society 2 Surveys of Modern Mathematics 1 Letters in Mathematical Physics 1 Journal of Geometry and Physics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Commentarii Mathematici Helvetici 1 Duke Mathematical Journal 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Annals of Global Analysis and Geometry 1 $$K$$-Theory 1 International Journal of Mathematics 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Communications in Analysis and Geometry 1 Bulletin des Sciences Mathématiques 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Oberwolfach Reports 1 Innovations in Incidence Geometry 1 Progress in Mathematics 1 IRMA Lectures in Mathematics and Theoretical Physics 1 Surveys in Differential Geometry 1 Journal of Topology 1 Science China. Mathematics
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#### Fields
46 Differential geometry (53-XX) 42 General and overarching topics; collections (00-XX) 38 Topological groups, Lie groups (22-XX) 37 History and biography (01-XX) 34 Several complex variables and analytic spaces (32-XX) 32 Functions of a complex variable (30-XX) 28 Algebraic geometry (14-XX) 27 Number theory (11-XX) 25 Group theory and generalizations (20-XX) 24 Global analysis, analysis on manifolds (58-XX) 22 Manifolds and cell complexes (57-XX) 10 Partial differential equations (35-XX) 8 Algebraic topology (55-XX) 7 Potential theory (31-XX) 6 $$K$$-theory (19-XX) 6 Quantum theory (81-XX) 5 Abstract harmonic analysis (43-XX) 4 Commutative algebra (13-XX) 4 General topology (54-XX) 3 Operator theory (47-XX) 3 Geometry (51-XX) 3 Probability theory and stochastic processes (60-XX) 3 Relativity and gravitational theory (83-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Numerical analysis (65-XX) 1 Systems theory; control (93-XX)
#### Citations contained in zbMATH Open
60 Publications have been cited 328 times in 270 Documents Cited by Year
Compactifications of symmetric and locally symmetric spaces. Zbl 1100.22001
Borel, Armand; Ji, Lizhen
2006
Heat kernel and Green function estimates on noncompact symmetric spaces. Zbl 0942.43005
Anker, J.-P.; Ji, L.
1999
Dynamics of the heat semigroup on symmetric spaces. Zbl 1185.37077
Ji, Lizhen; Weber, Andreas
2010
Compactifications of symmetric spaces. Zbl 1053.31006
Guivarc’h, Yves; Ji, Lizhen; Taylor, J. C.
1998
Spectral degeneration of hyperboloc Riemann surfaces. Zbl 0793.53051
Ji, Lizhen
1993
Geometry of compactifications of locally symmetric spaces. Zbl 1017.53039
Ji, Lizhen; MacPherson, Robert
2002
Ricci flow on surfaces with cusps. Zbl 1176.53067
Ji, Lizhen; Mazzeo, Rafe; Sesum, Natasa
2009
Asymptotic dimension and the integral $$K$$-theoretic Novikov conjecture for arithmetic groups. Zbl 1079.55012
Ji, Lizhen
2004
The asymptotic behavior of Green’s functions for degenerating hyperbolic surfaces. Zbl 0792.53040
Ji, Lizhen
1993
On the Künneth formula for intersection cohomology. Zbl 0765.57014
Cohen, Daniel C.; Goresky, Mark; Ji, Lizhen
1992
Integral Novikov conjectures and arithmetic groups containing torsion elements. Zbl 1225.22009
Ji, Lizhen
2007
Scattering matrices and scattering geodesics of locally symmetric spaces. Zbl 1026.53026
Ji, Lizhen; Zworski, Maciej
2001
The remainder estimate in spectral accumulation for degenerating hyperbolic surfaces. Zbl 0783.58078
Ji, Lizhen; Zworski, Maciej
1993
A cofinite universal space for proper actions for mapping class groups. Zbl 1205.57004
Ji, Lizhen; Wolpert, Scott A.
2010
Compactifications of locally symmetric spaces. Zbl 1122.22005
Borel, Armand; Ji, Lizhen
2006
Well-rounded equivariant deformation retracts of Teichmüller spaces. Zbl 1303.32007
Ji, Lizhen
2014
$$L^p$$ spectral theory and heat dynamics of locally symmetric spaces. Zbl 1190.58024
Ji, Lizhen; Weber, Andreas
2010
Buildings and their applications in geometry and topology. Zbl 1163.22010
Ji, Lizhen
2006
Metric compactifications of locally symmetric spaces. Zbl 0929.32017
Ji, Lizhen
1998
Riesz transform on locally symmetric spaces and Riemannian manifolds with a spectral gap. Zbl 1187.58029
Ji, Lizhen; Kunstmann, Peer; Weber, Andreas
2010
Pointwise bounds for $$L^{2}$$ eigenfunctions on locally symmetric spaces. Zbl 1154.58003
Ji, Lizhen; Weber, Andreas
2008
A summary of the work of Gregory Margulis. Zbl 1279.01039
Ji, Lizhen
2008
The integral Novikov conjectures for linear groups containing torsion elements. Zbl 1162.57022
Ji, Lizhen
2008
Heat kernel and Green function estimates on noncompact symmetric spaces. II. Zbl 0988.22006
Anker, Jean-Philippe; Ji, Lizhen
2001
The Weyl upper bound on the discrete spectrum of locally symmetric spaces. Zbl 1036.58028
Ji, Lizhen
1999
Exact behavior of the heat kernel and of the Green function on noncompact symmetric spaces. Zbl 0907.43010
Anker, Jean-Philippe; Ji, Lizhen
1998
The trace class conjecture for arithmetic groups. Zbl 0926.11034
Ji, Lizhen
1998
Spectral convergence on degenerating surfaces. Zbl 0774.58041
Ji, Lizhen; Wentworth, Richard
1992
Ends of locally symmetric spaces with maximal bottom spectrum. Zbl 1270.58018
Ji, Lizhen; Li, Peter; Wang, Jiaping
2009
Infinite topology of curve complexes and non-Poincaré duality of Teichmüller modular groups. Zbl 1162.57014
Ivanov, Nikolai; Ji, Lizhen
2008
The integral Novikov conjectures for $$S$$-arithmetic groups. I. Zbl 1130.22005
Ji, Lizhen
2007
Compactifications of symmetric spaces. Zbl 1110.53036
Borel, Armand; Ji, Lizhen
2007
Compactifications of symmetric and locally symmetric spaces. Zbl 1088.53034
Borel, Armand; Ji, Lizhen
2005
Convergence of heat kernels for degenerating hyperbolic surfaces. Zbl 0813.58057
Ji, Lizhen
1995
Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces. Zbl 0814.58039
Ji, Lizhen; Zelditch, Steven
1994
Metric Schottky problem and Satake compactifications of moduli spaces. Zbl 1427.53065
Ji, Lizhen
2019
Toric varieties vs. horofunction compactifications of polyhedral norms. Zbl 1402.14065
Ji, Lizhen; Schilling, Anna-Sofie
2017
Universal moduli spaces of Riemann surfaces. Zbl 1361.32018
Ji, Lizhen; Jost, Jürgen
2017
On Grothendieck’s tame topology. Zbl 1361.32017
A’Campo, Norbert; Ji, Lizhen; Papadopoulos, Athanase
2016
On Grothendieck’s construction of Teichmüller space. Zbl 1345.30051
A’Campo, Norbert; Ji, Lizhen; Papadopoulos, Athanase
2016
On the early history of moduli and Teichmüller spaces. Zbl 1361.30071
A’Campo, Norbert; Ji, Lizhen; Papadopoulos, Arthanase
2015
The $$L^{p}$$ spectrum and heat dynamics of locally symmetric spaces of higher rank. Zbl 1401.58014
Ji, Lizhen; Weber, Andreas
2015
The fundamental group of reductive Borel-Serre and Satake compactifications. Zbl 1329.20063
Ji, Lizhen; Murty, V. Kumar; Saper, Leslie; Scherk, John
2015
A commentary on Teichmüller’s paper “Veränderliche Riemannsche Flächen”. Zbl 1314.30078
A’Campo-Neuen, Annette; A’Campo, Norbert; Ji, Lizhen; Papadopoulos, Athanase
2014
Spectral theory for the Weil-Petersson Laplacian on the Riemann moduli space. Zbl 1323.35119
Ji, Lizhen; Mazzeo, Rafe; Müller, Werner; Vasy, Andras
2014
Historical development of Teichmüller theory. Zbl 1266.01022
2013
Buildings and their applications in geometry and topology. Zbl 1275.20025
Ji, Lizhen
2012
Arithmetic groups vs. mapping class groups: similarities, analogies and differences. Abstracts from the workshop held June 5–11, 2011. Zbl 1334.00092
Farb, Benson (ed.); Ji, Lizhen (ed.); Leuzinger, Enrico (ed.); Müller, Werner (ed.)
2011
Arithmetic groups, mapping class groups, related groups, and their associated spaces. Zbl 1210.22007
Ji, Lizhen
2010
Automorphic forms and the Langlands program. Selected papers of the conference on Langlands and geometric Langlands program, Guangzhou, China, June 18–21, 2007. Zbl 1185.11005
Ji, Lizhen (ed.); Liu, Kefeng (ed.); Yau, Shing-Tung (ed.); Zheng, Zhu-Jun (ed.)
2010
The asymptotic Schottky problem. Zbl 1193.14044
Ji, Lizhen; Leuzinger, Enrico
2010
From symmetric spaces to buildings, curve complexes and outer spaces. Zbl 1264.20031
Ji, Lizhen
2009
Large scale geometry, compactifications and the integral Novikov conjectures for arithmetic groups. Zbl 1179.19002
Ji, Lizhen
2008
Handbook of geometric analysis. No. 1. Zbl 1144.53004
Ji, Lizhen (ed.); Li, Peter (ed.); Schoen, Richard (ed.); Simon, Leon (ed.)
2008
Arithmetic groups and their generalizations. What, why and how. Zbl 1148.11019
Ji, Lizhen
2008
Armand Borel as a mentor. Zbl 1072.01536
Ji, Lizhen
2004
Satake and Martin compactifications of symmetric spaces are topological balls. Zbl 0883.53048
Ji, Lizhen
1997
Compactifications of symmetric spaces and locally symmetric spaces. Zbl 0936.53033
Ji, Lizhen
1996
Degeneration of pseudo-Laplace operators for hyperbolic Riemann surfaces. Zbl 0802.58061
Ji, Lizhen
1994
Compactifications of symmetric spaces. Zbl 0814.53038
Guivarc’h, Yves; Ji, Lizhen; Taylor, John
1993
Metric Schottky problem and Satake compactifications of moduli spaces. Zbl 1427.53065
Ji, Lizhen
2019
Toric varieties vs. horofunction compactifications of polyhedral norms. Zbl 1402.14065
Ji, Lizhen; Schilling, Anna-Sofie
2017
Universal moduli spaces of Riemann surfaces. Zbl 1361.32018
Ji, Lizhen; Jost, Jürgen
2017
On Grothendieck’s tame topology. Zbl 1361.32017
A’Campo, Norbert; Ji, Lizhen; Papadopoulos, Athanase
2016
On Grothendieck’s construction of Teichmüller space. Zbl 1345.30051
A’Campo, Norbert; Ji, Lizhen; Papadopoulos, Athanase
2016
On the early history of moduli and Teichmüller spaces. Zbl 1361.30071
A’Campo, Norbert; Ji, Lizhen; Papadopoulos, Arthanase
2015
The $$L^{p}$$ spectrum and heat dynamics of locally symmetric spaces of higher rank. Zbl 1401.58014
Ji, Lizhen; Weber, Andreas
2015
The fundamental group of reductive Borel-Serre and Satake compactifications. Zbl 1329.20063
Ji, Lizhen; Murty, V. Kumar; Saper, Leslie; Scherk, John
2015
Well-rounded equivariant deformation retracts of Teichmüller spaces. Zbl 1303.32007
Ji, Lizhen
2014
A commentary on Teichmüller’s paper “Veränderliche Riemannsche Flächen”. Zbl 1314.30078
A’Campo-Neuen, Annette; A’Campo, Norbert; Ji, Lizhen; Papadopoulos, Athanase
2014
Spectral theory for the Weil-Petersson Laplacian on the Riemann moduli space. Zbl 1323.35119
Ji, Lizhen; Mazzeo, Rafe; Müller, Werner; Vasy, Andras
2014
Historical development of Teichmüller theory. Zbl 1266.01022
2013
Buildings and their applications in geometry and topology. Zbl 1275.20025
Ji, Lizhen
2012
Arithmetic groups vs. mapping class groups: similarities, analogies and differences. Abstracts from the workshop held June 5–11, 2011. Zbl 1334.00092
Farb, Benson (ed.); Ji, Lizhen (ed.); Leuzinger, Enrico (ed.); Müller, Werner (ed.)
2011
Dynamics of the heat semigroup on symmetric spaces. Zbl 1185.37077
Ji, Lizhen; Weber, Andreas
2010
A cofinite universal space for proper actions for mapping class groups. Zbl 1205.57004
Ji, Lizhen; Wolpert, Scott A.
2010
$$L^p$$ spectral theory and heat dynamics of locally symmetric spaces. Zbl 1190.58024
Ji, Lizhen; Weber, Andreas
2010
Riesz transform on locally symmetric spaces and Riemannian manifolds with a spectral gap. Zbl 1187.58029
Ji, Lizhen; Kunstmann, Peer; Weber, Andreas
2010
Arithmetic groups, mapping class groups, related groups, and their associated spaces. Zbl 1210.22007
Ji, Lizhen
2010
Automorphic forms and the Langlands program. Selected papers of the conference on Langlands and geometric Langlands program, Guangzhou, China, June 18–21, 2007. Zbl 1185.11005
Ji, Lizhen (ed.); Liu, Kefeng (ed.); Yau, Shing-Tung (ed.); Zheng, Zhu-Jun (ed.)
2010
The asymptotic Schottky problem. Zbl 1193.14044
Ji, Lizhen; Leuzinger, Enrico
2010
Ricci flow on surfaces with cusps. Zbl 1176.53067
Ji, Lizhen; Mazzeo, Rafe; Sesum, Natasa
2009
Ends of locally symmetric spaces with maximal bottom spectrum. Zbl 1270.58018
Ji, Lizhen; Li, Peter; Wang, Jiaping
2009
From symmetric spaces to buildings, curve complexes and outer spaces. Zbl 1264.20031
Ji, Lizhen
2009
Pointwise bounds for $$L^{2}$$ eigenfunctions on locally symmetric spaces. Zbl 1154.58003
Ji, Lizhen; Weber, Andreas
2008
A summary of the work of Gregory Margulis. Zbl 1279.01039
Ji, Lizhen
2008
The integral Novikov conjectures for linear groups containing torsion elements. Zbl 1162.57022
Ji, Lizhen
2008
Infinite topology of curve complexes and non-Poincaré duality of Teichmüller modular groups. Zbl 1162.57014
Ivanov, Nikolai; Ji, Lizhen
2008
Large scale geometry, compactifications and the integral Novikov conjectures for arithmetic groups. Zbl 1179.19002
Ji, Lizhen
2008
Handbook of geometric analysis. No. 1. Zbl 1144.53004
Ji, Lizhen (ed.); Li, Peter (ed.); Schoen, Richard (ed.); Simon, Leon (ed.)
2008
Arithmetic groups and their generalizations. What, why and how. Zbl 1148.11019
Ji, Lizhen
2008
Integral Novikov conjectures and arithmetic groups containing torsion elements. Zbl 1225.22009
Ji, Lizhen
2007
The integral Novikov conjectures for $$S$$-arithmetic groups. I. Zbl 1130.22005
Ji, Lizhen
2007
Compactifications of symmetric spaces. Zbl 1110.53036
Borel, Armand; Ji, Lizhen
2007
Compactifications of symmetric and locally symmetric spaces. Zbl 1100.22001
Borel, Armand; Ji, Lizhen
2006
Compactifications of locally symmetric spaces. Zbl 1122.22005
Borel, Armand; Ji, Lizhen
2006
Buildings and their applications in geometry and topology. Zbl 1163.22010
Ji, Lizhen
2006
Compactifications of symmetric and locally symmetric spaces. Zbl 1088.53034
Borel, Armand; Ji, Lizhen
2005
Asymptotic dimension and the integral $$K$$-theoretic Novikov conjecture for arithmetic groups. Zbl 1079.55012
Ji, Lizhen
2004
Armand Borel as a mentor. Zbl 1072.01536
Ji, Lizhen
2004
Geometry of compactifications of locally symmetric spaces. Zbl 1017.53039
Ji, Lizhen; MacPherson, Robert
2002
Scattering matrices and scattering geodesics of locally symmetric spaces. Zbl 1026.53026
Ji, Lizhen; Zworski, Maciej
2001
Heat kernel and Green function estimates on noncompact symmetric spaces. II. Zbl 0988.22006
Anker, Jean-Philippe; Ji, Lizhen
2001
Heat kernel and Green function estimates on noncompact symmetric spaces. Zbl 0942.43005
Anker, J.-P.; Ji, L.
1999
The Weyl upper bound on the discrete spectrum of locally symmetric spaces. Zbl 1036.58028
Ji, Lizhen
1999
Compactifications of symmetric spaces. Zbl 1053.31006
Guivarc’h, Yves; Ji, Lizhen; Taylor, J. C.
1998
Metric compactifications of locally symmetric spaces. Zbl 0929.32017
Ji, Lizhen
1998
Exact behavior of the heat kernel and of the Green function on noncompact symmetric spaces. Zbl 0907.43010
Anker, Jean-Philippe; Ji, Lizhen
1998
The trace class conjecture for arithmetic groups. Zbl 0926.11034
Ji, Lizhen
1998
Satake and Martin compactifications of symmetric spaces are topological balls. Zbl 0883.53048
Ji, Lizhen
1997
Compactifications of symmetric spaces and locally symmetric spaces. Zbl 0936.53033
Ji, Lizhen
1996
Convergence of heat kernels for degenerating hyperbolic surfaces. Zbl 0813.58057
Ji, Lizhen
1995
Hyperbolic cusp forms and spectral simplicity on compact hyperbolic surfaces. Zbl 0814.58039
Ji, Lizhen; Zelditch, Steven
1994
Degeneration of pseudo-Laplace operators for hyperbolic Riemann surfaces. Zbl 0802.58061
Ji, Lizhen
1994
Spectral degeneration of hyperboloc Riemann surfaces. Zbl 0793.53051
Ji, Lizhen
1993
The asymptotic behavior of Green’s functions for degenerating hyperbolic surfaces. Zbl 0792.53040
Ji, Lizhen
1993
The remainder estimate in spectral accumulation for degenerating hyperbolic surfaces. Zbl 0783.58078
Ji, Lizhen; Zworski, Maciej
1993
Compactifications of symmetric spaces. Zbl 0814.53038
Guivarc’h, Yves; Ji, Lizhen; Taylor, John
1993
On the Künneth formula for intersection cohomology. Zbl 0765.57014
Cohen, Daniel C.; Goresky, Mark; Ji, Lizhen
1992
Spectral convergence on degenerating surfaces. Zbl 0774.58041
Ji, Lizhen; Wentworth, Richard
1992
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#### Cited by 343 Authors
20 Ji, Lizhen 8 Kostić, Marko 7 Weber, Andreas 5 Leuzinger, Enrico 5 Lohoué, Noël 4 Conejero, José Alberto 4 Dranishnikov, Alexander Nikolaevich 4 Jorgenson, Jay Alan 4 Lu, Guozhen 4 Meda, Stefano 4 Murillo-Arcila, Marina 4 Sarkar, Rudra P. 4 Vallarino, Maria 4 Yang, Qiaohua 3 Anker, Jean-Philippe 3 Biliotti, Leonardo 3 Friedman, Greg 3 Kaizuka, Koichi 3 Kim, Inkang 3 Kim, Sungwoon 3 Ledrappier, François 3 Li, Hongquan 3 Lundelius, Rolf E. 3 Murata, Minoru 3 Peris, Alfredo 3 Thangavelu, Sundaram 2 Aramayona, Javier 2 Attwell-Duval, Dylan 2 Banica, Valeria 2 Brasselet, Jean-Paul 2 Caprace, Pierre-Emmanuel 2 Chang, Stanley S. 2 Chen, Chung-Chuan 2 Cupit-Foutou, Stéphanie 2 Di Cerbo, Gabriele 2 Di Cerbo, Luca Fabrizio 2 Falliero, Thérèse 2 Finis, Tobias 2 Funke, Jens 2 Ghigi, Alessandro 2 Goldfarb, Boris 2 González, María del Mar 2 Gorodnik, Alexander 2 Ionescu, Alexandru D. 2 Itoh, Mitsuhiro 2 Jost, Jürgen 2 Judge, Christopher M. 2 Lacoste, Cyril 2 Lapid, Erez Moshe 2 Li, Jun-Gang 2 Mauceri, Giancarlo 2 Mazzeo, Rafe R. 2 McClure, James E. 2 Millson, John J. 2 Mondal, Sugata 2 Müller, Werner 2 Naik, Muna 2 Papadopoulos, Athanase 2 Parthasarathy, Aprameyan 2 Pierfelice, Vittoria 2 Punzo, Fabio 2 Ramacher, Pablo 2 Rochon, Frédéric 2 Sá Barreto, Antônio 2 Sáez, Mariel 2 Sarig, Omri M. 2 Topping, Peter Miles 2 Vasy, András 2 Wang, Yiran 2 Weinberger, Shmuel 2 Yu, Guoliang 1 Albin, Pierre 1 Aldana, Clara L. 1 Alldridge, Alexander 1 Álvarez López, Jesús A. 1 Ammann, Bernd Eberhard 1 Antonakoudis, Stergios M. 1 Aroza, Javier 1 Astengo, Francesca 1 Avdispahić, Muharem 1 Avramidi, Grigori 1 Ayoub, Joseph 1 Bader, Uri 1 Bahuaud, Eric 1 Bainbridge, Matt 1 Bakker, Benjamin 1 Bamler, Richard H. 1 Banagl, Markus 1 Bartels, Arthur C. 1 Behrstock, Jason A. 1 Bell, Gregory C. 1 Ben Farah, Slaïm 1 Benoist, Yves 1 Berger, Franz 1 Blackman, Terrence Richard 1 Boggarapu, Pradeep 1 Bohm, Christoph 1 Borthwick, David 1 Bougerol, Philippe 1 Broaddus, Nathan ...and 243 more Authors
all top 5
#### Cited in 118 Serials
19 Journal of Functional Analysis 13 Transactions of the American Mathematical Society 8 Duke Mathematical Journal 8 Mathematische Annalen 8 Mathematische Zeitschrift 7 Advances in Mathematics 6 Annales de l’Institut Fourier 6 Geometriae Dedicata 6 Differential Geometry and its Applications 5 Inventiones Mathematicae 5 The Journal of Geometric Analysis 5 Communications in Partial Differential Equations 4 Israel Journal of Mathematics 4 Journal of Mathematical Analysis and Applications 4 Topology and its Applications 4 Calculus of Variations and Partial Differential Equations 4 Geometry & Topology 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Groups, Geometry, and Dynamics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Manuscripta Mathematica 3 Proceedings of the American Mathematical Society 3 Bulletin des Sciences Mathématiques 3 Annals of Mathematics. Second Series 3 Journal of Topology and Analysis 2 Archive for History of Exact Sciences 2 Communications in Mathematical Physics 2 Communications on Pure and Applied Mathematics 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Journal of Differential Equations 2 Journal of Number Theory 2 Journal of Pure and Applied Algebra 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Ergodic Theory and Dynamical Systems 2 Annals of Global Analysis and Geometry 2 Revista Matemática Iberoamericana 2 Journal of the American Mathematical Society 2 Geometric and Functional Analysis. GAFA 2 Bulletin of the American Mathematical Society. New Series 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Potential Analysis 2 Journal of Lie Theory 2 Selecta Mathematica. New Series 2 Transformation Groups 2 Abstract and Applied Analysis 2 Acta Mathematica Sinica. English Series 2 Algebraic & Geometric Topology 2 International Journal of Number Theory 2 Annales Mathématiques du Québec 2 Open Mathematics 1 Bulletin of the Australian Mathematical Society 1 Discrete Mathematics 1 Journal d’Analyse Mathématique 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Russian Mathematical Surveys 1 Arkiv för Matematik 1 Journal of Geometry and Physics 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Acta Mathematica 1 The Annals of Probability 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Archiv der Mathematik 1 Commentarii Mathematici Helvetici 1 Functional Analysis and its Applications 1 Illinois Journal of Mathematics 1 Publications Mathématiques 1 Integral Equations and Operator Theory 1 Journal of Algebra 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik 1 Kodai Mathematical Journal 1 Mathematische Nachrichten 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the London Mathematical Society. Third Series 1 Quaestiones Mathematicae 1 Results in Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Probability Theory and Related Fields 1 $$K$$-Theory 1 International Journal of Algebra and Computation 1 IMRN. International Mathematics Research Notices 1 L’Enseignement Mathématique. 2e Série 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Russian Mathematics 1 Electronic Research Announcements of the American Mathematical Society 1 Differential Equations and Dynamical Systems 1 Mathematical Physics, Analysis and Geometry 1 Communications of the Korean Mathematical Society 1 Journal of Evolution Equations ...and 18 more Serials
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#### Cited in 38 Fields
77 Global analysis, analysis on manifolds (58-XX) 74 Differential geometry (53-XX) 57 Topological groups, Lie groups (22-XX) 47 Partial differential equations (35-XX) 43 Number theory (11-XX) 37 Algebraic geometry (14-XX) 34 Group theory and generalizations (20-XX) 34 Several complex variables and analytic spaces (32-XX) 33 Manifolds and cell complexes (57-XX) 30 Abstract harmonic analysis (43-XX) 28 Operator theory (47-XX) 20 Functions of a complex variable (30-XX) 17 Dynamical systems and ergodic theory (37-XX) 15 Algebraic topology (55-XX) 13 Functional analysis (46-XX) 12 Probability theory and stochastic processes (60-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 8 $$K$$-theory (19-XX) 8 General topology (54-XX) 7 Ordinary differential equations (34-XX) 6 Potential theory (31-XX) 5 Category theory; homological algebra (18-XX) 5 Geometry (51-XX) 5 Quantum theory (81-XX) 4 Combinatorics (05-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Measure and integration (28-XX) 3 Integral transforms, operational calculus (44-XX) 3 Convex and discrete geometry (52-XX) 2 General and overarching topics; collections (00-XX) 2 Special functions (33-XX) 2 Statistics (62-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Calculus of variations and optimal control; optimization (49-XX)
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https://www.zbmath.org/authors/?q=ai%3Ayadav.manoj-kumar | zbMATH — the first resource for mathematics
Compute Distance To:
Author ID: yadav.manoj-kumar Published as: Kumar, M.; Kumar, Manoj; Yadav, Manoj K.; Yadav, Manoj Kumar Homepage: http://www.hri.res.in/~myadav/ External Links: MGP · Wikidata
Documents Indexed: 108 Publications since 1997, including 3 Books
all top 5
Co-Authors
9 single-authored 4 Vermani, Lekh Raj 2 Bardakov, Valeriĭ Georgievich 2 Hatui, Sumana 2 Jain, Vivek Kumar 2 Nath, Rajat Kanti 2 Passi, Inder Bir Singh 2 Rai, Pradeep Kumar 2 Singh, Mahender 1 Dade, Everett C. 1 Dolfi, Silvio 1 Kakkar, Vipul 1 Neshchadim, Mikhail Vladimirovich 1 Vesnin, Andrei Yu.
all top 5
Serials
4 International Journal of Algebra and Computation 3 Communications in Algebra 3 Israel Journal of Mathematics 3 Journal of Algebra 3 Proceedings of the Japan Academy. Series A 2 Journal of Group Theory 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Springer Monographs in Mathematics
Fields
24 Group theory and generalizations (20-XX) 1 Associative rings and algebras (16-XX)
Citations contained in zbMATH
63 Publications have been cited 345 times in 256 Documents Cited by Year
On $$\mathrm\text{ Ш}$$-rigidity of groups of order $$p^6$$. Zbl 1310.20025
2015
On automorphisms of some finite $$p$$-groups. Zbl 1148.20014
2008
A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems. Zbl 0990.65086
Aziz, Tariq; Kumar, Manoj
2001
Numerical method for solving fractional coupled Burgers equations. Zbl 1410.65413
Prakash, Amit; Kumar, Manoj; Sharma, Kapil K.
2015
On central automorphisms fixing the center element-wise. Zbl 1187.20013
2009
A collection of computational techniques for solving singular boundary-value problems. Zbl 1159.65076
Kumar, Manoj; Singh, Neelima
2009
Methods for solving singular boundary value problems using splines: a review. Zbl 1186.65104
Kumar, Manoj; Gupta, Yogesh
2010
An initial-value technique for singularly perturbed boundary value problems via cubic spline. Zbl 1135.65350
Kumar, Manoj; Singh, P.; Mishra, Hradyesh Kumar
2007
A recent survey on computational techniques for solving singularly perturbed boundary value problems. Zbl 1127.65053
Kumar, Manoj; Singh, Pitam; Kumar Mishra, Hradyesh
2007
A non-uniform mesh finite difference method and its convergence for a class of singular two-point boundary value problems. Zbl 1063.65068
Kumar, M.; Aziz, T.
2004
Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey. Zbl 1236.65107
Kumar, Manoj; Yadav, Neha
2011
Methods for solving singular perturbation problems arising in science and engineering. Zbl 1225.65077
Kumar, Manoj; Parul
2011
A uniform mesh finite difference method for a class of singular two-point boundary value problems. Zbl 1103.65088
Kumar, Manoj; Aziz, Tariq
2006
“Hasse principle” for groups of order $$p^4$$. Zbl 1008.20014
Kumar, Manoj; Vermani, Lekh Raj
2001
“Hasse principle” for extraspecial $$p$$-groups. Zbl 0995.20034
Kumar, Manoj; Vermani, Lekh Raj
2000
An introduction to neural network methods for differential equations. Zbl 1328.92006
2015
Quintic nonpolynomial spline method for the solution of a second-order boundary-value problem with engineering applications. Zbl 1231.65120
Srivastava, Pankaj Kumar; Kumar, Manoj; Mohapatra, R. N.
2011
Automorphisms of Abelian group extensions. Zbl 1209.20021
Passi, I. B. S.; Singh, Mahender; Yadav, Manoj K.
2010
A boundary value approach for a class of linear singularly perturbed boundary value problems. Zbl 1159.65075
Kumar, Manoj; Mishra, Hradyesh Kumar; Singh, Peetam
2009
Class preserving automorphisms of finite $$p$$-groups. Zbl 1129.20017
2007
On automorphisms of some $$p$$-groups. Zbl 1062.20021
Kumar, Manoj; Vermani, Lekh Raj
2002
On finite $$p$$-groups whose central automorphisms are all class preserving. Zbl 1291.20023
2013
On finite $$p$$-groups whose automorphisms are all central. Zbl 1262.20030
Jain, Vivek K.; Yadav, Manoj K.
2012
Class preserving automorphisms of finite $$p$$-groups: a survey. Zbl 1231.20024
2011
Computational techniques for solving differential equations by cubic, quintic, and sextic spline. Zbl 1183.65097
Kumar, Manoj; Srivastava, Pankaj Kumar
2009
Estimation of parameters of generalized inverted exponential distribution for progressive type-II censored sample with binomial removals. Zbl 1307.62060
Singh, Sanjay Kumar; Singh, Umesh; Kumar, Manoj
2013
Numerical treatment of singularly perturbed two point boundary value problems using initial-value method. Zbl 1177.65109
Kumar, Manoj; Mishra, Hradyesh Kumar; Singh, P.
2009
Computational method for finding various solutions for a quasilinear elliptic equation of Kirchhoff type. Zbl 1171.74044
Kumar, Manoj; Kumar, Prashant
2009
Finite groups with many product conjugacy classes. Zbl 1139.20027
2006
Multi-time-step domain decomposition method with non-matching grids for parabolic problems. Zbl 1410.65364
Beneš, Michal; Nekvinda, Aleš; Yadav, Manoj Kumar
2015
Some results on relative commutativity degree. Zbl 1332.20027
Nath, Rajat Kanti; Yadav, Manoj Kumar
2015
Numerical algorithm based on quintic nonpolynomial spline for solving third-order boundary value problems associated with draining and coating flows. Zbl 1260.65068
Srivastava, Pankaj Kumar; Kumar, Manoj
2012
Non-inner automorphisms of order $$p$$ in finite $$p$$-groups of coclass 3. Zbl 1378.20030
Ruscitti, Marco; Legarreta, Leire; Yadav, Manoj K.
2017
Finite groups whose non-linear irreducible characters of the same degree are Galois conjugate. Zbl 1342.20005
Dolfi, Silvio; Yadav, Manoj K.
2016
On the probability distribution associated to commutator word map in finite groups. Zbl 1346.20083
Nath, Rajat Kanti; Yadav, Manoj Kumar
2015
On finite $$p$$-groups with Abelian automorphism group. Zbl 1288.20028
Jain, Vivek K.; Rai, Pradeep K.; Yadav, Manoj K.
2013
Class preserving automorphisms of unitriangular groups. Zbl 1256.20036
Bardakov, Valeriy; Vesnin, Andrei; Yadav, Manoj K.
2012
Radiation effect on unsteady MHD heat and mass transfer flow on a moving inclined porous heated plate in the presence of chemical reaction. Zbl 1305.76115
Uddin, Ziya; Kumar, Manoj
2010
Simulation of a nonlinear Steklov eigenvalue problem using finite-element approximation. Zbl 1197.65179
Kumar, Prashant; Kumar, Manoj
2010
On automorphisms of finite $$p$$-groups. Zbl 1131.20015
2007
Class of dual to ratio estimators for double sampling. Zbl 1115.62305
Kumar, Manoj; Bahl, Shashi
2006
A new iterative technique for a fractional model of nonlinear Zakharov-Kuznetsov equations via Sumudu transform. Zbl 1427.65322
Prakash, Amit; Kumar, Manoj; Baleanu, Dumitru
2018
Finite $$p$$-groups of conjugate type $$\{1,p^{3}\}$$. Zbl 1392.20008
Naik, Tushar Kanta; Yadav, Manoj K.
2018
Bayesian estimation for Poisson-exponential model under progressive type-II censoring data with binomial removal and its application to Ovarian cancer data. Zbl 1349.62487
Singh, Sanjay Kumar; Singh, Umesh; Kumar, Manoj
2016
A recent development of computer methods for solving singularly perturbed boundary value problems. Zbl 1242.34002
Kumar, Manoj; Parul
2011
A finite element approach for finding positive solutions of semilinear elliptic Dirichlet problems. Zbl 1172.65063
Kumar, Manoj; Kumar, Prashant
2009
Direct and inverse estimates for a new family of linear positive operators. Zbl 1111.41016
Gupta, M. K.; Gupta, Vijay; Kumar, Manoj
2007
Estimation of finite population mean using multi-auxiliary variables. Zbl 0952.62011
Bahl, S.; Kumar, Manoj
2000
Exact solutions of fractional partial differential equations by Sumudu transform iterative method. Zbl 1444.35149
Kumar, Manoj; Daftardar-Gejji, Varsha
2019
A new family of predictor-corrector methods for solving fractional differential equations. Zbl 1433.65133
Kumar, Manoj; Daftardar-Gejji, Varsha
2019
The Schur multiplier of groups of order $$\mathrm{p}^{5}$$. Zbl 07076608
Hatui, Sumana; Kakkar, Vipul; Yadav, Manoj K.
2019
A new trigonometrical algorithm for computing real root of non-linear transcendental equations. Zbl 1415.65116
Srivastav, Vivek Kumar; Thota, Srinivasarao; Kumar, Manoj
2019
MHD slips flow of a micro-polar fluid due to moving plate in porous medium with chemical reaction and thermal radiation: a Lie group analysis. Zbl 1401.76019
Singh, Khilap; Kumar, Manoj
2018
Group theory and computation. Invited papers based on the presentations at the workshop ‘Group theory and computational methods’, Bangalore, India, November 5–14, 2016. Zbl 1401.20004
Sastry, N. S. Narasimha (ed.); Yadav, Manoj Kumar (ed.)
2018
The Schur multiplier of central product of groups. Zbl 06867617
Hatui, Sumana; Vermani, L. R.; Yadav, Manoj K.
2018
Note on Caranti’s method of construction of Miller groups. Zbl 1425.20013
Kitture, Rahul Dattatraya; Yadav, Manoj K.
2018
Class-preserving automorphisms of finite $$p$$-groups. II. Zbl 1382.20027
2015
Buckling analysis of a beam-column using multilayer perceptron neural network technique. Zbl 1293.93084
Kumar, Manoj; Yadav, Neha
2013
Phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution. Zbl 1268.76006
Kumar, Manoj; Singh, Neelima
2012
Computer simulation of third-order nonlinear singular problems arising in draining and coating flows. Zbl 1253.76097
Kumar, Manoj; Singh, Neelima
2012
Application of B-spline to numerical solution of a system of singularly perturbed problems. Zbl 1306.65235
Gupta, Yogesh; Srivastava, Pankaj Kumar; Kumar, Manoj
2011
Predictive performance of the improved estimators with exact restrictions in linear regression models. Zbl 1175.62022
Kumar, Manoj; Mishra, Nutan; Gupta, Rajinder
2008
Common coincidence points of $$R$$-weakly commuting fuzzy maps. Zbl 1169.47063
Saini, R. K.; Kumar, M.; Gupta, V.; Singh, S. B.
2008
Exact solutions of fractional partial differential equations by Sumudu transform iterative method. Zbl 1444.35149
Kumar, Manoj; Daftardar-Gejji, Varsha
2019
A new family of predictor-corrector methods for solving fractional differential equations. Zbl 1433.65133
Kumar, Manoj; Daftardar-Gejji, Varsha
2019
The Schur multiplier of groups of order $$\mathrm{p}^{5}$$. Zbl 07076608
Hatui, Sumana; Kakkar, Vipul; Yadav, Manoj K.
2019
A new trigonometrical algorithm for computing real root of non-linear transcendental equations. Zbl 1415.65116
Srivastav, Vivek Kumar; Thota, Srinivasarao; Kumar, Manoj
2019
A new iterative technique for a fractional model of nonlinear Zakharov-Kuznetsov equations via Sumudu transform. Zbl 1427.65322
Prakash, Amit; Kumar, Manoj; Baleanu, Dumitru
2018
Finite $$p$$-groups of conjugate type $$\{1,p^{3}\}$$. Zbl 1392.20008
Naik, Tushar Kanta; Yadav, Manoj K.
2018
MHD slips flow of a micro-polar fluid due to moving plate in porous medium with chemical reaction and thermal radiation: a Lie group analysis. Zbl 1401.76019
Singh, Khilap; Kumar, Manoj
2018
Group theory and computation. Invited papers based on the presentations at the workshop ‘Group theory and computational methods’, Bangalore, India, November 5–14, 2016. Zbl 1401.20004
Sastry, N. S. Narasimha (ed.); Yadav, Manoj Kumar (ed.)
2018
The Schur multiplier of central product of groups. Zbl 06867617
Hatui, Sumana; Vermani, L. R.; Yadav, Manoj K.
2018
Note on Caranti’s method of construction of Miller groups. Zbl 1425.20013
Kitture, Rahul Dattatraya; Yadav, Manoj K.
2018
Non-inner automorphisms of order $$p$$ in finite $$p$$-groups of coclass 3. Zbl 1378.20030
Ruscitti, Marco; Legarreta, Leire; Yadav, Manoj K.
2017
Finite groups whose non-linear irreducible characters of the same degree are Galois conjugate. Zbl 1342.20005
Dolfi, Silvio; Yadav, Manoj K.
2016
Bayesian estimation for Poisson-exponential model under progressive type-II censoring data with binomial removal and its application to Ovarian cancer data. Zbl 1349.62487
Singh, Sanjay Kumar; Singh, Umesh; Kumar, Manoj
2016
On $$\mathrm\text{ Ш}$$-rigidity of groups of order $$p^6$$. Zbl 1310.20025
2015
Numerical method for solving fractional coupled Burgers equations. Zbl 1410.65413
Prakash, Amit; Kumar, Manoj; Sharma, Kapil K.
2015
An introduction to neural network methods for differential equations. Zbl 1328.92006
2015
Multi-time-step domain decomposition method with non-matching grids for parabolic problems. Zbl 1410.65364
Beneš, Michal; Nekvinda, Aleš; Yadav, Manoj Kumar
2015
Some results on relative commutativity degree. Zbl 1332.20027
Nath, Rajat Kanti; Yadav, Manoj Kumar
2015
On the probability distribution associated to commutator word map in finite groups. Zbl 1346.20083
Nath, Rajat Kanti; Yadav, Manoj Kumar
2015
Class-preserving automorphisms of finite $$p$$-groups. II. Zbl 1382.20027
2015
On finite $$p$$-groups whose central automorphisms are all class preserving. Zbl 1291.20023
2013
Estimation of parameters of generalized inverted exponential distribution for progressive type-II censored sample with binomial removals. Zbl 1307.62060
Singh, Sanjay Kumar; Singh, Umesh; Kumar, Manoj
2013
On finite $$p$$-groups with Abelian automorphism group. Zbl 1288.20028
Jain, Vivek K.; Rai, Pradeep K.; Yadav, Manoj K.
2013
Buckling analysis of a beam-column using multilayer perceptron neural network technique. Zbl 1293.93084
Kumar, Manoj; Yadav, Neha
2013
On finite $$p$$-groups whose automorphisms are all central. Zbl 1262.20030
Jain, Vivek K.; Yadav, Manoj K.
2012
Numerical algorithm based on quintic nonpolynomial spline for solving third-order boundary value problems associated with draining and coating flows. Zbl 1260.65068
Srivastava, Pankaj Kumar; Kumar, Manoj
2012
Class preserving automorphisms of unitriangular groups. Zbl 1256.20036
Bardakov, Valeriy; Vesnin, Andrei; Yadav, Manoj K.
2012
Phase plane analysis and traveling wave solution of third order nonlinear singular problems arising in thin film evolution. Zbl 1268.76006
Kumar, Manoj; Singh, Neelima
2012
Computer simulation of third-order nonlinear singular problems arising in draining and coating flows. Zbl 1253.76097
Kumar, Manoj; Singh, Neelima
2012
Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey. Zbl 1236.65107
Kumar, Manoj; Yadav, Neha
2011
Methods for solving singular perturbation problems arising in science and engineering. Zbl 1225.65077
Kumar, Manoj; Parul
2011
Quintic nonpolynomial spline method for the solution of a second-order boundary-value problem with engineering applications. Zbl 1231.65120
Srivastava, Pankaj Kumar; Kumar, Manoj; Mohapatra, R. N.
2011
Class preserving automorphisms of finite $$p$$-groups: a survey. Zbl 1231.20024
2011
A recent development of computer methods for solving singularly perturbed boundary value problems. Zbl 1242.34002
Kumar, Manoj; Parul
2011
Application of B-spline to numerical solution of a system of singularly perturbed problems. Zbl 1306.65235
Gupta, Yogesh; Srivastava, Pankaj Kumar; Kumar, Manoj
2011
Methods for solving singular boundary value problems using splines: a review. Zbl 1186.65104
Kumar, Manoj; Gupta, Yogesh
2010
Automorphisms of Abelian group extensions. Zbl 1209.20021
Passi, I. B. S.; Singh, Mahender; Yadav, Manoj K.
2010
Radiation effect on unsteady MHD heat and mass transfer flow on a moving inclined porous heated plate in the presence of chemical reaction. Zbl 1305.76115
Uddin, Ziya; Kumar, Manoj
2010
Simulation of a nonlinear Steklov eigenvalue problem using finite-element approximation. Zbl 1197.65179
Kumar, Prashant; Kumar, Manoj
2010
On central automorphisms fixing the center element-wise. Zbl 1187.20013
2009
A collection of computational techniques for solving singular boundary-value problems. Zbl 1159.65076
Kumar, Manoj; Singh, Neelima
2009
A boundary value approach for a class of linear singularly perturbed boundary value problems. Zbl 1159.65075
Kumar, Manoj; Mishra, Hradyesh Kumar; Singh, Peetam
2009
Computational techniques for solving differential equations by cubic, quintic, and sextic spline. Zbl 1183.65097
Kumar, Manoj; Srivastava, Pankaj Kumar
2009
Numerical treatment of singularly perturbed two point boundary value problems using initial-value method. Zbl 1177.65109
Kumar, Manoj; Mishra, Hradyesh Kumar; Singh, P.
2009
Computational method for finding various solutions for a quasilinear elliptic equation of Kirchhoff type. Zbl 1171.74044
Kumar, Manoj; Kumar, Prashant
2009
A finite element approach for finding positive solutions of semilinear elliptic Dirichlet problems. Zbl 1172.65063
Kumar, Manoj; Kumar, Prashant
2009
On automorphisms of some finite $$p$$-groups. Zbl 1148.20014
2008
Predictive performance of the improved estimators with exact restrictions in linear regression models. Zbl 1175.62022
Kumar, Manoj; Mishra, Nutan; Gupta, Rajinder
2008
Common coincidence points of $$R$$-weakly commuting fuzzy maps. Zbl 1169.47063
Saini, R. K.; Kumar, M.; Gupta, V.; Singh, S. B.
2008
An initial-value technique for singularly perturbed boundary value problems via cubic spline. Zbl 1135.65350
Kumar, Manoj; Singh, P.; Mishra, Hradyesh Kumar
2007
A recent survey on computational techniques for solving singularly perturbed boundary value problems. Zbl 1127.65053
Kumar, Manoj; Singh, Pitam; Kumar Mishra, Hradyesh
2007
Class preserving automorphisms of finite $$p$$-groups. Zbl 1129.20017
2007
On automorphisms of finite $$p$$-groups. Zbl 1131.20015
2007
Direct and inverse estimates for a new family of linear positive operators. Zbl 1111.41016
Gupta, M. K.; Gupta, Vijay; Kumar, Manoj
2007
A uniform mesh finite difference method for a class of singular two-point boundary value problems. Zbl 1103.65088
Kumar, Manoj; Aziz, Tariq
2006
Finite groups with many product conjugacy classes. Zbl 1139.20027
2006
Class of dual to ratio estimators for double sampling. Zbl 1115.62305
Kumar, Manoj; Bahl, Shashi
2006
A non-uniform mesh finite difference method and its convergence for a class of singular two-point boundary value problems. Zbl 1063.65068
Kumar, M.; Aziz, T.
2004
On automorphisms of some $$p$$-groups. Zbl 1062.20021
Kumar, Manoj; Vermani, Lekh Raj
2002
A fourth-order finite-difference method based on non-uniform mesh for a class of singular two-point boundary value problems. Zbl 0990.65086
Aziz, Tariq; Kumar, Manoj
2001
“Hasse principle” for groups of order $$p^4$$. Zbl 1008.20014
Kumar, Manoj; Vermani, Lekh Raj
2001
“Hasse principle” for extraspecial $$p$$-groups. Zbl 0995.20034
Kumar, Manoj; Vermani, Lekh Raj
2000
Estimation of finite population mean using multi-auxiliary variables. Zbl 0952.62011
Bahl, S.; Kumar, Manoj
2000
all top 5
all top 5
Cited in 110 Serials
16 Applied Mathematics and Computation 13 Analysis Mathematica 11 Communications in Algebra 11 Computers & Mathematics with Applications 10 Journal of Computational and Applied Mathematics 9 Journal of Algebra and its Applications 8 International Journal of Computer Mathematics 7 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Israel Journal of Mathematics 5 Journal of Algebra 5 Computational Mathematics and Modeling 5 Advances in Difference Equations 5 International Journal of Differential Equations 5 International Journal of Applied and Computational Mathematics 4 Abstract and Applied Analysis 4 Journal of Applied Mathematics and Computing 3 Indian Journal of Pure & Applied Mathematics 3 Monatshefte für Mathematik 3 Semigroup Forum 3 Numerical Algorithms 3 Mathematical Problems in Engineering 3 Cogent Mathematics 2 Journal of Mathematical Physics 2 Russian Mathematical Surveys 2 Archiv der Mathematik 2 Proceedings of the Japan Academy. Series A 2 Applied Numerical Mathematics 2 Applied Mathematics Letters 2 International Journal of Algebra and Computation 2 Advances in Engineering Software 2 Journal of the Egyptian Mathematical Society 2 Journal of Difference Equations and Applications 2 Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences 2 Mediterranean Journal of Mathematics 2 International Journal for Computational Methods in Engineering Science and Mechanics 2 Asian-European Journal of Mathematics 2 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie 2 International Journal of Group Theory 2 S$$\vec{\text{e}}$$MA Journal 2 Arabian Journal of Mathematics 2 Communications in Mathematics and Statistics 2 Journal of Computational and Engineering Mathematics 2 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematika. Mekhanika. Fizika 1 Bulletin of the Australian Mathematical Society 1 Computers and Fluids 1 Computer Physics Communications 1 International Journal for Numerical Methods in Fluids 1 Journal of the Franklin Institute 1 Lithuanian Mathematical Journal 1 Chaos, Solitons and Fractals 1 Advances in Mathematics 1 Calcolo 1 Computing 1 International Journal of Mathematics and Mathematical Sciences 1 Kyungpook Mathematical Journal 1 Proceedings of the American Mathematical Society 1 Quaestiones Mathematicae 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Ricerche di Matematica 1 Note di Matematica 1 Applied Mathematics and Mechanics. (English Edition) 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematica Hungarica 1 Bulletin of the Iranian Mathematical Society 1 Statistics 1 Journal of Symbolic Computation 1 Sequential Analysis 1 Mathematical and Computer Modelling 1 Journal of Scientific Computing 1 Computational Mathematics and Mathematical Physics 1 Automation and Remote Control 1 Journal of Statistical Computation and Simulation 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Computational and Applied Mathematics 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Turkish Journal of Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Journal of Mathematical Chemistry 1 European Mathematical Society Newsletter 1 Transformation Groups 1 Differential Equations and Dynamical Systems 1 Nonlinear Dynamics 1 Journal of Inequalities and Applications 1 Journal of Group Theory 1 Lobachevskii Journal of Mathematics 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Journal of the Australian Mathematical Society 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Journal of Industrial and Management Optimization 1 Statistical Methodology 1 Thailand Statistician 1 Proyecciones 1 Applications and Applied Mathematics 1 Optimization Letters 1 Mathematical Modelling of Natural Phenomena 1 Advances in High Energy Physics 1 Discrete and Continuous Dynamical Systems. Series S 1 Acta Universitatis Sapientiae. Mathematica ...and 10 more Serials
all top 5
Cited in 40 Fields
112 Numerical analysis (65-XX) 66 Group theory and generalizations (20-XX) 62 Ordinary differential equations (34-XX) 41 Partial differential equations (35-XX) 15 Fluid mechanics (76-XX) 13 Biology and other natural sciences (92-XX) 10 Statistics (62-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 8 Nonassociative rings and algebras (17-XX) 8 Approximations and expansions (41-XX) 6 Associative rings and algebras (16-XX) 6 Functional analysis (46-XX) 6 Computer science (68-XX) 5 Real functions (26-XX) 5 Systems theory; control (93-XX) 4 History and biography (01-XX) 4 Algebraic geometry (14-XX) 4 Operations research, mathematical programming (90-XX) 3 Number theory (11-XX) 3 Commutative algebra (13-XX) 3 Category theory; homological algebra (18-XX) 3 Integral equations (45-XX) 2 Sequences, series, summability (40-XX) 2 Operator theory (47-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Information and communication theory, circuits (94-XX)
Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-03-01T05:07:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4727800190448761, "perplexity": 4895.085189093016}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178361849.27/warc/CC-MAIN-20210301030155-20210301060155-00054.warc.gz"} |
https://par.nsf.gov/biblio/10024074-projected-nesterov-proximal-gradient-algorithm-sparse-signal-recovery | Projected Nesterov's Proximal-Gradient Algorithm for Sparse Signal Recovery
We develop a projected Nesterov’s proximal-gradient (PNPG) approach for sparse signal reconstruction that combines adaptive step size with Nesterov’s momentum acceleration. The objective function that we wish to minimize is the sum of a convex differentiable data-fidelity (negative log-likelihood (NLL)) term and a convex regularization term. We apply sparse signal regularization where the signal belongs to a closed convex set within the closure of the domain of the NLL; the convex-set constraint facilitates flexible NLL domains and accurate signal recovery. Signal sparsity is imposed using the ℓ₁-norm penalty on the signal’s linear transform coefficients. The PNPG approach employs a projected Nesterov’s acceleration step with restart and a duality-based inner iteration to compute the proximal mapping. We propose an adaptive step-size selection scheme to obtain a good local majorizing function of the NLL and reduce the time spent backtracking. Thanks to step-size adaptation, PNPG converges faster than the methods that do not adjust to the local curvature of the NLL. We present an integrated derivation of the momentum acceleration and proofs of O(k⁻²) objective function convergence rate and convergence of the iterates, which account for adaptive step size, inexactness of the iterative proximal mapping, and the convex-set constraint. The tuning of PNPG more »
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10024074
Journal Name:
IEEE Transactions on Signal Processing
Volume:
65
Issue:
13
Page Range or eLocation-ID:
3510-3525
ISSN:
1053-587X | 2022-08-17T21:48:27 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8358715176582336, "perplexity": 1569.1206598488034}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573118.26/warc/CC-MAIN-20220817213446-20220818003446-00315.warc.gz"} |
https://pvpmc.sandia.gov/pv-research/bifacial-pv-project/outdoor-bifacial-pv-performance-data/ | Sandia is building an outdoor bifacial PV performance test bed in Albuquerque, NM to collect data to be analyzed and shared with the community. This data will be used to develop predictive performance models that can eventually be included in commercial applications. Based on a review of literature on this topic, we designed our test facilities to be able to vary design parameters that are known to affect bifacial PV performance.
The amount of additional energy generated from the backside of a bifacial module can be analyzed by calculating the bifacial gain. Bifacial gain is measured using two modules, one bifacial and another monofacial reference module at the same orientation. Both modules should ideally have the same front-side power rating, but corrections can be made for differences in the ratings. Bifacial gain is then defined as:
$BG_{i}=&space;100\times&space;\left&space;(&space;\frac{P_{bifacial}/Pmp_{bifacial}}{P_{monofacial}/Pmp_{monofacial}}-1&space;\right&space;)$,
where $P_{bifacial}$ and $P_{monofacial}$ are the energy measured from the bifacial and monofacial arrays, respectively. $Pmp_{bifacial&space;}$ and $Pmp_{monofacial}$ are the STC power ratings from the modules measured on the front side only (with backside of bifacial module covered).
An integrated bifacial gain in energy, $BG_{E}$ (for example, one month) can be calculated as:
$BG_{E}=&space;100\times&space;\left&space;(&space;\frac{\sum&space;P_{bifacial}/Pmp_{bifacial}}{\sum&space;P_{monofacial}/Pmp_{monofacial}}-1&space;\right&space;)$. | 2017-09-21T21:22:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46975815296173096, "perplexity": 1791.7545116501087}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687906.71/warc/CC-MAIN-20170921205832-20170921225832-00421.warc.gz"} |
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_I_-_Mechanics%2C_Sound%2C_Oscillations%2C_and_Waves_(OpenStax)/14%3A_Fluid_Mechanics/14.7%3A_Viscosity_and_Turbulence | $$\require{cancel}$$
# 14.7: Viscosity and Turbulence
Skills to Develop
• Explain what viscosity is
• Calculate flow and resistance with Poiseuille's law
• Explain how pressure drops due to resistance
• Calculate the Reynolds number for an object moving through a fluid
• Use the Reynolds number for a system to determine whether it is laminar or turbulent
• Describe the conditions under which an object has a terminal speed
In Applications of Newton’s Laws, which introduced the concept of friction, we saw that an object sliding across the floor with an initial velocity and no applied force comes to rest due to the force of friction. Friction depends on the types of materials in contact and is proportional to the normal force. We also discussed drag and air resistance in that same chapter. We explained that at low speeds, the drag is proportional to the velocity, whereas at high speeds, drag is proportional to the velocity squared. In this section, we introduce the forces of friction that act on fluids in motion. For example, a fluid flowing through a pipe is subject to resistance, a type of friction, between the fluid and the walls. Friction also occurs between the different layers of fluid. These resistive forces affect the way the fluid flows through the pipe.
### Viscosity and Laminar Flow
When you pour yourself a glass of juice, the liquid flows freely and quickly. But if you pour maple syrup on your pancakes, that liquid flows slowly and sticks to the pitcher. The difference is fluid friction, both within the fluid itself and between the fluid and its surroundings. We call this property of fluids viscosity. Juice has low viscosity, whereas syrup has high viscosity.
The precise definition of viscosity is based on laminar, or nonturbulent, flow. Figure 14.34 shows schematically how laminar and turbulent flow differ. When flow is laminar, layers flow without mixing. When flow is turbulent, the layers mix, and significant velocities occur in directions other than the overall direction of flow.
Figure $$\PageIndex{1}$$: (a) Laminar flow occurs in layers without mixing. Notice that viscosity causes drag between layers as well as with the fixed surface. The speed near the bottom of the flow (vb) is less than speed near the top (vt) because in this case, the surface of the containing vessel is at the bottom. (b) An obstruction in the vessel causes turbulent flow. Turbulent flow mixes the fluid. There is more interaction, greater heating, and more resistance than in laminar flow.
Turbulence is a fluid flow in which layers mix together via eddies and swirls. It has two main causes. First, any obstruction or sharp corner, such as in a faucet, creates turbulence by imparting velocities perpendicular to the flow. Second, high speeds cause turbulence. The drag between adjacent layers of fluid and between the fluid and its surroundings can form swirls and eddies if the speed is great enough. In Figure 14.35, the speed of the accelerating smoke reaches the point that it begins to swirl due to the drag between the smoke and the surrounding air.
Figure $$\PageIndex{2}$$: Smoke rises smoothly for a while and then begins to form swirls and eddies. The smooth flow is called laminar flow, whereas the swirls and eddies typify turbulent flow. Smoke rises more rapidly when flowing smoothly than after it becomes turbulent, suggesting that turbulence poses more resistance to flow. (credit: “Creativity103”/Flickr)
Figure $$\PageIndex{3}$$: shows how viscosity is measured for a fluid. The fluid to be measured is placed between two parallel plates. The bottom plate is held fixed, while the top plate is moved to the right, dragging fluid with it. The layer (or lamina) of fluid in contact with either plate does not move relative to the plate, so the top layer moves at speed v while the bottom layer remains at rest. Each successive layer from the top down exerts a force on the one below it, trying to drag it along, producing a continuous variation in speed from v to 0 as shown. Care is taken to ensure that the flow is laminar, that is, the layers do not mix. The motion in the figure is like a continuous shearing motion. Fluids have zero shear strength, but the rate at which they are sheared is related to the same geometrical factors A and L as is shear deformation for solids. In the diagram, the fluid is initially at rest. The layer of fluid in contact with the moving plate is accelerated and starts to move due to the internal friction between moving plate and the fluid. The next layer is in contact with the moving layer; since there is internal friction between the two layers, it also accelerates, and so on through the depth of the fluid. There is also internal friction between the stationary plate and the lowest layer of fluid, next to the station plate. The force is required to keep the plate moving at a constant velocity due to the internal friction.
Figure $$\PageIndex{3}$$: Measurement of viscosity for laminar flow of fluid between two plates of area A. The bottom plate is fixed. When the top plate is pushed to the right, it drags the fluid along with it.
A force F is required to keep the top plate in Figure 14.36 moving at a constant velocity v, and experiments have shown that this force depends on four factors. First, F is directly proportional to v (until the speed is so high that turbulence occurs—then a much larger force is needed, and it has a more complicated dependence on v). Second, F is proportional to the area A of the plate. This relationship seems reasonable, since A is directly proportional to the amount of fluid being moved. Third, F is inversely proportional to the distance between the plates L. This relationship is also reasonable; L is like a lever arm, and the greater the lever arm, the less the force that is needed. Fourth, F is directly proportional to the coefficient of viscosity, $$\eta$$ The greater the viscosity, the greater the force required. These dependencies are combined into the equation
$$F = \eta \frac{vA}{L} \ldotp$$
This equation gives us a working definition of fluid viscosity $$\eta$$. Solving for $$\eta$$ gives
$$\eta = \frac{FL}{vA} \tag{14.17}$$
which defines viscosity in terms of how it is measured. The SI unit of viscosity is $$\frac{N\; \cdotp m}{[(m/s)m^{2}]}$$ = (N/m2)s or Pa • s. Table 14.4 lists the coefficients of viscosity for various fluids. Viscosity varies from one fluid to another by several orders of magnitude. As you might expect, the viscosities of gases are much less than those of liquids, and these viscosities often depend on temperature.
#### Table 14.4 - Coefficients of Viscosity of Various Fluids
Fluid Temperature (°C) Viscosity $$\eta$$ (Pa • s)
Air 0 0.0171
20 0.0181
40 0.0190
100 0.0218
Ammonia 20 0.00974
Carbon dioxide 20 0.0147
Helium 20 0.0196
Hydrogen 0 0.0090
Mercury 20 0.0450
Oxygen 20 0.0203
Steam 100 0.0130
Liquid water 0 1.792
20 1.002
37 0.6947
40 0.653
100 0.282
Whole blood 20 3.015
37 2.084
Blood plasma 20 1.810
37 1.257
Ethyl alcohol 20 1.20
Methanol 20 0.584
Oil (heavy machine) 20 660
Oil (motor, SAE 10) 30 200
Oil (olive) 20 138
Glycerin 20 1500
Honey 20 2000-10000
Maple syrup 20 2000-3000
Milk 20 3.0
Oil (corn) 20 65
### Laminar Flow Confined to Tubes: Poiseuille’s Law
What causes flow? The answer, not surprisingly, is a pressure difference. In fact, there is a very simple relationship between horizontal flow and pressure. Flow rate Q is in the direction from high to low pressure. The greater the pressure differential between two points, the greater the flow rate. This relationship can be stated as
$$Q = \frac{p_{2} - p_{1}}{R}$$
where p1 and p2 are the pressures at two points, such as at either end of a tube, and R is the resistance to flow. The resistance R includes everything, except pressure, that affects flow rate. For example, R is greater for a long tube than for a short one. The greater the viscosity of a fluid, the greater the value of R. Turbulence greatly increases R, whereas increasing the diameter of a tube decreases R.
If viscosity is zero, the fluid is frictionless and the resistance to flow is also zero. Comparing frictionless flow in a tube to viscous flow, as in Figure 14.37, we see that for a viscous fluid, speed is greatest at midstream because of drag at the boundaries. We can see the effect of viscosity in a Bunsen burner flame [part (c)], even though the viscosity of natural gas is small.
Figure $$\PageIndex{4}$$: (a) If fluid flow in a tube has negligible resistance, the speed is the same all across the tube. (b) When a viscous fluid flows through a tube, its speed at the walls is zero, increasing steadily to its maximum at the center of the tube. (c) The shape of a Bunsen burner flame is due to the velocity profile across the tube. (credit c: modification of work by Jason Woodhead)
The resistance R to laminar flow of an incompressible fluid with viscosity $$\eta$$ through a horizontal tube of uniform radius r and length l, is given by
$$R = \frac{8 \eta l}{\pi r^{4}} \ldotp \tag{14.18}$$
This equation is called Poiseuille’s law for resistance, named after the French scientist J. L. Poiseuille (1799–1869), who derived it in an attempt to understand the flow of blood through the body.
Let us examine Poiseuille’s expression for R to see if it makes good intuitive sense. We see that resistance is directly proportional to both fluid viscosity $$\eta$$ and the length l of a tube. After all, both of these directly affect the amount of friction encountered—the greater either is, the greater the resistance and the smaller the flow. The radius r of a tube affects the resistance, which again makes sense, because the greater the radius, the greater the flow (all other factors remaining the same). But it is surprising that r is raised to the fourth power in Poiseuille’s law. This exponent means that any change in the radius of a tube has a very large effect on resistance. For example, doubling the radius of a tube decreases resistance by a factor of 24 = 16.
Taken together $$Q = \frac{p_{2} - p_{1}}{R}$$ and $$R = \frac{8 \eta l}{\pi r^{4}}$$ give the following expression for flow rate:
$$Q = \frac{(p_{2} - p_{1}) \pi r^{4}}{8 \eta l} \ldotp \tag{14.19}$$
This equation describes laminar flow through a tube. It is sometimes called Poiseuille’s law for laminar flow, or simply Poiseuille’s law (Figure 14.38).
Figure $$\PageIndex{5}$$: Poiseuille’s law applies to laminar flow of an incompressible fluid of viscosity η through a tube of length l and radius r. The direction of flow is from greater to lower pressure. Flow rate Q is directly proportional to the pressure difference p2 − p1, and inversely proportional to the length l of the tube and viscosity $$\eta$$ of the fluid. Flow rate increases with radius by a factor of r4.
Example 14.8
##### Using Flow Rate: Air Conditioning Systems
An air conditioning system is being designed to supply air at a gauge pressure of 0.054 Pa at a temperature of 20 °C. The air is sent through an insulated, round conduit with a diameter of 18.00 cm. The conduit is 20-meters long and is open to a room at atmospheric pressure 101.30 kPa. The room has a length of 12 meters, a width of 6 meters, and a height of 3 meters. (a) What is the volume flow rate through the pipe, assuming laminar flow? (b) Estimate the length of time to completely replace the air in the room. (c) The builders decide to save money by using a conduit with a diameter of 9.00 cm. What is the new flow rate?
##### Strategy
Assuming laminar flow, Poiseuille’s law states that
$$Q = \frac{(p_{2} - p_{1}) \pi r^{4}}{8 \eta l} = \frac{dV}{dt} \ldotp$$
We need to compare the artery radius before and after the flow rate reduction. Note that we are given the diameter of the conduit, so we must divide by two to get the radius.
##### Solution
1. Assuming a constant pressure difference and using the viscosity $$\eta = 0.0181\; mPa\; \cdotp s$$, $$Q = \frac{(0.054\; Pa)(3.14)(0.09\; m)^{4}}{8(0.0181 \times 10^{-3}\; Pa\; \cdotp s)(20\; m)} = 3.84 \times 10^{-3}\; m^{3}/s \ldotp$$
2. Assuming constant flow $$Q = \frac{dV}{dt} \approx \frac{\Delta V}{\Delta t}$$ $$\Delta t = \frac{\Delta V}{Q} = \frac{(12\; m)(6\; m)(3\; m)}{3.84 \times 10^{-3}\; m^{3}/s} = 5.63 \times 10^{4}\; s = 15.63\; hr \ldotp$$
3. Using laminar flow, Poiseuille’s law yields $$Q = \frac{(0.054\; Pa)(3.14)(0.045\; m){4}}{8(0.0181 \times 10^{-3}\; Pa\; \cdotp s)(20\; m)} = 22.40 \times 10^{-4}\; m^{3}/s \ldotp$$Thus, the radius of the conduit decreases by half reduces the flow rate to 6.25% of the original value.
##### Significance
In general, assuming laminar flow, decreasing the radius has a more dramatic effect than changing the length. If the length is increased and all other variables remain constant, the flow rate is decreased:
$$\begin{split} \frac{Q_{A}}{Q_{B}} & = \frac{\frac{(p_{2} - p_{1}) \pi r_{A}^{4}}{8 \eta l_{A}}}{\frac{(p_{2} - p_{1}) \pi r_{B}^{4}}{8 \eta l_{B}}} = \frac{l_{B}}{l_{A}} \\ Q_{B} & = \frac{l_{A}}{l_{B}} Q_{A} \ldotp \end{split}$$
Doubling the length cuts the flow rate to one-half the original flow rate.
If the radius is decreased and all other variables remain constant, the volume flow rate decreases by a much larger factor.
$$\begin{split} \frac{Q_{A}}{Q_{B}} & = \frac{\frac{(p_{2} - p_{1}) \pi r_{A}^{4}}{8 \eta l_{A}}}{\frac{(p_{2} - p_{1}) \pi r_{B}^{4}}{8 \eta l_{B}}} = \left(\dfrac{r_{A}}{r_{B}}\right)^{4} \\ Q_{B} & = \left(\dfrac{r_{B}}{r_{A}}\right)^{4} Q_{A} \end{split}$$
Cutting the radius in half decreases the flow rate to one-sixteenth the original flow rate.
### Flow and Resistance as Causes of Pressure Drops
Water pressure in homes is sometimes lower than normal during times of heavy use, such as hot summer days. The drop in pressure occurs in the water main before it reaches individual homes. Let us consider flow through the water main as illustrated in Figure 14.39. We can understand why the pressure p1 to the home drops during times of heavy use by rearranging the equation for flow rate:
$$\begin{split} Q & = \frac{p_{2} - p_{1}}{R} \\ p_{2} - p_{1} & = RQ \ldotp \end{split}$$
In this case, p2 is the pressure at the water works and R is the resistance of the water main. During times of heavy use, the flow rate Q is large. This means that p2 − p1 must also be large. Thus p1 must decrease. It is correct to think of flow and resistance as causing the pressure to drop from p2 to p1. The equation p2 − p1 = RQ is valid for both laminar and turbulent flows.
Figure $$\PageIndex{6}$$: During times of heavy use, there is a significant pressure drop in a water main, and p1 supplied to users is significantly less than p2 created at the water works. If the flow is very small, then the pressure drop is negligible, and p2 ≈ p1.
We can also use p2 − p1 = RQ to analyze pressure drops occurring in more complex systems in which the tube radius is not the same everywhere. Resistance is much greater in narrow places, such as in an obstructed coronary artery. For a given flow rate Q, the pressure drop is greatest where the tube is most narrow. This is how water faucets control flow. Additionally, R is greatly increased by turbulence, and a constriction that creates turbulence greatly reduces the pressure downstream. Plaque in an artery reduces pressure and hence flow, both by its resistance and by the turbulence it creates.
### Measuring Turbulence
An indicator called the Reynolds number NR can reveal whether flow is laminar or turbulent. For flow in a tube of uniform diameter, the Reynolds number is defined as
$$N_{R} = \frac{2 \rho vr}{\eta}\; (flow\; in\; tube) \tag{14.20}$$
where $$\rho$$ is the fluid density, v its speed, $$\eta$$ its viscosity, and r the tube radius. The Reynolds number is a dimensionless quantity. Experiments have revealed that NR is related to the onset of turbulence. For NR below about 2000, flow is laminar. For NR above about 3000, flow is turbulent.
For values of NR between about 2000 and 3000, flow is unstable—that is, it can be laminar, but small obstructions and surface roughness can make it turbulent, and it may oscillate randomly between being laminar and turbulent. In fact, the flow of a fluid with a Reynolds number between 2000 and 3000 is a good example of chaotic behavior. A system is defined to be chaotic when its behavior is so sensitive to some factor that it is extremely difficult to predict. It is difficult, but not impossible, to predict whether flow is turbulent or not when a fluid’s Reynold’s number falls in this range due to extremely sensitive dependence on factors like roughness and obstructions on the nature of the flow. A tiny variation in one factor has an exaggerated (or nonlinear) effect on the flow.
Example 14.9
##### Using Flow Rate: Turbulent Flow or Laminar Flow
In Example 14.8, we found the volume flow rate of an air conditioning system to be Q = 3.84 x 10−3 m3/s. This calculation assumed laminar flow. (a) Was this a good assumption? (b) At what velocity would the flow become turbulent?
##### Strategy
To determine if the flow of air through the air conditioning system is laminar, we first need to find the velocity, which can be found by
$$Q = Av = \pi r^{2} v \ldotp$$
Then we can calculate the Reynold’s number, using the equation below, and determine if it falls in the range for laminar flow
$$R = \frac{2 \rho vr}{\eta} \ldotp$$
##### Solution
1. Using the values given: $$\begin{split} v & = \frac{Q}{\pi r^{2}} = \frac{3.84 \times 10^{-3}\; m^{3}/s}{3.14 (0.09\; m)^{2}} = 0.15\; m/s \\ R & = \frac{2 \rho vr}{\eta} = \frac{2 (1.23\; kg/m^{3})(0.15\; m/s)(0.09\; m)}{0.0181 \times 10^{-3}\; Pa\; \cdotp s} = 1835 \ldotp \end{split}$$Since the Reynolds number is 1835 < 2000, the flow is laminar and not turbulent. The assumption that the flow was laminar is valid.
2. To find the maximum speed of the air to keep the flow laminar, consider the Reynold’s number. $$\begin{split} R & = \frac{2 \rho vr}{\eta} \leq 2000 \\ v & = \frac{2000(0.0181 \times 10^{-3}\; Pa\; \cdotp s)}{2(1.23\; kg/m^{3})(0.09\; m)} = 0.16\; m/s \ldotp \end{split}$$
##### Significance
When transferring a fluid from one point to another, it desirable to limit turbulence. Turbulence results in wasted energy, as some of the energy intended to move the fluid is dissipated when eddies are formed. In this case, the air conditioning system will become less efficient once the velocity exceeds 0.16 m/s, since this is the point at which turbulence will begin to occur.
### Contributors
• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2019-01-16T15:13:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.730268120765686, "perplexity": 606.8858390868503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583657510.42/warc/CC-MAIN-20190116134421-20190116160421-00402.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Agillespie.james | # zbMATH — the first resource for mathematics
## Gillespie, James
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Author ID: gillespie.james Published as: Gillespie, James Homepage: https://phobos.ramapo.edu/~jgillesp/ External Links: MGP · Wikidata
Documents Indexed: 25 Publications since 2004 Reviewing Activity: 1 Review
#### Co-Authors
20 single-authored 2 Estrada, Sergio 1 Bravo, Daniel 1 Hovey, Mark A. 1 Odabaşı, Sinem
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#### Serials
3 Communications in Algebra 3 Journal of Pure and Applied Algebra 3 Homology, Homotopy and Applications 2 Transactions of the American Mathematical Society 2 Journal of Homotopy and Related Structures 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Bulletin of the London Mathematical Society 1 Fundamenta Mathematicae 1 Journal of Algebra 1 Mathematische Zeitschrift 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Frontiers of Mathematics in China
#### Fields
22 Category theory; homological algebra (18-XX) 14 Algebraic topology (55-XX) 5 Associative rings and algebras (16-XX) 2 Algebraic geometry (14-XX) 1 Commutative algebra (13-XX)
#### Citations contained in zbMATH
24 Publications have been cited 407 times in 181 Documents Cited by Year
The flat model structure on $$\mathbf{Ch}(R)$$. Zbl 1056.55011
Gillespie, James
2004
Model structures on modules over Ding-Chen rings. Zbl 1231.16005
Gillespie, James
2010
Kaplansky classes and derived categories. Zbl 1134.55016
Gillespie, James
2007
Model structures on exact categories. Zbl 1315.18019
Gillespie, James
2011
Cotorsion pairs and degreewise homological model structures. Zbl 1140.18011
Gillespie, James
2008
Gorenstein complexes and recollements from cotorsion pairs. Zbl 1343.18013
Gillespie, James
2016
The flat model structure on complexes of sheaves. Zbl 1094.55016
Gillespie, James
2006
Gorenstein model structures and generalized derived categories. Zbl 1230.18008
Gillespie, James; Hovey, Mark
2010
Absolutely clean, level, and Gorenstein AC-injective complexes. Zbl 1346.18021
Bravo, Daniel; Gillespie, James
2016
How to construct a Hovey triple from two cotorsion pairs. Zbl 1316.18012
Gillespie, James
2015
Hereditary abelian model categories. Zbl 1372.18001
Gillespie, James
2016
On Ding injective, Ding projective and Ding flat modules and complexes. Zbl 1443.16006
Gillespie, James
2017
The flat stable module category of a coherent ring. Zbl 1392.16012
Gillespie, James
2017
Exact model structures and recollements. Zbl 1386.18041
Gillespie, James
2016
The derived category with respect to a generator. Zbl 1342.18021
Gillespie, James
2016
The homotopy category of $$N$$-complexes is a homotopy category. Zbl 1310.18006
Gillespie, James
2015
The projective stable category of a coherent scheme. Zbl 1423.18053
2019
Models for homotopy categories of injectives and Gorenstein injectives. Zbl 1373.18007
Gillespie, James
2017
Pure exact structures and the pure derived category of a scheme. Zbl 1396.18006
Estrada, Sergio; Gillespie, James; Odabaşi, Sinem
2017
Models for mock homotopy categories of projectives. Zbl 1346.14041
Gillespie, James
2016
Duality pairs and stable module categories. Zbl 1409.13034
Gillespie, James
2019
AC-Gorenstein rings and their stable module categories. Zbl 1437.16010
Gillespie, James
2019
On the homotopy category of AC-injective complexes. Zbl 1397.18035
Gillespie, James
2017
Gorenstein AC-projective complexes. Zbl 1408.18034
Gillespie, James
2018
The projective stable category of a coherent scheme. Zbl 1423.18053
2019
Duality pairs and stable module categories. Zbl 1409.13034
Gillespie, James
2019
AC-Gorenstein rings and their stable module categories. Zbl 1437.16010
Gillespie, James
2019
Gorenstein AC-projective complexes. Zbl 1408.18034
Gillespie, James
2018
On Ding injective, Ding projective and Ding flat modules and complexes. Zbl 1443.16006
Gillespie, James
2017
The flat stable module category of a coherent ring. Zbl 1392.16012
Gillespie, James
2017
Models for homotopy categories of injectives and Gorenstein injectives. Zbl 1373.18007
Gillespie, James
2017
Pure exact structures and the pure derived category of a scheme. Zbl 1396.18006
Estrada, Sergio; Gillespie, James; Odabaşi, Sinem
2017
On the homotopy category of AC-injective complexes. Zbl 1397.18035
Gillespie, James
2017
Gorenstein complexes and recollements from cotorsion pairs. Zbl 1343.18013
Gillespie, James
2016
Absolutely clean, level, and Gorenstein AC-injective complexes. Zbl 1346.18021
Bravo, Daniel; Gillespie, James
2016
Hereditary abelian model categories. Zbl 1372.18001
Gillespie, James
2016
Exact model structures and recollements. Zbl 1386.18041
Gillespie, James
2016
The derived category with respect to a generator. Zbl 1342.18021
Gillespie, James
2016
Models for mock homotopy categories of projectives. Zbl 1346.14041
Gillespie, James
2016
How to construct a Hovey triple from two cotorsion pairs. Zbl 1316.18012
Gillespie, James
2015
The homotopy category of $$N$$-complexes is a homotopy category. Zbl 1310.18006
Gillespie, James
2015
Model structures on exact categories. Zbl 1315.18019
Gillespie, James
2011
Model structures on modules over Ding-Chen rings. Zbl 1231.16005
Gillespie, James
2010
Gorenstein model structures and generalized derived categories. Zbl 1230.18008
Gillespie, James; Hovey, Mark
2010
Cotorsion pairs and degreewise homological model structures. Zbl 1140.18011
Gillespie, James
2008
Kaplansky classes and derived categories. Zbl 1134.55016
Gillespie, James
2007
The flat model structure on complexes of sheaves. Zbl 1094.55016
Gillespie, James
2006
The flat model structure on $$\mathbf{Ch}(R)$$. Zbl 1056.55011
Gillespie, James
2004
all top 5
#### Cited by 132 Authors
29 Liu, Zhong-kui 19 Gillespie, James 17 Estrada, Sergio 16 Yang, Gang 14 Liang, Li 14 Yang, Xiaoyan 11 Di, Zhenxing 8 Šťovíček, Jan 7 Ding, Nanqing 7 Hu, Jiangsheng 7 Lu, Bo 6 Hafezi, Rasool 6 Iacob, Alina C. 6 Wang, Zhanping 6 Zhang, Xiaoxiang 5 Chen, Wenjing 5 Guil Asensio, Pedro A. 5 Odabaşı, Sinem 5 Pérez, Marco A. 4 Asadollahi, Javad J. 4 Bahiraei, Payam 4 Bazzoni, Silvana 4 Geng, Yuxian 4 Ren, Wei 4 Thompson, Peder 4 Trlifaj, Jan jun. 4 Winther Christensen, Lars 4 Xu, Aimin 3 Gao, Zenghui 3 Holm, Henrik 3 Huang, Zhaoyong 3 Li, Zhiwei 3 Positselski, Leonid Efimovich 3 Torrecillas Jover, Blas 3 Wang, Junpeng 3 Yang, Chunhua 3 Zhao, Tiwei 2 Alonso Tarrío, Leovigildo M. 2 Becerril, Víctor 2 Chen, Jianlong 2 Cortés-Izurdiaga, Manuel 2 Dalezios, Georgios 2 Di Brino, Gennaro 2 Enochs, Edgar E. 2 Fu, Xianhui 2 Groth, Moritz 2 Hosseini, Esmaeil 2 Jeremías López, Ana 2 Jørgensen, Peter Bjørn 2 Mao, Lixin 2 Mendoza, Octavio 2 Pérez Rodríguez, Marta 2 Pištalo, Damjan 2 Poncin, Norbert 2 Prest, Mike 2 Ren, Wei 2 Santiago, Valente 2 Šaroch, Jan 2 Vahed, Razieh 2 Vale Gonsalves, María J. 2 Virili, Simone 2 Zhang, Chunxia 2 Zhang, Dongdong 2 Zhao, Renyu 2 Zhongkui, Liu 2 Zhu, Haiyan 1 Asgharzadeh, Mohsen 1 Bahlekeh, Abdolnaser 1 Becker, Hanno 1 Bravo, Daniel 1 Bravo, Diego 1 Cheng, Haixia 1 Crivei, Septimiu 1 Da, Xuanshang 1 Dehghanpour, Tahereh 1 Divaani-Aazar, Kamran 1 Du, Ruijuan 1 Eshraghi, Hossein 1 Hassoun, Souheila 1 Herbera, Dolors 1 Herzog, Ivo 1 Hörmann, Fritz 1 Hovey, Mark A. 1 Hu, Kui 1 Jenda, Overtoun M. G. 1 Jiang, Qinghua 1 Li, Yunxia 1 Liang, Li 1 Lim, Jung Wook 1 Liu, Haiyu 1 Liu, Yifu 1 Liu, Yu 1 Makkai, Michael 1 Nakamura, Tsutomu 1 Nakaoka, Hiroyuki 1 Neeman, Amnon 1 Nematbakhsh, Ali 1 Nuiten, Joost Jakob 1 Peng, Jie 1 Rada, Juan ...and 32 more Authors
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#### Cited in 47 Serials
35 Communications in Algebra 17 Journal of Algebra and its Applications 15 Journal of Algebra 14 Journal of Pure and Applied Algebra 12 Advances in Mathematics 6 Glasgow Mathematical Journal 5 Algebra Colloquium 5 Acta Mathematica Sinica. English Series 5 Journal of Homotopy and Related Structures 4 Rocky Mountain Journal of Mathematics 4 Proceedings of the American Mathematical Society 4 Frontiers of Mathematics in China 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Rendiconti del Seminario Matematico della Università di Padova 3 Bulletin of the Iranian Mathematical Society 3 Selecta Mathematica. New Series 3 Journal of the Australian Mathematical Society 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Quaestiones Mathematicae 2 Transactions of the American Mathematical Society 2 Bulletin of the Korean Mathematical Society 2 Forum Mathematicum 2 Applied Categorical Structures 2 Turkish Journal of Mathematics 1 Bulletin of the Australian Mathematical Society 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Fundamenta Mathematicae 1 Journal of the Korean Mathematical Society 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Chinese Annals of Mathematics. Series B 1 Applied Mathematics. Series B (English Edition) 1 Vietnam Journal of Mathematics 1 Taiwanese Journal of Mathematics 1 Algebras and Representation Theory 1 Annals of Mathematics. Second Series 1 Communications of the Korean Mathematical Society 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Mediterranean Journal of Mathematics 1 Science China. Mathematics 1 Kyoto Journal of Mathematics 1 Arabian Journal of Mathematics
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#### Cited in 10 Fields
151 Category theory; homological algebra (18-XX) 100 Associative rings and algebras (16-XX) 40 Algebraic topology (55-XX) 22 Commutative algebra (13-XX) 11 Algebraic geometry (14-XX) 3 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-01-26T03:36:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31005677580833435, "perplexity": 7985.101746026001}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704795033.65/warc/CC-MAIN-20210126011645-20210126041645-00050.warc.gz"} |
https://par.nsf.gov/biblio/10078500-power-shared-randomness-uncertain-communication | The Power of Shared Randomness in Uncertain Communication
In a recent work (Ghazi et al., SODA 2016), the authors with Komargodski and Kothari initiated the study of communication with contextual uncertainty, a setup aiming to understand how efficient communication is possible when the communicating parties imperfectly share a huge context. In this setting, Alice is given a function f and an input string x, and Bob is given a function g and an input string y. The pair (x,y) comes from a known distribution mu and f and g are guaranteed to be close under this distribution. Alice and Bob wish to compute g(x,y) with high probability. The lack of agreement between Alice and Bob on the function that is being computed captures the uncertainty in the context. The previous work showed that any problem with one-way communication complexity k in the standard model (i.e., without uncertainty, in other words, under the promise that f=g) has public-coin communication at most O(k(1+I)) bits in the uncertain case, where I is the mutual information between x and y. Moreover, a lower bound of Omega(sqrt{I}) bits on the public-coin uncertain communication was also shown. However, an important question that was left open is related to the power that public randomness brings to more »
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10078500
Journal Name:
44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)
ISSN:
1868-8969
3. Abstract The production of $$\pi ^{\pm }$$ π ± , $$\mathrm{K}^{\pm }$$ K ± , $$\mathrm{K}^{0}_{S}$$ K S 0 , $$\mathrm{K}^{*}(892)^{0}$$ K ∗ ( 892 ) 0 , $$\mathrm{p}$$ p , $$\phi (1020)$$ ϕ ( 1020 ) , $$\Lambda$$ Λ , $$\Xi ^{-}$$ Ξ - , $$\Omega ^{-}$$ Ω - , and their antiparticles was measured in inelastic proton–proton (pp) collisions at a center-of-mass energy of $$\sqrt{s}$$ s = 13 TeV at midrapidity ( $$|y|<0.5$$ | y | < 0.5 ) as a function of transverse momentum ( $$p_{\mathrm{T}}$$ p T ) using the ALICE detector at the CERN LHC. Furthermore, the single-particle $$p_{\mathrm{T}}$$ p T distributions of $$\mathrm{K}^{0}_{S}$$ K S 0 , $$\Lambda$$ Λ , and $$\overline{\Lambda }$$ Λ ¯ in inelastic pp collisions at $$\sqrt{s} = 7$$ s = 7 TeV are reported here for the first time. The $$p_{\mathrm{T}}$$ p T distributions are studied at midrapidity within the transverse momentum range $$0\le p_{\mathrm{T}}\le 20$$ 0 ≤ p T ≤ 20 GeV/ c , depending on the particle species. The $$p_{\mathrm{T}}$$ p T spectra, integrated yields, and particle yield ratios are discussed as a function of collision energy and compared with measurements at lower $$\sqrt{s}$$ smore » | 2022-12-10T02:59:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7870809435844421, "perplexity": 791.3894852105545}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711637.64/warc/CC-MAIN-20221210005738-20221210035738-00818.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Aloday.jean-louis | ## Loday, Jean-Louis
Compute Distance To:
Author ID: loday.jean-louis Published as: Loday, Jean-Louis; Loday, J.-L.; Zinbiel, G. W.; Loday, J. L. Homepage: http://www-irma.u-strasbg.fr/~loday/ External Links: MacTutor · MGP · Wikidata · GND · IdRef · theses.fr
Documents Indexed: 83 Publications since 1971, including 5 Books 5 Contributions as Editor · 1 Further Contribution Biographic References: 2 Publications Co-Authors: 40 Co-Authors with 39 Joint Publications 1,051 Co-Co-Authors
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### Co-Authors
47 single-authored 9 Ronco, María Ofelia 4 Pirashvili, Teimuraz 3 Brown, Ronald 3 Popov, Todor 2 Kassel, Christian 2 Procesi, Claudio 2 Quillen, Daniel Gray 2 Vallette, Bruno 1 Aguiar, Marcelo 1 Atiyah, Michael Francis 1 Bai, Chengming 1 Bass, Hyman 1 Bergeron, Nantel 1 Brown, Ken 1 Casas Miras, José Manuel 1 Chapoton, Frédéric 1 Cuntz, Joachim 1 Dokas, Ioannis 1 Duflot, Jeanne 1 Fiedorowicz, Zbigniew 1 Frabetti, Alessandra 1 Friedlander, Eric Mark 1 Gillet, Henri A. 1 Goichot, François 1 Grayson, Daniel Richard 1 Guin-Walery, Dominique 1 Guo, Li 1 Holtkamp, Ralf 1 Latschev, Janko 1 Lluis-Puebla, Emilio 1 Mazur, Barry 1 Nikolov, Nikolay M. 1 Quillen, Jean 1 Ranicki, Andrew Alexander 1 Schappacher, Norbert 1 Segal, Graeme B. 1 Snaith, Victor Percy 1 Soulé, Christophe 1 Stasheff, James D. 1 Stein, Michael R. 1 Sullivan, Dennis Parnell 1 Tillmann, Ulrike 1 Voronov, Alexander A.
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### Serials
5 Comptes Rendus de l’Académie des Sciences. Série I 3 Advances in Mathematics 3 Journal of Algebra 3 Georgian Mathematical Journal 3 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 3 Grundlehren der Mathematischen Wissenschaften 2 Annales de l’Institut Fourier 2 Journal of Pure and Applied Algebra 2 Journal of Algebraic Combinatorics 2 Astérisque 2 Lecture Notes in Mathematics 1 Communications in Algebra 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Archiv der Mathematik 1 Commentarii Mathematici Helvetici 1 Inventiones Mathematicae 1 Journal of Combinatorial Theory. Series A 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematica Scandinavica 1 Mathematische Zeitschrift 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Topology 1 Transactions of the American Mathematical Society 1 Bulgarian Journal of Physics 1 $$K$$-Theory 1 Forum Mathematicum 1 L’Enseignement Mathématique. 2e Série 1 Expositiones Mathematicae 1 Notices of the American Mathematical Society 1 Documenta Mathematica 1 Séminaire Lotharingien de Combinatoire 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 International Journal of Geometric Methods in Modern Physics 1 Bulletin of the American Mathematical Society 1 Contemporary Mathematics 1 Séminaires et Congrès 1 Nankai Series in Pure, Applied Mathematics and Theoretical Physics 1 Journal of $$K$$-Theory
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### Fields
56 Category theory; homological algebra (18-XX) 38 Nonassociative rings and algebras (17-XX) 30 Associative rings and algebras (16-XX) 30 Algebraic topology (55-XX) 14 $$K$$-theory (19-XX) 9 Group theory and generalizations (20-XX) 9 Manifolds and cell complexes (57-XX) 8 Combinatorics (05-XX) 5 General and overarching topics; collections (00-XX) 5 Quantum theory (81-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Commutative algebra (13-XX) 3 Algebraic geometry (14-XX) 3 Convex and discrete geometry (52-XX) 2 History and biography (01-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 1 General algebraic systems (08-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Computer science (68-XX)
### Citations contained in zbMATH Open
76 Publications have been cited 3,212 times in 2,157 Documents Cited by Year
Loday, Jean-Louis; Vallette, Bruno
2012
A noncommutative version of Lie algebras: Leibniz algebras. (Une version non commutative des algèbres de Lie: les algèbres de Leibniz.) Zbl 0806.55009
Loday, Jean-Louis
1993
Universal enveloping algebras of Leibniz algebras and (co)homology. Zbl 0821.17022
Loday, Jean-Louis; Pirashvili, Teimuraz
1993
Cyclic homology. Zbl 0780.18009
Loday, Jean-Louis
1992
Cyclic homology. 2nd ed. Zbl 0885.18007
Loday, Jean-Louis
1998
Van Kampen theorems for diagrams of spaces. Zbl 0622.55009
Brown, Ronald; Loday, Jean-Louis
1987
Cyclic homology and the Lie algebra homology of matrices. Zbl 0565.17006
Loday, Jean-Louis; Quillen, Daniel
1984
Hopf algebra of the planar binary trees. Zbl 0926.16032
Loday, Jean-Louis; Ronco, María O.
1998
Spaces with finitely many non-trivial homotopy groups. Zbl 0491.55004
Loday, Jean-Louis
1982
Dialgebras. Zbl 0999.17002
Loday, Jean-Louis
2001
Trialgebras and families of polytopes. Zbl 1065.18007
Loday, Jean-Louis; Ronco, María
2004
Central extensions of Lie algebras. (Extensions centrales d’algèbres de Lie.) Zbl 0485.17006
Kassel, Christian; Loday, Jean-Louis
1982
Opérations sur l’homologie cyclique des algèbres commutatives. (Operations on the cyclic homology of commutative algebras). Zbl 0686.18006
Loday, Jean-Louis
1989
Cup-product for Leibniz cohomology and dual Leibniz algebras. Zbl 0859.17015
Loday, Jean-Louis
1995
Cohomologie et groupe de Steinberg rélatifs. Zbl 0391.20040
Loday, Jean-Louis
1978
K-théorie algébrique et représentations de groupes. Zbl 0362.18014
Loday, Jean-Louis
1976
Realization of the Stasheff polytope. Zbl 1059.52017
Loday, Jean-Louis
2004
On the structure of cofree Hopf algebras. Zbl 1096.16019
Loday, Jean-Louis; Ronco, María
2006
Dialgebras and related operads. Zbl 0970.00010
2001
Order structure on the algebra of permutations and of planar binary trees. Zbl 0998.05013
Loday, Jean-Louis; Ronco, María O.
2002
Leibniz $$n$$-algebras. Zbl 1037.17002
Casas, J. M.; Loday, J.-L.; Pirashvili, T.
2002
Generalized bialgebras and triples of operads. Zbl 1178.18001
Loday, Jean-Louis
2008
Crossed simplicial groups and their associated homology. Zbl 0755.18005
Fiedorowicz, Zbigniew; Loday, Jean-Louis
1991
Aguiar, Marcelo; Loday, Jean-Louis
2004
Excision homotopique en basse dimension. (Homotopical excision in low dimension). Zbl 0573.55011
Brown, Ronald; Loday, Jean-Louis
1984
Cyclic homology and lambda operations. Zbl 0719.19002
Loday, J.-L.; Procesi, C.
1989
Leibniz representations of Lie algebras. Zbl 0855.17018
Loday, Jean-Louis; Pirashvili, Teimuraz
1996
Combinatorial Hopf algebras. Zbl 1217.16033
Loday, Jean-Louis; Ronco, María
2010
Arithmetree. Zbl 1063.16044
Loday, Jean-Louis
2002
On the algebra of quasi-shuffles. Zbl 1126.16029
Loday, Jean-Louis
2007
Homologies diédrale et quaternionique. (Dihedral and quaternionic homology). Zbl 0627.18006
Loday, Jean-Louis
1987
Encyclopedia of types of algebras 2010. Zbl 1351.17001
Zinbiel, G. W.
2012
Algebras with two associative operations (dialgebras). (Algèbres ayant deux opérations associatives (digèbres).) Zbl 0845.16036
Loday, Jean-Louis
1995
Homotopical excision, and Hurewicz theorems, for n-cubes of spaces. Zbl 0584.55012
Brown, Ronald; Loday, Jean-Louis
1987
Cofree Hopf algebras. (Algèbres de Hopf colibres.) Zbl 1060.16039
Loday, Jean-Louis; Ronco, María
2003
Obstruction à l’excision en K-théorie algébrique. Zbl 0461.18007
Guin-Walery, Dominique; Loday, Jean-Louis
1981
The tensor category of linear maps and Leibniz algebras. Zbl 0909.18003
Loday, J. L.; Pirashvili, T.
1998
Splitting associativity and Hopf algebras. (Scindement d’associativité et algèbres de Hopf.) Zbl 1073.16032
Loday, Jean-Louis
2004
Homology of symplectic and orthogonal algebras. Zbl 0716.17019
Loday, Jean-Louis; Procesi, Claudio
1988
On the operad of associative algebras with derivation. Zbl 1237.18007
Loday, Jean-Louis
2010
Loday, Jean-Louis
1996
Hausdorff series, Eulerian idempotents and Hopf algebras. (Série de Hausdorff, idempotents eulériens et algèbres de Hopf.) Zbl 0807.17003
Loday, Jean-Louis
1994
Overview on Leibniz algebras, dialgebras and their homology. Zbl 0893.17001
Loday, Jean-Louis
1997
Algebraic $$K$$-theory and the conjectural Leibniz $$K$$-theory. Zbl 1048.18005
Loday, Jean-Louis
2003
The diagonal of the Stasheff polytope. Zbl 1220.18007
Loday, Jean-Louis
2011
Künneth-style formula for the homology of Leibniz algebras. Zbl 0880.17001
Loday, Jean-Louis
1996
Homotopical syzygies. Zbl 0978.20022
Loday, Jean-Louis
2000
The symmetric operation in a free pre-Lie algebra is magmatic. Zbl 1264.17001
Bergeron, Nantel; Loday, Jean-Louis
2011
Symboles en K-théorie algébrique supérieure. Zbl 0493.18006
Loday, Jean-Louis
1981
Parking functions and triangulation of the associahedron. Zbl 1130.52006
Loday, Jean-Louis
2007
Parastatistics algebra, Young tableaux and the super plactic monoid. Zbl 1165.81029
Loday, Jean-Louis; Popov, Todor
2008
Cyclic homology, a survey. Zbl 0637.16013
Loday, Jean-Louis
1986
Partition eulérienne et opérations en homologie cyclique. (Eulerian partition and operations in cyclic homology). Zbl 0669.13006
Loday, Jean-Louis
1988
On restricted Leibniz algebras. Zbl 1162.17001
Dokas, Ioannis; Loday, Jean-Louis
2006
Higher Witt groups: A survey. Zbl 0356.18016
Loday, J.-L.
1976
Algebraic $$K$$-theory and cyclic homology. Zbl 1286.19004
Loday, Jean-Louis
2013
Comparaison des homologies du groupe linéaire et de son algèbre de Lie. (Comparison of homologies of a linear group and its Lie algebra). Zbl 0619.20025
Loday, Jean-Louis
1987
Operads: Proceedings of renaissance conferences. Special session and international conference on moduli spaces, operads, and representation theory/operads and homotopy algebra, March 1995/May–June 1995, Hartford, CT, USA/Luminy, France. Zbl 0855.00018
1997
Completing the operadic butterfly. Zbl 1187.18005
Loday, Jean-Louis
2006
Free loop space and homology. Zbl 1386.55011
Loday, Jean-Louis
2015
Cyclic homology and homology of the Lie algebra of matrices. (Homologie cyclique et homologie de l’algèbre de Lie des matrices.) Zbl 0536.17006
Loday, Jean-Louis; Quillen, Daniel
1983
A duality between standard simplices and Stasheff polytopes. (Une dualité entre simplexes standards et polytopes de Stasheff.) Zbl 1010.18007
Loday, Jean-Louis; Ronco, María O.
2001
Higher Whitehead groups and stable homotopy. Zbl 0337.55015
Loday, Jean-Louis
1976
Coassociative magmatic bialgebras and the Fine numbers. Zbl 1175.16027
Holtkamp, Ralf; Loday, Jean-Louis; Ronco, María
2008
Structure multiplicative en K-théorie algébrique. Zbl 0293.18019
Loday, Jean-Louis
1974
Loday, Jean-Louis; Ronco, María
2013
Dichotomy of the addition of natural numbers. Zbl 1284.06007
Loday, Jean-Louis
2012
Inversion of integral series enumerating planar trees. Zbl 1085.05009
Loday, Jean-Louis
2005
Operadic construction of the renormalization group. Zbl 1269.81091
Loday, Jean-Louis; Nikolov, Nikolay M.
2013
Homotopie des espaces de concordances. Zbl 0443.57023
Loday, Jean-Louis
1979
Hopf structures on standard Young tableaux. Zbl 1219.81169
Loday, Jean-Louis; Poppov, Todor
2010
Parametrized braid groups of Chevalley groups. Zbl 1147.20034
Loday, Jean-Louis; Stein, Michael R.
2005
Les matrices monomiales et le groupe de Whitehead $$Wh_2$$. Zbl 0348.55007
Loday, Jean-Louis
1976
On the boundary map $$K_ 3(\Lambda/I) > K_ 2(\Lambda,I)$$. Zbl 0467.18003
Loday, Jean-Louis
1981
From diffeomorphism groups to loop spaces via cyclic homology. Zbl 0928.19001
Loday, Jean-Louis
1998
Multiplicative structures in K-theory. (Structures multiplicatives en K-théorie.) Zbl 0228.55005
Loday, Jean-Louis
1972
Free loop space and homology. Zbl 1386.55011
Loday, Jean-Louis
2015
Algebraic $$K$$-theory and cyclic homology. Zbl 1286.19004
Loday, Jean-Louis
2013
Loday, Jean-Louis; Ronco, María
2013
Operadic construction of the renormalization group. Zbl 1269.81091
Loday, Jean-Louis; Nikolov, Nikolay M.
2013
Loday, Jean-Louis; Vallette, Bruno
2012
Encyclopedia of types of algebras 2010. Zbl 1351.17001
Zinbiel, G. W.
2012
Dichotomy of the addition of natural numbers. Zbl 1284.06007
Loday, Jean-Louis
2012
The diagonal of the Stasheff polytope. Zbl 1220.18007
Loday, Jean-Louis
2011
The symmetric operation in a free pre-Lie algebra is magmatic. Zbl 1264.17001
Bergeron, Nantel; Loday, Jean-Louis
2011
Combinatorial Hopf algebras. Zbl 1217.16033
Loday, Jean-Louis; Ronco, María
2010
On the operad of associative algebras with derivation. Zbl 1237.18007
Loday, Jean-Louis
2010
Hopf structures on standard Young tableaux. Zbl 1219.81169
Loday, Jean-Louis; Poppov, Todor
2010
Generalized bialgebras and triples of operads. Zbl 1178.18001
Loday, Jean-Louis
2008
Parastatistics algebra, Young tableaux and the super plactic monoid. Zbl 1165.81029
Loday, Jean-Louis; Popov, Todor
2008
Coassociative magmatic bialgebras and the Fine numbers. Zbl 1175.16027
Holtkamp, Ralf; Loday, Jean-Louis; Ronco, María
2008
On the algebra of quasi-shuffles. Zbl 1126.16029
Loday, Jean-Louis
2007
Parking functions and triangulation of the associahedron. Zbl 1130.52006
Loday, Jean-Louis
2007
On the structure of cofree Hopf algebras. Zbl 1096.16019
Loday, Jean-Louis; Ronco, María
2006
On restricted Leibniz algebras. Zbl 1162.17001
Dokas, Ioannis; Loday, Jean-Louis
2006
Completing the operadic butterfly. Zbl 1187.18005
Loday, Jean-Louis
2006
Inversion of integral series enumerating planar trees. Zbl 1085.05009
Loday, Jean-Louis
2005
Parametrized braid groups of Chevalley groups. Zbl 1147.20034
Loday, Jean-Louis; Stein, Michael R.
2005
Trialgebras and families of polytopes. Zbl 1065.18007
Loday, Jean-Louis; Ronco, María
2004
Realization of the Stasheff polytope. Zbl 1059.52017
Loday, Jean-Louis
2004
Aguiar, Marcelo; Loday, Jean-Louis
2004
Splitting associativity and Hopf algebras. (Scindement d’associativité et algèbres de Hopf.) Zbl 1073.16032
Loday, Jean-Louis
2004
Cofree Hopf algebras. (Algèbres de Hopf colibres.) Zbl 1060.16039
Loday, Jean-Louis; Ronco, María
2003
Algebraic $$K$$-theory and the conjectural Leibniz $$K$$-theory. Zbl 1048.18005
Loday, Jean-Louis
2003
Order structure on the algebra of permutations and of planar binary trees. Zbl 0998.05013
Loday, Jean-Louis; Ronco, María O.
2002
Leibniz $$n$$-algebras. Zbl 1037.17002
Casas, J. M.; Loday, J.-L.; Pirashvili, T.
2002
Arithmetree. Zbl 1063.16044
Loday, Jean-Louis
2002
Dialgebras. Zbl 0999.17002
Loday, Jean-Louis
2001
Dialgebras and related operads. Zbl 0970.00010
2001
A duality between standard simplices and Stasheff polytopes. (Une dualité entre simplexes standards et polytopes de Stasheff.) Zbl 1010.18007
Loday, Jean-Louis; Ronco, María O.
2001
Homotopical syzygies. Zbl 0978.20022
Loday, Jean-Louis
2000
Cyclic homology. 2nd ed. Zbl 0885.18007
Loday, Jean-Louis
1998
Hopf algebra of the planar binary trees. Zbl 0926.16032
Loday, Jean-Louis; Ronco, María O.
1998
The tensor category of linear maps and Leibniz algebras. Zbl 0909.18003
Loday, J. L.; Pirashvili, T.
1998
From diffeomorphism groups to loop spaces via cyclic homology. Zbl 0928.19001
Loday, Jean-Louis
1998
Overview on Leibniz algebras, dialgebras and their homology. Zbl 0893.17001
Loday, Jean-Louis
1997
Operads: Proceedings of renaissance conferences. Special session and international conference on moduli spaces, operads, and representation theory/operads and homotopy algebra, March 1995/May–June 1995, Hartford, CT, USA/Luminy, France. Zbl 0855.00018
1997
Leibniz representations of Lie algebras. Zbl 0855.17018
Loday, Jean-Louis; Pirashvili, Teimuraz
1996
Loday, Jean-Louis
1996
Künneth-style formula for the homology of Leibniz algebras. Zbl 0880.17001
Loday, Jean-Louis
1996
Cup-product for Leibniz cohomology and dual Leibniz algebras. Zbl 0859.17015
Loday, Jean-Louis
1995
Algebras with two associative operations (dialgebras). (Algèbres ayant deux opérations associatives (digèbres).) Zbl 0845.16036
Loday, Jean-Louis
1995
Hausdorff series, Eulerian idempotents and Hopf algebras. (Série de Hausdorff, idempotents eulériens et algèbres de Hopf.) Zbl 0807.17003
Loday, Jean-Louis
1994
A noncommutative version of Lie algebras: Leibniz algebras. (Une version non commutative des algèbres de Lie: les algèbres de Leibniz.) Zbl 0806.55009
Loday, Jean-Louis
1993
Universal enveloping algebras of Leibniz algebras and (co)homology. Zbl 0821.17022
Loday, Jean-Louis; Pirashvili, Teimuraz
1993
Cyclic homology. Zbl 0780.18009
Loday, Jean-Louis
1992
Crossed simplicial groups and their associated homology. Zbl 0755.18005
Fiedorowicz, Zbigniew; Loday, Jean-Louis
1991
Opérations sur l’homologie cyclique des algèbres commutatives. (Operations on the cyclic homology of commutative algebras). Zbl 0686.18006
Loday, Jean-Louis
1989
Cyclic homology and lambda operations. Zbl 0719.19002
Loday, J.-L.; Procesi, C.
1989
Homology of symplectic and orthogonal algebras. Zbl 0716.17019
Loday, Jean-Louis; Procesi, Claudio
1988
Partition eulérienne et opérations en homologie cyclique. (Eulerian partition and operations in cyclic homology). Zbl 0669.13006
Loday, Jean-Louis
1988
Van Kampen theorems for diagrams of spaces. Zbl 0622.55009
Brown, Ronald; Loday, Jean-Louis
1987
Homologies diédrale et quaternionique. (Dihedral and quaternionic homology). Zbl 0627.18006
Loday, Jean-Louis
1987
Homotopical excision, and Hurewicz theorems, for n-cubes of spaces. Zbl 0584.55012
Brown, Ronald; Loday, Jean-Louis
1987
Comparaison des homologies du groupe linéaire et de son algèbre de Lie. (Comparison of homologies of a linear group and its Lie algebra). Zbl 0619.20025
Loday, Jean-Louis
1987
Cyclic homology, a survey. Zbl 0637.16013
Loday, Jean-Louis
1986
Cyclic homology and the Lie algebra homology of matrices. Zbl 0565.17006
Loday, Jean-Louis; Quillen, Daniel
1984
Excision homotopique en basse dimension. (Homotopical excision in low dimension). Zbl 0573.55011
Brown, Ronald; Loday, Jean-Louis
1984
Cyclic homology and homology of the Lie algebra of matrices. (Homologie cyclique et homologie de l’algèbre de Lie des matrices.) Zbl 0536.17006
Loday, Jean-Louis; Quillen, Daniel
1983
Spaces with finitely many non-trivial homotopy groups. Zbl 0491.55004
Loday, Jean-Louis
1982
Central extensions of Lie algebras. (Extensions centrales d’algèbres de Lie.) Zbl 0485.17006
Kassel, Christian; Loday, Jean-Louis
1982
Obstruction à l’excision en K-théorie algébrique. Zbl 0461.18007
Guin-Walery, Dominique; Loday, Jean-Louis
1981
Symboles en K-théorie algébrique supérieure. Zbl 0493.18006
Loday, Jean-Louis
1981
On the boundary map $$K_ 3(\Lambda/I) > K_ 2(\Lambda,I)$$. Zbl 0467.18003
Loday, Jean-Louis
1981
Homotopie des espaces de concordances. Zbl 0443.57023
Loday, Jean-Louis
1979
Cohomologie et groupe de Steinberg rélatifs. Zbl 0391.20040
Loday, Jean-Louis
1978
K-théorie algébrique et représentations de groupes. Zbl 0362.18014
Loday, Jean-Louis
1976
Higher Witt groups: A survey. Zbl 0356.18016
Loday, J.-L.
1976
Higher Whitehead groups and stable homotopy. Zbl 0337.55015
Loday, Jean-Louis
1976
Les matrices monomiales et le groupe de Whitehead $$Wh_2$$. Zbl 0348.55007
Loday, Jean-Louis
1976
Structure multiplicative en K-théorie algébrique. Zbl 0293.18019
Loday, Jean-Louis
1974
Multiplicative structures in K-theory. (Structures multiplicatives en K-théorie.) Zbl 0228.55005
Loday, Jean-Louis
1972
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### Cited by 1,741 Authors
61 Ladra González, Manuel 52 Omirov, Bakhrom A. 49 Casas Miras, José Manuel 29 Ellis, Graham J. 27 Khudoyberdiyev, Abror Kh. 27 Zhuchok, Anatolii V. 24 Loday, Jean-Louis 23 Pilaud, Vincent 22 Camacho, Luisa Maria 22 Pirashvili, Teimuraz 21 Foissy, Loïc 21 Guo, Li 19 Bai, Chengming 19 Bremner, Murray R. 19 Novelli, Jean-Christophe 19 Thibon, Jean-Yves 18 Giraudo, Samuele 17 Cortiñas, Guillermo H. 17 Ebrahimi-Fard, Kurusch 17 Khmaladze, Emzar 15 Makhlouf, Abdenacer 15 Rocco, Noraí Romeu 14 Chapoton, Frédéric 14 Dotsenko, Vladimir Viktorovich 14 Ronco, María Ofelia 13 Biyogmam, Guy Roger 13 Inassaridze, Nikoloz 13 Niroomand, Peyman 13 Sheng, Yunhe 12 García-Martínez, Xabier 12 Patras, Frédéric 12 Rakhimov, Isamiddin Sattarovich 12 Vallette, Bruno 12 Weibel, Charles A. 12 Wu, Jie 11 Brown, Ronald 11 Burde, Dietrich 11 Cegarra, Antonio Martínez 11 Donadze, Guram 11 Gao, Xing 11 Salemkar, Ali Reza 11 Wagemann, Friedrich 11 Willwacher, Thomas Hans 10 Dzhumadil’daev, Askar Serkulovich 10 Hivert, Florent 10 Kurdachenko, Leonid Andriĭovych 10 Liu, Dong 10 Manchon, Dominique 10 Mikhaĭlov, Roman Valer’evich 9 Bergeron, Nantel 9 Fialowski, Alice 9 Gómez, José R. 9 Jafari, Seid Hadi 9 Kaĭgorodov, Ivan B. 9 Kassel, Christian 9 Livernet, Muriel 9 Markl, Martin 9 Porter, Timothy 8 Ayupov, Shavkat Abdullaevich 8 de Araujo Bastos, Raimundo jun. 8 Benayadi, Saïd 8 Carey, Alan L. 8 Chen, Xiaojun 8 Datuashvili, Tamar 8 Edalatzadeh, Behrouz 8 Igusa, Kiyoshi 8 Kaledin, Dmitry B. 8 Karimjanov, Ikboljon Abdulazizovich 8 Liu, Zhangju 8 Lodder, Gerald Matthew 8 Mandal, Ashis 8 Moravec, Primož 8 Saha, Ripan 8 Stitzinger, Ernest Lester 8 Turdibaev, Rustam Mirzalievich 8 van der Linden, Tim 7 Aguiar, Marcelo 7 Barnes, Donald W. 7 Calderón Martín, Antonio Jesús 7 Chen, Liangyun 7 Drummond-Cole, Gabriel C. 7 Ginzburg, Victor 7 Gubarev, Vsevolod Yur’evich 7 Guin, Daniel 7 Hu, Naihong 7 Ismailov, Nurlan A. 7 Liu, Jiefeng 7 Madariaga, Sara 7 Nistor, Victor 7 Parvizi, Mohsen 7 Przytycki, Józef H. 7 Remm, Elisabeth 7 Russo, Francesco Giuseppe 7 Subbotin, Igor Yakov 7 Tabuada, Gonçalo 6 Baues, Hans-Joachim 6 Carrasco, Pilar C. 6 Chen, Yuqun 6 Connes, Alain 6 Dolgushev, Vasily A. ...and 1,641 more Authors
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### Cited in 255 Serials
191 Journal of Algebra 183 Journal of Pure and Applied Algebra 155 Communications in Algebra 110 Advances in Mathematics 48 Transactions of the American Mathematical Society 45 $$K$$-Theory 38 Journal of Geometry and Physics 38 Algebraic & Geometric Topology 37 Communications in Mathematical Physics 37 Journal of Algebra and its Applications 34 Proceedings of the American Mathematical Society 33 Journal of Algebraic Combinatorics 29 Journal of Homotopy and Related Structures 28 Annales de l’Institut Fourier 26 Letters in Mathematical Physics 25 Journal of Combinatorial Theory. Series A 24 Applied Categorical Structures 23 Linear Algebra and its Applications 23 Comptes Rendus. Mathématique. Académie des Sciences, Paris 22 Linear and Multilinear Algebra 20 Journal of Mathematical Physics 20 Inventiones Mathematicae 19 International Journal of Algebra and Computation 19 Journal of Noncommutative Geometry 18 Mathematische Zeitschrift 18 Topology and its Applications 17 Glasgow Mathematical Journal 17 Advances in Applied Mathematics 17 Algebras and Representation Theory 16 Selecta Mathematica. New Series 16 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 15 Discrete Mathematics 14 European Journal of Combinatorics 13 Duke Mathematical Journal 13 Georgian Mathematical Journal 12 Cahiers de Topologie et Géométrie Différentielle Catégoriques 12 Algebra Colloquium 12 Journal of Mathematical Sciences (New York) 12 Theory and Applications of Categories 11 Mathematical Notes 11 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 11 Mathematische Annalen 11 Journal of High Energy Physics 11 Frontiers of Mathematics in China 11 Asian-European Journal of Mathematics 10 Compositio Mathematica 10 Journal of Functional Analysis 10 Semigroup Forum 10 Forum Mathematicum 10 Séminaire Lotharingien de Combinatoire 10 Higher Structures 9 Journal für die Reine und Angewandte Mathematik 9 Journal of the American Mathematical Society 9 Documenta Mathematica 9 Journal of Group Theory 9 Algebra and Discrete Mathematics 8 Mathematical Proceedings of the Cambridge Philosophical Society 8 Archiv der Mathematik 8 Journal of Symbolic Computation 8 Differential Geometry and its Applications 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 7 Bulletin of the Australian Mathematical Society 7 Israel Journal of Mathematics 7 Ukrainian Mathematical Journal 7 Algebra Universalis 7 Manuscripta Mathematica 7 Geometry & Topology 6 Bulletin de la Société Mathématique de France 6 Memoirs of the American Mathematical Society 6 Proceedings of the Edinburgh Mathematical Society. Series II 6 Annales Mathématiques Blaise Pascal 6 The Electronic Journal of Combinatorics 6 Journal of Lie Theory 6 Acta Mathematica Sinica. English Series 6 Hacettepe Journal of Mathematics and Statistics 6 Journal of $$K$$-Theory 6 Journal de l’École Polytechnique – Mathématiques 5 Indian Journal of Pure & Applied Mathematics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Colloquium Mathematicum 5 Siberian Mathematical Journal 5 Bulletin of the American Mathematical Society. New Series 5 Turkish Journal of Mathematics 5 Bulletin des Sciences Mathématiques 5 Annals of Combinatorics 5 Communications in Contemporary Mathematics 5 International Journal of Geometric Methods in Modern Physics 5 Mediterranean Journal of Mathematics 5 Afrika Matematika 5 Communications in Mathematics 5 Open Mathematics 5 Algebraic Combinatorics 4 Nuclear Physics. B 4 Reports on Mathematical Physics 4 Publications Mathématiques 4 Monatshefte für Mathematik 4 Quaestiones Mathematicae 4 Discrete & Computational Geometry 4 Indagationes Mathematicae. New Series 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI ...and 155 more Serials
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### Cited in 51 Fields
787 Nonassociative rings and algebras (17-XX) 715 Category theory; homological algebra (18-XX) 605 Associative rings and algebras (16-XX) 380 Group theory and generalizations (20-XX) 349 Algebraic topology (55-XX) 248 Combinatorics (05-XX) 246 $$K$$-theory (19-XX) 161 Algebraic geometry (14-XX) 133 Commutative algebra (13-XX) 125 Differential geometry (53-XX) 110 Manifolds and cell complexes (57-XX) 99 Quantum theory (81-XX) 97 Global analysis, analysis on manifolds (58-XX) 87 Functional analysis (46-XX) 62 Order, lattices, ordered algebraic structures (06-XX) 52 General algebraic systems (08-XX) 52 Convex and discrete geometry (52-XX) 36 Number theory (11-XX) 33 Topological groups, Lie groups (22-XX) 30 Computer science (68-XX) 18 Dynamical systems and ergodic theory (37-XX) 16 Operator theory (47-XX) 16 Probability theory and stochastic processes (60-XX) 15 Relativity and gravitational theory (83-XX) 14 Mathematical logic and foundations (03-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 12 Several complex variables and analytic spaces (32-XX) 10 Mechanics of particles and systems (70-XX) 9 Field theory and polynomials (12-XX) 7 General topology (54-XX) 6 History and biography (01-XX) 6 Partial differential equations (35-XX) 5 General and overarching topics; collections (00-XX) 4 Ordinary differential equations (34-XX) 3 Special functions (33-XX) 3 Integral equations (45-XX) 3 Geometry (51-XX) 3 Systems theory; control (93-XX) 2 Difference and functional equations (39-XX) 2 Statistics (62-XX) 2 Numerical analysis (65-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Fluid mechanics (76-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-05-28T07:19:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3315941393375397, "perplexity": 8211.298038733546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663013003.96/warc/CC-MAIN-20220528062047-20220528092047-00140.warc.gz"} |
http://pdglive.lbl.gov/ParticleGroup.action;jsessionid=EF7001A4EA8910D978621488AF03EF33?node=BXXX010&init=0 | # ${{\mathit \Delta}}$ BARYONS ($\mathit S$ = 0, $\mathit I$ = 3/2)
${{\mathit \Delta}^{++}}$ = ${{\mathit u}}{{\mathit u}}{{\mathit u}}$ , ${{\mathit \Delta}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$, ${{\mathit \Delta}^{0}}$ = ${\mathit {\mathit u}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$, ${{\mathit \Delta}^{-}}$ = ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$ ${\mathit {\mathit d}}$
${{\mathit \Delta}{(1232)}}$ $3/2{}^{+}$**** ${{\mathit \Delta}{(1600)}}$ $3/2{}^{+}$*** ${{\mathit \Delta}{(1620)}}$ $1/2{}^{-}$**** ${{\mathit \Delta}{(1700)}}$ $3/2{}^{-}$**** ${{\mathit \Delta}{(1750)}}$ $1/2{}^{+}$* ${{\mathit \Delta}{(1900)}}$ $1/2{}^{-}$** ${{\mathit \Delta}{(1905)}}$ $5/2{}^{+}$**** ${{\mathit \Delta}{(1910)}}$ $1/2{}^{+}$**** ${{\mathit \Delta}{(1920)}}$ $3/2{}^{+}$*** ${{\mathit \Delta}{(1930)}}$ $5/2{}^{-}$*** ${{\mathit \Delta}{(1940)}}$ $3/2{}^{-}$** ${{\mathit \Delta}{(1950)}}$ $7/2{}^{+}$**** ${{\mathit \Delta}{(2000)}}$ $5/2{}^{+}$** ${{\mathit \Delta}{(2150)}}$ $1/2{}^{-}$* ${{\mathit \Delta}{(2200)}}$ $7/2{}^{-}$* ${{\mathit \Delta}{(2300)}}$ $9/2{}^{+}$** ${{\mathit \Delta}{(2350)}}$ $5/2{}^{-}$* ${{\mathit \Delta}{(2390)}}$ $7/2{}^{+}$* ${{\mathit \Delta}{(2400)}}$ $9/2{}^{-}$** ${{\mathit \Delta}{(2420)}}$ $11/2{}^{+}$**** ${{\mathit \Delta}{(2750)}}$ $13/2{}^{-}$** ${{\mathit \Delta}{(2950)}}$ $15/2{}^{+}$** ${{\mathit \Delta}{(\sim3000 \text{ Region})}}$Partial-Wave Analyses | 2018-02-17T19:08:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9538609981536865, "perplexity": 4986.527511361907}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891807660.32/warc/CC-MAIN-20180217185905-20180217205905-00115.warc.gz"} |
https://phys.libretexts.org/Bookshelves/College_Physics/Book%3A_College_Physics_(OpenStax)/32%3A_Medical_Applications_of_Nuclear_Physics/32.0%3A_Prelude_to_Applications_of_Nuclear_Physics | $$\require{cancel}$$
# 32.0: Prelude to Applications of Nuclear Physics
Applications of nuclear physics have become an integral part of modern life. From the bone scan that detects a cancer to the radioiodine treatment that cures another, nuclear radiation has diagnostic and therapeutic effects on medicine. From the fission power reactor to the hope of controlled fusion, nuclear energy is now commonplace and is a part of our plans for the future. Yet, the destructive potential of nuclear weapons haunts us, as does the possibility of nuclear reactor accidents.
Figure $$\PageIndex{1}$$: Tori Randall, Ph.D., curator for the Department of Physical Anthropology at the San Diego Museum of Man, prepares a 550-year-old Peruvian child mummy for a CT scan at Naval Medical Center San Diego. (credit: U.S. Navy photo by Mass Communication Specialist 3rd Class Samantha A. Lewis).
Certainly, several applications of nuclear physics escape our view, as seen in Figure $$\PageIndex{1}$$. Not only has nuclear physics revealed secrets of nature, it has an inevitable impact based on its applications, as they are intertwined with human values. Because of its potential for alleviation of suffering, and its power as an ultimate destructor of life, nuclear physics is often viewed with ambivalence. But it provides perhaps the best example that applications can be good or evil, while knowledge itself is neither.
Figure $$\PageIndex{2}$$: Customs officers inspect vehicles using neutron irradiation. Cars and trucks pass through portable x-ray machines that reveal their contents. (credit: Gerald L. Nino, CBP, U.S. Dept. of Homeland Security)
Figure $$\PageIndex{3}$$: This image shows two stowaways caught illegally entering the United States from Canada. (credit: U.S. Customs and Border Protection)
## Contributors
• Paul Peter Urone (Professor Emeritus at California State University, Sacramento) and Roger Hinrichs (State University of New York, College at Oswego) with Contributing Authors: Kim Dirks (University of Auckland) and Manjula Sharma (University of Sydney). This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2019-03-18T23:10:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17547693848609924, "perplexity": 6575.392755808771}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201707.53/warc/CC-MAIN-20190318211849-20190318233849-00399.warc.gz"} |
https://pos.sissa.it/398/364/ | Volume 398 - The European Physical Society Conference on High Energy Physics (EPS-HEP2021) - T06: QCD and Hadronic Physics
Measurement of the primary Lund jet plane density in pp collisions at $\sqrt{s} = \rm{13}$ TeV with ALICE
L.B. Havener
Full text: pdf
Pre-published on: January 17, 2022
Published on:
Abstract
Precision measurements of jet substructure are used as a probe of fundamental QCD processes. The primary Lund jet plane density is a two-dimensional visual representation of the radiation off the primary emitter within the jet that can be used to isolate different regions of the QCD phase space.
A new measurement of the primary Lund plane density for inclusive charged-particle jets in the transverse momentum range of 20 and 120 GeV/$c$ in pp collisions at $\sqrt{s} =$ 13 TeV with the ALICE detector will be presented. This is the first measurement of the Lund plane density in an intermediate jet $p_{\rm T}$ range where hadronization and underlying event effects play a dominant role. The projections of the Lund plane density onto the splitting scale $k_{\rm T}$ and splitting angle $\Delta{R}$ axis are shown, highlighting the perturbative/non-perturbative and wide/narrow angle regions of the splitting phase space. Through a 3D unfolding procedure, the Lund plane density is corrected for detector effects which allows for quantitative comparisons to MC generators to provide insight into how well generators describe different features of the parton shower and hadronization.
DOI: https://doi.org/10.22323/1.398.0364
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Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2022-01-22T08:32:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5660985708236694, "perplexity": 2028.1109319305156}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303779.65/warc/CC-MAIN-20220122073422-20220122103422-00690.warc.gz"} |
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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp015q47rn73z
Title: CO2 trapping in sloping aqiufers: High resolution numerical simulations Contributors: Elenius, MariaTchelepi, HamdiJohannsen, Klaus Keywords: capillary forcesdissolution Issue Date: 13-May-2010 Series/Report no.: XVIII International Conference on Water Resources, CMWR 2010, J. Carrera (Ed), Barcelona, 2010 Abstract: We performed numerical simulations of the migration of a supercritical CO2 current in a sloping aquifer in the presence of residual and solubility trapping. Compared to simulations with residual trapping only, when dissolution is accounted for the trapping efficiency is nearly doubled and the speed and maximum up-dip extent of the plume are affected. The saturations in the plume correspond well to transition zones consistent with capillary equilibrium. The pressure gradients slightly ahead of the leading tip of the current remain at the initial values, and that opens up the possibility to use a simple moving boundary to model extremely long aquifers. URI: http://arks.princeton.edu/ark:/88435/dsp015q47rn73z Appears in Collections: Princeton-Bergen Series on Carbon Storage
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https://gateway.ipfs.io/ipfs/QmXoypizjW3WknFiJnKLwHCnL72vedxjQkDDP1mXWo6uco/wiki/Spectral_density_estimation.html | # Spectral density estimation
For the statistical concept, see probability density estimation.
For a broader coverage related to this topic, see Spectral density.
In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density (also known as the power spectral density) of a random signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content of the signal. One purpose of estimating the spectral density is to detect any periodicities in the data, by observing peaks at the frequencies corresponding to these periodicities.
Some SDE techniques assume that a signal is composed of a limited (usually small) number of generating frequencies plus noise and seek to find the location and intensity of the generated frequencies. Others make no assumption on the number of components and seek to estimate the whole generating spectrum.
## Overview
Example of voice waveform and its frequency spectrum
A periodic waveform (triangle wave) and its frequency spectrum, showing a "fundamental" frequency at 220 Hz followed by multiples (harmonics) of 220 Hz.
The power spectral density of a segment of music is estimated by two different methods, for comparison.
Spectrum analysis, also referred to as frequency domain analysis or spectral density estimation, is the technical process of decomposing a complex signal into simpler parts. As described above, many physical processes are best described as a sum of many individual frequency components. Any process that quantifies the various amounts (e.g. amplitudes, powers, intensities, or phases), versus frequency can be called spectrum analysis.
Spectrum analysis can be performed on the entire signal. Alternatively, a signal can be broken into short segments (sometimes called frames), and spectrum analysis may be applied to these individual segments. Periodic functions (such as ) are particularly well-suited for this sub-division. General mathematical techniques for analyzing non-periodic functions fall into the category of Fourier analysis.
The Fourier transform of a function produces a frequency spectrum which contains all of the information about the original signal, but in a different form. This means that the original function can be completely reconstructed (synthesized) by an inverse Fourier transform. For perfect reconstruction, the spectrum analyzer must preserve both the amplitude and phase of each frequency component. These two pieces of information can be represented as a 2-dimensional vector, as a complex number, or as magnitude (amplitude) and phase in polar coordinates (i.e., as a phasor). A common technique in signal processing is to consider the squared amplitude, or power; in this case the resulting plot is referred to as a power spectrum.
Because of reversibility, the Fourier transform is called a representation of the function, in terms of frequency instead of time; thus, it is a frequency domain representation. Linear operations that could be performed in the time domain have counterparts that can often be performed more easily in the frequency domain. Frequency analysis also simplifies the understanding and interpretation of the effects of various time-domain operations, both linear and non-linear. For instance, only non-linear or time-variant operations can create new frequencies in the frequency spectrum.
In practice, nearly all software and electronic devices that generate frequency spectra utilize a discrete Fourier transform (DFT), which operates on samples of the signal, and which provides a mathematical approximation to the full integral solution. The DFT is almost invariably implemented by an efficient algorithm called fast Fourier transform (FFT). The squared-magnitude components of a DFT are a type of power spectrum called periodogram, which is widely used for examining the frequency characteristics of noise-free functions such as filter impulse responses and window functions. But the periodogram does not provide processing-gain when applied to noiselike signals or even sinusoids at low signal-to-noise ratios. In other words, the variance of its spectral estimate at a given frequency does not decrease as the number of samples used in the computation increases. This can be mitigated by averaging over time (Welch's method[1]) or over frequency (smoothing). Welch's method is widely used for SDE. However, periodogram-based techniques introduce small biases that are unacceptable in some applications. So other alternatives are presented in the next section.
## Techniques
Many other techniques for spectral estimation have been developed to mitigate the disadvantages of the basic periodogram. These techniques can generally be divided into non-parametric and parametric methods. The non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Some of the most common estimators in use for basic applications (e.g. Welch's method) are non-parametric estimators closely related to the periodogram. By contrast, the parametric approaches assume that the underlying stationary stochastic process has a certain structure that can be described using a small number of parameters (for example, using an auto-regressive or moving average model). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process.
Following is a partial list of non-parametric spectral density estimation techniques:
Below is a partial list of parametric techniques:
### Parametric estimation
In parametric spectral estimation, one assumes that the signal is modeled by a stationary process which has a spectral density function (SDF) that is a function of the frequency and parameters .[2] The estimation problem then becomes one of estimating these parameters.
The most common form of parametric SDF estimate uses as a model an autoregressive model of order .[2]:392 A signal sequence obeying a zero mean process satisfies the equation
where the are fixed coefficients and is a white noise process with zero mean and innovation variance . The SDF for this process is
with the sampling time interval and the Nyquist frequency.
There are a number of approaches to estimating the parameters of the process and thus the spectral density:[2]:452-453
• The Yule-Walker estimators are found by recursively solving the Yule-Walker equations for an process
• The Burg estimators are found by treating the Yule-Walker equations as a form of ordinary least squares problem. The Burg estimators are generally considered superior to the Yule-Walker estimators.[2]:452 Burg associated these with maximum entropy spectral estimation.[3]
• The forward-backward least-squares estimators treat the process as a regression problem and solves that problem using forward-backward method. They are competitive with the Burg estimators.
• The maximum likelihood estimators assume the white noise is a Gaussian process and estimates the parameters using a maximum likelihood approach. This involves a nonlinear optimization and is more complex than the first three.
Alternative parametric methods include fitting to a moving average model (MA) and to a full autoregressive moving average model (ARMA).
## Frequency estimation
Frequency estimation is the process of estimating the complex frequency components of a signal in the presence of noise given assumptions about the number of the components.[4] This contrasts with the general methods above, which do not make prior assumptions about the components.
### Finite number of tones
A typical model for a signal consists of a sum of complex exponentials in the presence of white noise,
.
The power spectral density of is composed of impulse functions in addition to the spectral density function due to noise.
The most common methods for frequency estimation involve identifying the noise subspace to extract these components. These methods are based on eigen decomposition of the autocorrelation matrix into a signal subspace and a noise subspace. After these subspaces are identified, a frequency estimation function is used to find the component frequencies from the noise subspace. The most popular methods of noise subspace based frequency estimation are Pisarenko's method, the multiple signal classification (MUSIC) method, the eigenvector method, and the minimum norm method.
,
• Eigenvector method
• Minimum norm method
### Single tone
If one only wants to estimate the single loudest frequency, one can use a pitch detection algorithm. If the dominant frequency changes over time, then the problem becomes the estimation of the instantaneous frequency as defined in the time–frequency representation. Methods for instantaneous frequency estimation include those based on the Wigner-Ville distribution and higher order ambiguity functions.[5]
If one wants to know all the (possibly complex) frequency components of a received signal (including transmitted signal and noise), one uses a discrete Fourier transform or some other Fourier-related transform.
## Example calculation
Suppose , from to is a time series (discrete time) with zero mean. Suppose that it is a sum of a finite number of periodic components (all frequencies are positive):
The variance of is, for a zero-mean function as above, given by . If these data were samples taken from an electrical signal, this would be its average power (power is energy per unit time, so it is analogous to variance if energy is analogous to the amplitude squared).
Now, for simplicity, suppose the signal extends infinitely in time, so we pass to the limit as . If the average power is bounded, which is almost always the case in reality, then the following limit exists and is the variance of the data.
Again, for simplicity, we will pass to continuous time, and assume that the signal extends infinitely in time in both directions. Then these two formulas become
and
The root mean square of is , so the variance of is . Hence, the contribution to the average power of coming from the component with frequency is . All these contributions add up to the average power of .
Then the power as a function of frequency is , and its statistical cumulative distribution function will be
is a step function, monotonically non-decreasing. Its jumps occur at the frequencies of the periodic components of , and the value of each jump is the power or variance of that component.
The variance is the covariance of the data with itself. If we now consider the same data but with a lag of , we can take the covariance of with , and define this to be the autocorrelation function of the signal (or data) :
If it exists, it is an even function of . If the average power is bounded, then exists everywhere, is finite, and is bounded by , which is the average power or variance of the data.
It can be shown that can be decomposed into periodic components with the same periods as :
This is in fact the spectral decomposition of over the different frequencies, and is related to the distribution of power of over the frequencies: the amplitude of a frequency component of is its contribution to the average power of the signal.
The power spectrum of this example is not continuous, and therefore does not have a derivative, and therefore this signal does not have a power spectral density function. In general, the power spectrum will usually be the sum of two parts: a line spectrum such as in this example, which is not continuous and does not have a density function, and a residue, which is absolutely continuous and does have a density function.
## References
1. Welch, P. D. (1967), "The use of Fast Fourier Transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms", IEEE Transactions on Audio and Electroacoustics, AU-15 (2): 70–73, doi:10.1109/TAU.1967.1161901
2. Percival, Donald B.; Walden, Andrew T. (1992). Spectral Analysis for Physical Applications. Cambridge University Press. ISBN 9780521435413.
3. Burg, J.P. (1967) "Maximum Entropy Spectral Analysis", Proceedings of the 37th Meeting of the Society of Exploration Geophysicists, Oklahoma City, Oklahoma.
4. Hayes, Monson H., Statistical Digital Signal Processing and Modeling, John Wiley & Sons, Inc., 1996. ISBN 0-471-59431-8.
5. Lerga, Jonatan. "Overview of Signal Instantaneous Frequency Estimation Methods" (PDF). University of Rijeka. Retrieved 22 March 2014.
• Porat, B. (1994). Digital Processing of Random Signals: Theory & Methods. Prentice Hall. ISBN 0-13-063751-3.
• Priestley, M.B. (1991). Spectral Analysis and Time Series. Academic Press. ISBN 0-12-564922-3.
• Stoica, P.; Moses, R. (2005). Spectral Analysis of Signals. Prentice Hall. ISBN 0-13-113956-8.
• Thomson, D. J. (1982). "Spectrum estimation and harmonic analysis". Proceedings of the IEEE. 70 (9): 1055. doi:10.1109/PROC.1982.12433.
This article is issued from Wikipedia - version of the 11/30/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files. | 2022-05-28T20:53:58 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8843340277671814, "perplexity": 507.1247667769583}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663019783.90/warc/CC-MAIN-20220528185151-20220528215151-00538.warc.gz"} |
http://dlmf.nist.gov/27.7 | # §27.7 Lambert Series as Generating Functions
Lambert series have the form
27.7.1 $\sum_{n=1}^{\infty}f(n)\frac{x^{n}}{1-x^{n}}.$ Symbols: $n$: positive integer and $x$: real number Referenced by: §27.7 Permalink: http://dlmf.nist.gov/27.7.E1 Encodings: TeX, pMML, png
If $|x|<1$, then the quotient $x^{n}/(1-x^{n})$ is the sum of a geometric series, and when the series (27.7.1) converges absolutely it can be rearranged as a power series:
27.7.2 $\sum_{n=1}^{\infty}f(n)\frac{x^{n}}{1-x^{n}}=\sum_{n=1}^{\infty}\sum_{d% \divides n}f(d)x^{n}.$ Symbols: $d$: positive integer, $n$: positive integer and $x$: real number Referenced by: §27.7 Permalink: http://dlmf.nist.gov/27.7.E2 Encodings: TeX, pMML, png
Again with $|x|<1$, special cases of (27.7.2) include:
27.7.3 $\displaystyle\sum_{n=1}^{\infty}\mathop{\mu\/}\nolimits\!\left(n\right)\frac{x% ^{n}}{1-x^{n}}$ $\displaystyle=x,$ Symbols: $\mathop{\mu\/}\nolimits\!\left(n\right)$: Möbius function, $n$: positive integer and $x$: real number A&S Ref: 24.3.1 I.B Permalink: http://dlmf.nist.gov/27.7.E3 Encodings: TeX, pMML, png 27.7.4 $\displaystyle\sum_{n=1}^{\infty}\mathop{\phi\/}\nolimits\!\left(n\right)\frac{% x^{n}}{1-x^{n}}$ $\displaystyle=\frac{x}{(1-x)^{2}},$ 27.7.5 $\displaystyle\sum_{n=1}^{\infty}n^{\alpha}\frac{x^{n}}{1-x^{n}}$ $\displaystyle=\sum_{n=1}^{\infty}\mathop{\sigma_{\alpha}\/}\nolimits\!\left(n% \right)x^{n},$ 27.7.6 $\displaystyle\sum_{n=1}^{\infty}\mathop{\lambda\/}\nolimits\!\left(n\right)% \frac{x^{n}}{1-x^{n}}$ $\displaystyle=\sum_{n=1}^{\infty}x^{n^{2}}.$ | 2014-11-26T07:46:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 32, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9734867811203003, "perplexity": 9823.389350452464}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931006593.41/warc/CC-MAIN-20141125155646-00129-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://par.nsf.gov/biblio/10281975-sn-aspherical-type-iin-supernova-low-polarization | SN 2014ab: an aspherical Type IIn supernova with low polarization
ABSTRACT We present photometry, spectra, and spectropolarimetry of supernova (SN) 2014ab, obtained through ∼200 d after peak brightness. SN 2014ab was a luminous Type IIn SN (MV < −19.14 mag) discovered after peak brightness near the nucleus of its host galaxy, VV 306c. Pre-discovery upper limits constrain the time of explosion to within 200 d prior to discovery. While SN 2014ab declined by ∼1 mag over the course of our observations, the observed spectrum remained remarkably unchanged. Spectra exhibit an asymmetric emission-line profile with a consistently stronger blueshifted component, suggesting the presence of dust or a lack of symmetry between the far side and near side of the SN. The Pa β emission line shows a profile very similar to that of H α, implying that this stronger blueshifted component is caused either through obscuration by large dust grains, occultation by optically thick material, or a lack of symmetry between the far side and near side of the interaction region. Despite these asymmetric line profiles, our spectropolarimetric data show that SN 2014ab has little detected polarization after accounting for the interstellar polarization. We are likely seeing emission from a photosphere that has only small deviation from circular symmetry in the plane normal to our line of sight, but with either more »
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10281975
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Monthly Notices of the Royal Astronomical Society
Volume:
498
Issue:
3
Page Range or eLocation-ID:
3835 to 3851
ISSN:
0035-8711
2. ABSTRACT We observed the Brackett α emission line (4.05 μm) within the nuclear starburst of NGC 253 to measure the kinematics of ionized gas, and distinguish motions driven by star formation feedback from gravitational motions induced by the central mass structure. Using NIRSPEC on Keck II, we obtained 30 spectra through a $0^{\prime \prime }_{.}5$ slit stepped across the central ∼5 arcsec × 25 arcsec (85 × 425 pc) region to produce a spectral cube. The Br α emission resolves into four nuclear sources: S1 at the infrared core (IRC), N1 at the radio core, and the fainter sources N2 and N3 in the northeast. The line profile is characterized by a primary component with Δvprimary ∼90–130 $\rm km\, s^{-1}$ (full width at half-maximum) on top of a broad blue 2wing with Δvbroad ∼300–350 $\rm km\, s^{-1}$, and an additional redshifted narrow component in the west. The velocity field generated from our cube reveals several distinct patterns. A mean NE–SW velocity gradient of +10 $\rm km\, s^{-1}$ arcsec−1 along the major axis traces the solid-body rotation curve of the nuclear disc. At the radio core, isovelocity contours become S-shaped, indicating the presence of secondary nuclear bar of total extent ∼5 arcsec (90 pc). The symmetry of the bar places the galactic centre, and potential supermassivemore »
5. ABSTRACT After correcting for their light-curve shape and colour, Type Ia supernovae (SNe Ia) are precise cosmological distance indicators. However, there remains a non-zero intrinsic scatter in the differences between measured distance and that inferred from a cosmological model (i.e. Hubble residuals or HRs), indicating that SN Ia distances can potentially be further improved. We use the open-source relational data base kaepora to generate composite spectra with desired average properties of phase, light-curve shape, and HR. At many phases, the composite spectra from two subsamples with positive and negative average HRs are significantly different. In particular, in all spectra from 9 d before to 15 d after peak brightness, we find that SNe with negative HRs have, on average, higher ejecta velocities (as seen in nearly every optical spectral feature) than SNe with positive HRs. At +4 d relative to B-band maximum, using a sample of 62 SNe Ia, we measure a 0.091 ± 0.035 mag (2.7σ) HR step between SNe with Si ii λ6355 line velocities ($v_{Si\, rm{\small II}}$) higher/lower than −11 000 km s−1 (the median velocity). After light-curve shape and colour correction, SNe with higher velocities tend to have underestimated distance moduli relative to a cosmological model. The intrinsic scatter in our sample reduces from 0.094 to 0.082 mag after making thismore » | 2022-10-05T09:51:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6660070419311523, "perplexity": 3372.866195841658}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337595.1/warc/CC-MAIN-20221005073953-20221005103953-00003.warc.gz"} |
https://par.nsf.gov/biblio/10190072-edge-expansion-spectral-gap-nonnegative-matrices | Edge Expansion and Spectral Gap of Nonnegative Matrices
The classic graphical Cheeger inequalities state that if $M$ is an $n\times n$ \emph{symmetric} doubly stochastic matrix, then $\frac{1-\lambda_{2}(M)}{2}\leq\phi(M)\leq\sqrt{2\cdot(1-\lambda_{2}(M))}$ where $\phi(M)=\min_{S\subseteq[n],|S|\leq n/2}\left(\frac{1}{|S|}\sum_{i\in S,j\not\in S}M_{i,j}\right)$ is the edge expansion of $M$, and $\lambda_{2}(M)$ is the second largest eigenvalue of $M$. We study the relationship between $\phi(A)$ and the spectral gap $1-\re\lambda_{2}(A)$ for \emph{any} doubly stochastic matrix $A$ (not necessarily symmetric), where $\lambda_{2}(A)$ is a nontrivial eigenvalue of $A$ with maximum real part. Fiedler showed that the upper bound on $\phi(A)$ is unaffected, i.e., $\phi(A)\leq\sqrt{2\cdot(1-\re\lambda_{2}(A))}$. With regards to the lower bound on $\phi(A)$, there are known constructions with $\phi(A)\in\Theta\left(\frac{1-\re\lambda_{2}(A)}{\log n}\right),$ indicating that at least a mild dependence on $n$ is necessary to lower bound $\phi(A)$. In our first result, we provide an \emph{exponentially} better construction of $n\times n$ doubly stochastic matrices $A_{n}$, for which $\phi(A_{n})\leq\frac{1-\re\lambda_{2}(A_{n})}{\sqrt{n}}.$ In fact, \emph{all} nontrivial eigenvalues of our matrices are $0$, even though the matrices are highly \emph{nonexpanding}. We further show that this bound is in the correct range (up to the exponent of $n$), by showing that for any doubly stochastic matrix $A$, $\phi(A)\geq\frac{1-\re\lambda_{2}(A)}{35\cdot n}.$ As a consequence, unlike the symmetric case, there is a (necessary) loss of a factor of $n^{\alpha}$ for $\frac{1}{2}\leq\alpha\leq1$ in lower bounding $\phi$ by the spectral gap in the nonsymmetric setting. Our second result extends these bounds to general matrices $R$ with nonnegative entries, to obtain a more »
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10190072
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Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms
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##### More Like this
1. The cumulative empirical spectral measure (CESM) $\Phi[\mathbf{A}] : \mathbb{R} \to [0,1]$ of a $n\times n$ symmetric matrix $\mathbf{A}$ is defined as the fraction of eigenvalues of $\mathbf{A}$ less than a given threshold, i.e., $\Phi[\mathbf{A}](x) := \sum_{i=1}^{n} \frac{1}{n} {\large\unicode{x1D7D9}}[ \lambda_i[\mathbf{A}]\leq x]$. Spectral sums $\operatorname{tr}(f[\mathbf{A}])$ can be computed as the Riemann–Stieltjes integral of $f$ against $\Phi[\mathbf{A}]$, so the task of estimating CESM arises frequently in a number of applications, including machine learning. We present an error analysis for stochastic Lanczos quadrature (SLQ). We show that SLQ obtains an approximation to the CESM within a Wasserstein distance of $t \: | \lambda_{\text{max}}[\mathbf{A}] - \lambda_{\text{min}}[\mathbf{A}] |$ with probability at least $1-\eta$, by applying the Lanczos algorithm for $\lceil 12 t^{-1} + \frac{1}{2} \rceil$ iterations to $\lceil 4 ( n+2 )^{-1}t^{-2} \ln(2n\eta^{-1}) \rceil$ vectors sampled independently and uniformly from the unit sphere. We additionally provide (matrix-dependent) a posteriori error bounds for the Wasserstein and Kolmogorov–Smirnov distances between the output of this algorithm and the true CESM. The quality of our bounds is demonstrated using numerical experiments.
2. Abstract
Given a sequence $\{Z_d\}_{d\in \mathbb{N}}$ of smooth and compact hypersurfaces in ${\mathbb{R}}^{n-1}$, we prove that (up to extracting subsequences) there exists a regular definable hypersurface $\Gamma \subset {\mathbb{R}}\textrm{P}^n$ such that each manifold $Z_d$ is diffeomorphic to a component of the zero set on $\Gamma$ of some polynomial of degree $d$. (This is in sharp contrast with the case when $\Gamma$ is semialgebraic, where for example the homological complexity of the zero set of a polynomial $p$ on $\Gamma$ is bounded by a polynomial in $\deg (p)$.) More precisely, given the above sequence of hypersurfaces, we construct a regular, compact, semianalytic hypersurface $\Gamma \subset {\mathbb{R}}\textrm{P}^{n}$ containing a subset $D$ homeomorphic to a disk, and a family of polynomials $\{p_m\}_{m\in \mathbb{N}}$ of degree $\deg (p_m)=d_m$ such that $(D, Z(p_m)\cap D)\sim ({\mathbb{R}}^{n-1}, Z_{d_m}),$ i.e. the zero set of $p_m$ in $D$ is isotopic to $Z_{d_m}$ in ${\mathbb{R}}^{n-1}$. This says that, up to extracting subsequences, the intersection of $\Gamma$ with a hypersurface of degree $d$ can be as complicated as we want. We call these ‘pathological examples’. In particular, we show that for every $0 \leq k \leq n-2$ and every sequence of natural numbers $a=\{a_d\}_{d\in \mathbb{N}}$ there is a regular, compact semianalyticmore »
3. The densest subgraph problem in a graph (\dsg), in the simplest form, is the following. Given an undirected graph $G=(V,E)$ find a subset $S \subseteq V$ of vertices that maximizes the ratio $|E(S)|/|S|$ where $E(S)$ is the set of edges with both endpoints in $S$. \dsg and several of its variants are well-studied in theory and practice and have many applications in data mining and network analysis. In this paper we study fast algorithms and structural aspects of \dsg via the lens of \emph{supermodularity}. For this we consider the densest supermodular subset problem (\dssp): given a non-negative supermodular function $f: 2^V \rightarrow \mathbb{R}_+$, maximize $f(S)/|S|$. For \dsg we describe a simple flow-based algorithm that outputs a $(1-\eps)$-approximation in deterministic $\tilde{O}(m/\eps)$ time where $m$ is the number of edges. Our algorithm is the first to have a near-linear dependence on $m$ and $1/\eps$ and improves previous methods based on an LP relaxation. It generalizes to hypergraphs, and also yields a faster algorithm for directed \dsg. Greedy peeling algorithms have been very popular for \dsg and several variants due to their efficiency, empirical performance, and worst-case approximation guarantees. We describe a simple peeling algorithm for \dssp and analyze its approximation guarantee inmore »
4. Abstract
In this paper, we consider discrete Schrödinger operators of the form, $$\begin{equation*} (Hu)(n) = u({n+1})+u({n-1})+V(n)u(n). \end{equation*}$$We view $H$ as a perturbation of the free operator $H_0$, where $(H_0u)(n)= u({n+1})+u({n-1})$. For $H_0$ (no perturbation), $\sigma _{\textrm{ess}}(H_0)=\sigma _{\textrm{ac}}(H)=[-2,2]$ and $H_0$ does not have eigenvalues embedded into $(-2,2)$. It is an interesting and important problem to identify the perturbation such that the operator $H_0+V$ has one eigenvalue (finitely many eigenvalues or countable eigenvalues) embedded into $(-2,2)$. We introduce the almost sign type potentials and develop the Prüfer transformation to address this problem, which leads to the following five results. 1: We obtain the sharp spectral transition for the existence of irrational type eigenvalues or rational type eigenvalues with even denominators.2: Suppose $\limsup _{n\to \infty } n|V(n)|=a<\infty .$ We obtain a lower/upper bound of $a$ such that $H_0+V$ has one rational type eigenvalue with odd denominator.3: We obtain the asymptotical behavior of embedded eigenvalues around the boundaries of $(-2,2)$.4: Given any finite set of points $\{ E_j\}_{j=1}^N$ in $(-2,2)$ with $0\notin \{ E_j\}_{j=1}^N+\{ E_j\}_{j=1}^N$, we construct the explicit potential $V(n)=\frac{O(1)}{1+|n|}$ such that $H=H_0+V$ has eigenvalues $\{ E_j\}_{j=1}^N$.5: Given any countable set of points $\{ E_j\}$ in $(-2,2)$ with $0\notin \{ E_j\}+\{ E_j\}$, andmore »
5. Abstract
Let $f(z) = \sum_{n=1}^\infty a_f(n)q^n$ be a holomorphic cuspidal newform with even integral weight $k\geq 2$, level N, trivial nebentypus and no complex multiplication. For all primes p, we may define $\theta_p\in [0,\pi]$ such that $a_f(p) = 2p^{(k-1)/2}\cos \theta_p$. The Sato–Tate conjecture states that the angles θp are equidistributed with respect to the probability measure $\mu_{\textrm{ST}}(I) = \frac{2}{\pi}\int_I \sin^2 \theta \; d\theta$, where $I\subseteq [0,\pi]$. Using recent results on the automorphy of symmetric power L-functions due to Newton and Thorne, we explicitly bound the error term in the Sato–Tate conjecture when f corresponds to an elliptic curve over $\mathbb{Q}$ of arbitrary conductor or when f has square-free level. In these cases, if $\pi_{f,I}(x) := \#\{p \leq x : p \nmid N, \theta_p\in I\}$ and $\pi(x) := \# \{p \leq x \}$, we prove the following bound: $$\left| \frac{\pi_{f,I}(x)}{\pi(x)} - \mu_{\textrm{ST}}(I)\right| \leq 58.1\frac{\log((k-1)N \log{x})}{\sqrt{\log{x}}} \qquad \text{for} \quad x \geq 3.$$ As an application, we give an explicit bound for the number of primes up to x that violate the Atkin–Serre conjecture for f. | 2023-03-24T12:22:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.9415880441665649, "perplexity": 178.36563162857266}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945282.33/warc/CC-MAIN-20230324113500-20230324143500-00581.warc.gz"} |
https://zbmath.org/authors/?s=0&q=Kumano-Go%2C+Hitoshi | ## Kumano-go, Hitoshi
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Author ID: kumano-go.hitoshi Published as: Kumano-go, Hitoshi; Kumano-go, H.; Kumano-Go, Hitoshi; Kumano-Go, H. more...less External Links: MacTutor · Wikidata · GND · IdRef
Documents Indexed: 33 Publications since 1959, including 1 Book Biographic References: 1 Publication Co-Authors: 11 Co-Authors with 13 Joint Publications 26 Co-Co-Authors
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### Co-Authors
20 single-authored 3 Taniguchi, Kazuo 2 Nagase, Michihiro 1 Hayakawa, Kantaro 1 Ichinose, Wataru 1 Ise, Kusuo 1 Kitada, Hitoshi 1 Koshiba, Zen’ichiro 1 Matsuda, Michihiko 1 Shinkai, Kenzo 1 Tozaki, Yoshiharu 1 Tsutsumi, Chisato
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### Serials
12 Proceedings of the Japan Academy 5 Osaka Journal of Mathematics 3 Funkcialaj Ekvacioj. Serio Internacia 3 Journal of the Mathematical Society of Japan 3 Communications in Partial Differential Equations 2 Communications on Pure and Applied Mathematics 2 Osaka Mathematical Journal 1 Journal of the Faculty of Science. Section I A
### Fields
19 Partial differential equations (35-XX) 6 Operator theory (47-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 Numerical analysis (65-XX) 1 Global analysis, analysis on manifolds (58-XX)
### Citations contained in zbMATH Open
28 Publications have been cited 398 times in 319 Documents Cited by Year
A family of Fourier integral operators and the fundamental solution for a Schrödinger equation. Zbl 0472.35034
1981
Remarks on pseudo-differential operators. Zbl 0179.42201
Kumano-go, H.
1969
Algebras of pseudo-differential operators. Zbl 0206.10501
Kumano-go, H.
1970
Pseudo-differential operators. (Updated transl. from the Japanese by the author, Remi Vaillancourt, and Michihiro Nagase). Zbl 0489.35003
Kumano-go, Hitoshi
1982
Pseudo-differential operators with non-regular symbols and applications. Zbl 0395.35089
Kumano-Go, Hitoshi; Nagase, Michihiro
1978
Oscillatory integrals of symbols of pseudo-differential operators on R$$^n$$ and operators of Fredholm type. Zbl 0272.47032
Kumano-go, Hitoshi; Taniguchi, Kazuo
1973
Complex powers of hypoelliptic pseudo-differential operators with applications. Zbl 0264.35019
Kumano-go, Hitoshi; Tsutsumi, Chisato
1973
Multi-products of phase functions for Fourier integral operators with an application. Zbl 0383.35073
Kumano-go, Hitoshi; Taniguchi, Kazuo; Tozaki, Yoshiharu
1978
Pseudo-differential operators of multiple symbol and the Calderon- Vaillancourt theorem. Zbl 0294.35068
Kumano-go, H.
1975
A calculus of Fourier integral operators on $$R^n$$ and the fundamental solution for an operator of hyperbolic type. Zbl 0331.42012
Kumano-go, Hitoshi
1976
Fundamental solution for a hyperbolic system with diagonal principal part. Zbl 0431.35062
Kumano-go, Hitoshi
1979
$$L^ p$$-theory of pseudo-differential operators. Zbl 0206.10404
Kumano-go, H.; Nagase, M.
1970
Pseudo-differential operators and the uniqueness of the Cauchy problem. Zbl 0157.16901
Kumano-go, H.
1969
Fourier integral operators of multiphase and the fundamental solution for a hyperbolic system. Zbl 0568.35092
Kumano-go, Hitoshi; Taniguchi, Kazuo
1979
A problem of Nirenberg on pseudo-differential operators. Zbl 0186.16405
Kumano-go, Hitoshi
1970
On the uniqueness of the solution of the Cauchy problem and the unique continuation theorem for elliptic equation. Zbl 0106.07602
Kumano-Go, Hitoshi
1962
Fundamental solutions for operators of regularly hyperbolic type. Zbl 0351.35058
Kumano-go, Hitoshi
1978
Factorizations and fundamental solutions for differential operators of elliptic-hyperbolic type. Zbl 0374.35031
Kumano-go, Hitoshi
1976
A family of pseudo-differential operators and a stability theorem for the Friedrichs scheme. Zbl 0342.35056
Koshiba, Zen’ichiro; Kumano-go, Hitoshi
1976
On an example of non-uniqueness of solutions of the Cauchy problem for the wyve equation. Zbl 0148.08502
Kumano-go, H.
1963
The characterization of differential operators with respect to the characteristic Cauchy problem. Zbl 0148.34104
Kumano-go, Hitoshi; Shinkai, Kenzo
1966
Complex powers of a system of pseudo-differential operators. Zbl 0247.47047
Hayakawa, Kantaro; Kumano-go, Hitoshi
1971
On the characteristic Cauchy problem for partial differential equations. Zbl 0142.36903
Kumano-go, H.; Ise, K.
1965
On propagation of regularity in space-variables for the solutions of differential equations with constant coefficients. Zbl 0145.35301
Kumano-go, H.
1966
On the uniqueness for the solution of the Cauchy problem. Zbl 0154.35304
Kumano-go, H.
1963
On the index of hypoelliptic pseudo-differential operators on R$$^n$$. Zbl 0252.35066
Kumano-go, Hitoshi
1972
On singular perturbation of linear partial differential equations with constant coefficients. II. Zbl 0100.30204
Kumano-Go, Hitoshi
1959
On the propagation of singularities with infinitely many branching points for a hyperbolic equation of second order. Zbl 0463.35050
Ichinose, Wataru; Kumano-go, Hitoshi
1981
Pseudo-differential operators. (Updated transl. from the Japanese by the author, Remi Vaillancourt, and Michihiro Nagase). Zbl 0489.35003
Kumano-go, Hitoshi
1982
A family of Fourier integral operators and the fundamental solution for a Schrödinger equation. Zbl 0472.35034
1981
On the propagation of singularities with infinitely many branching points for a hyperbolic equation of second order. Zbl 0463.35050
Ichinose, Wataru; Kumano-go, Hitoshi
1981
Fundamental solution for a hyperbolic system with diagonal principal part. Zbl 0431.35062
Kumano-go, Hitoshi
1979
Fourier integral operators of multiphase and the fundamental solution for a hyperbolic system. Zbl 0568.35092
Kumano-go, Hitoshi; Taniguchi, Kazuo
1979
Pseudo-differential operators with non-regular symbols and applications. Zbl 0395.35089
Kumano-Go, Hitoshi; Nagase, Michihiro
1978
Multi-products of phase functions for Fourier integral operators with an application. Zbl 0383.35073
Kumano-go, Hitoshi; Taniguchi, Kazuo; Tozaki, Yoshiharu
1978
Fundamental solutions for operators of regularly hyperbolic type. Zbl 0351.35058
Kumano-go, Hitoshi
1978
A calculus of Fourier integral operators on $$R^n$$ and the fundamental solution for an operator of hyperbolic type. Zbl 0331.42012
Kumano-go, Hitoshi
1976
Factorizations and fundamental solutions for differential operators of elliptic-hyperbolic type. Zbl 0374.35031
Kumano-go, Hitoshi
1976
A family of pseudo-differential operators and a stability theorem for the Friedrichs scheme. Zbl 0342.35056
Koshiba, Zen’ichiro; Kumano-go, Hitoshi
1976
Pseudo-differential operators of multiple symbol and the Calderon- Vaillancourt theorem. Zbl 0294.35068
Kumano-go, H.
1975
Oscillatory integrals of symbols of pseudo-differential operators on R$$^n$$ and operators of Fredholm type. Zbl 0272.47032
Kumano-go, Hitoshi; Taniguchi, Kazuo
1973
Complex powers of hypoelliptic pseudo-differential operators with applications. Zbl 0264.35019
Kumano-go, Hitoshi; Tsutsumi, Chisato
1973
On the index of hypoelliptic pseudo-differential operators on R$$^n$$. Zbl 0252.35066
Kumano-go, Hitoshi
1972
Complex powers of a system of pseudo-differential operators. Zbl 0247.47047
Hayakawa, Kantaro; Kumano-go, Hitoshi
1971
Algebras of pseudo-differential operators. Zbl 0206.10501
Kumano-go, H.
1970
$$L^ p$$-theory of pseudo-differential operators. Zbl 0206.10404
Kumano-go, H.; Nagase, M.
1970
A problem of Nirenberg on pseudo-differential operators. Zbl 0186.16405
Kumano-go, Hitoshi
1970
Remarks on pseudo-differential operators. Zbl 0179.42201
Kumano-go, H.
1969
Pseudo-differential operators and the uniqueness of the Cauchy problem. Zbl 0157.16901
Kumano-go, H.
1969
The characterization of differential operators with respect to the characteristic Cauchy problem. Zbl 0148.34104
Kumano-go, Hitoshi; Shinkai, Kenzo
1966
On propagation of regularity in space-variables for the solutions of differential equations with constant coefficients. Zbl 0145.35301
Kumano-go, H.
1966
On the characteristic Cauchy problem for partial differential equations. Zbl 0142.36903
Kumano-go, H.; Ise, K.
1965
On an example of non-uniqueness of solutions of the Cauchy problem for the wyve equation. Zbl 0148.08502
Kumano-go, H.
1963
On the uniqueness for the solution of the Cauchy problem. Zbl 0154.35304
Kumano-go, H.
1963
On the uniqueness of the solution of the Cauchy problem and the unique continuation theorem for elliptic equation. Zbl 0106.07602
Kumano-Go, Hitoshi
1962
On singular perturbation of linear partial differential equations with constant coefficients. II. Zbl 0100.30204
Kumano-Go, Hitoshi
1959
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### Cited in 83 Serials
25 Communications in Partial Differential Equations 21 Proceedings of the Japan Academy 21 Journal of Pseudo-Differential Operators and Applications 19 Journal of Functional Analysis 19 Publications of the Research Institute for Mathematical Sciences, Kyoto University 16 Journal of Differential Equations 15 Proceedings of the Japan Academy. Series A 10 Communications in Mathematical Physics 10 Journal of Mathematical Analysis and Applications 9 The Journal of Fourier Analysis and Applications 8 Bulletin des Sciences Mathématiques 6 Proceedings of the American Mathematical Society 6 Transactions of the American Mathematical Society 5 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 5 Mathematische Zeitschrift 5 Siberian Mathematical Journal 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Integral Equations and Operator Theory 4 Tohoku Mathematical Journal. Second Series 4 Annals of Global Analysis and Geometry 3 Archive for Rational Mechanics and Analysis 3 Mathematical Notes 3 Advances in Mathematics 3 Annales de l’Institut Fourier 3 Duke Mathematical Journal 3 Journal of Soviet Mathematics 3 Mathematische Annalen 3 Monatshefte für Mathematik 3 Osaka Journal of Mathematics 3 Stochastic Processes and their Applications 3 Annales de l’Institut Henri Poincaré. Physique Théorique 2 Journal d’Analyse Mathématique 2 Arkiv för Matematik 2 Reviews in Mathematical Physics 2 Collectanea Mathematica 2 Dissertationes Mathematicae 2 Inventiones Mathematicae 2 Kodai Mathematical Journal 2 Manuscripta Mathematica 2 Mathematische Nachrichten 2 Nagoya Mathematical Journal 2 Japan Journal of Industrial and Applied Mathematics 2 The Journal of Geometric Analysis 2 Mediterranean Journal of Mathematics 2 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 2 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Israel Journal of Mathematics 1 Journal of Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Transport Theory and Statistical Physics 1 Acta Mathematica 1 Calcolo 1 Czechoslovak Mathematical Journal 1 Functional Analysis and its Applications 1 Journal of the Mathematical Society of Japan 1 Mathematica Scandinavica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Rendiconti del Seminario Matematico della Università di Padova 1 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 1 Bulletin of the Korean Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Probability Theory and Related Fields 1 Revista Matemática Iberoamericana 1 Journal of Scientific Computing 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Bulletin of the American Mathematical Society. New Series 1 Potential Analysis 1 Russian Journal of Mathematical Physics 1 Advances in Applied Clifford Algebras 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Mathematical Physics, Analysis and Geometry 1 Communications in Contemporary Mathematics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Journal of the Institute of Mathematics of Jussieu 1 Analysis in Theory and Applications 1 Analysis and Applications (Singapore) 1 Communications in Mathematical Analysis 1 Banach Journal of Mathematical Analysis 1 Asian-European Journal of Mathematics 1 Science China. Mathematics 1 Advances in Pure and Applied Mathematics 1 Axioms 1 Stochastic and Partial Differential Equations. Analysis and Computations
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### Cited in 31 Fields
254 Partial differential equations (35-XX) 97 Operator theory (47-XX) 56 Global analysis, analysis on manifolds (58-XX) 44 Functional analysis (46-XX) 36 Quantum theory (81-XX) 26 Harmonic analysis on Euclidean spaces (42-XX) 20 Probability theory and stochastic processes (60-XX) 9 Numerical analysis (65-XX) 7 Differential geometry (53-XX) 7 Fluid mechanics (76-XX) 6 Topological groups, Lie groups (22-XX) 5 Integral equations (45-XX) 4 Mechanics of deformable solids (74-XX) 3 Abstract harmonic analysis (43-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Real functions (26-XX) 2 Potential theory (31-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Difference and functional equations (39-XX) 2 Geophysics (86-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Systems theory; control (93-XX)
### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2022-06-26T22:59:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45673322677612305, "perplexity": 1978.4499113771349}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103322581.16/warc/CC-MAIN-20220626222503-20220627012503-00760.warc.gz"} |
https://par.nsf.gov/biblio/10365864-thermal-emission-scattering-aligned-grains-plane-parallel-model-application-multiwavelength-polarization-hl-tau-disc | Thermal emission and scattering by aligned grains: Plane-parallel model and application to multiwavelength polarization of the HL Tau disc
ABSTRACT
Telescopes are now able to resolve dust polarization across circumstellar discs at multiple wavelengths, allowing the study of the polarization spectrum. Most discs show clear evidence of dust scattering through their unidirectional polarization pattern typically at the shorter wavelength of $\sim 870 \, \mu$m. However, certain discs show an elliptical pattern at ∼3 mm, which is likely due to aligned grains. With HL Tau, its polarization pattern at ∼1.3 mm shows a transition between the two patterns making it the first example to reveal such transition. We use the T-matrix method to model elongated dust grains and properly treat scattering of aligned non-spherical grains with a plane-parallel slab model. We demonstrate that a change in optical depth can naturally explain the polarization transition of HL Tau. At low optical depths, the thermal polarization dominates, while at high optical depths, dichroic extinction effectively takes out the thermal polarization and scattering polarization dominates. Motivated by results from the plane-parallel slab, we develop a simple technique to disentangle thermal polarization of the aligned grains T0 and polarization due to scattering S using the azimuthal variation of the polarization fraction. We find that, with increasing wavelength, the fractional polarization spectrum of the scattering component S more »
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NSF-PAR ID:
10365864
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
512
Issue:
3
Page Range or eLocation-ID:
p. 3922-3947
ISSN:
0035-8711
Publisher:
Oxford University Press
The size of dust grains, a, is key to the physical and chemical processes in circumstellar discs, but observational constraints of grain size remain challenging. (Sub)millimetre continuum observations often show a per cent-level polarization parallel to the disc minor axis, which is generally attributed to scattering by ${\sim}100\, \mu{\rm m}$-sized spherical grains (with a size parameter x ≡ 2$\pi$a/λ < 1, where λ is the wavelength). Larger spherical grains (with x greater than unity) would produce opposite polarization direction. However, the inferred size is in tension with the opacity index β that points to larger mm/cm-sized grains. We investigate the scattering-produced polarization by large irregular grains with a range of x greater than unity with optical properties obtained from laboratory experiments. Using the radiation transfer code, RADMC-3D, we find that large irregular grains still produce polarization parallel to the disc minor axis. If the original forsterite refractive index in the optical is adopted, then all samples can produce the typically observed level of polarization. Accounting for the more commonly adopted refractive index using the DSHARP dust model, only grains with x of several (corresponding to ∼mm-sized grains) can reach the same polarization level. Our results suggest that grains in discs canmore »
ABSTRACT Polarized dust continuum emission has been observed with Atacama Large Millimeter/submillimeter Array in an increasing number of deeply embedded protostellar systems. It generally shows a sharp transition going from the protostellar envelope to the disc scale, with the polarization fraction typically dropping from ${\sim } 5{{\ \rm per\ cent}}$ to ${\sim } 1{{\ \rm per\ cent}}$ and the inferred magnetic field orientations becoming more aligned with the major axis of the system. We quantitatively investigate these observational trends using a sample of protostars in the Perseus molecular cloud and compare these features with a non-ideal magnetohydrodynamic disc formation simulation. We find that the gas density increases faster than the magnetic field strength in the transition from the envelope to the disc scale, which makes it more difficult to magnetically align the grains on the disc scale. Specifically, to produce the observed ${\sim } 1{{\ \rm per\ cent}}$ polarization at ${\sim } 100\, \mathrm{au}$ scale via grains aligned with the B-field, even relatively small grains of $1\, \mathrm{\mu m}$ in size need to have their magnetic susceptibilities significantly enhanced (by a factor of ∼20) over the standard value, potentially through superparamagnetic inclusions. This requirement is more stringent for larger grains,more » | 2023-03-27T16:51:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6275834441184998, "perplexity": 2356.0434567988177}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948673.1/warc/CC-MAIN-20230327154814-20230327184814-00113.warc.gz"} |
https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Book%3A_Elementary_Number_Theory_(Raji)/2%3A_Prime_Numbers/2.2%3A_The_Infinitude_of_Primes | Skip to main content
# 2.2: The Infinitude of Primes
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$
$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$
We now show that there are infinitely many primes. There are several ways to prove this result. An alternative proof to the one presented here is given as an exercise. The proof we will provide was presented by Euclid in his book the Elements.
There are infinitely many primes.
We present the proof by contradiction. Suppose there are finitely many primes $$p_1, p_2, ...,p_n$$, where $$n$$ is a positive integer. Consider the integer $$Q$$ such that
$Q=p_1p_2...p_n+1.$
By Lemma 3, $$Q$$ has at least a prime divisor, say $$q$$. If we prove that $$q$$ is not one of the primes listed then we obtain a contradiction. Suppose now that $$q=p_i$$ for $$1\leq i\leq n$$. Thus $$q$$ divides $$p_1p_2...p_n$$ and as a result $$q$$ divides $$Q-p_1p_2...p_n$$. Therefore $$q$$ divides 1. But this is impossible since there is no prime that divides 1 and as a result $$q$$ is not one of the primes listed.
The following theorem discusses the large gaps between primes. It simply states that there are arbitrary large gaps in the series of primes and that the primes are spaced irregularly.
Given any positive integer $$n$$, there exists $$n$$ consecutive composite integers.
Consider the sequence of integers
$(n+1)!+2, (n+1)!+3,...,(n+1)!+n, (n+1)!+n+1$
Notice that every integer in the above sequence is composite because $$k$$ divides $$(n+1)!+k$$ if $$2\leq k\leq n+1$$ by [thm4].
Exercises
1. Show that the integer $$Q_n=n!+1$$, where $$n$$ is a positive integer, has a prime divisor greater than $$n$$. Conclude that there are infinitely many primes. Notice that this exercise is another proof of the infinitude of primes.
2. Find the smallest five consecutive composite integers.
3. Find one million consecutive composite integers.
4. Show that there are no prime triplets other than 3,5,7.
## Contributors
• Dr. Wissam Raji, Ph.D., of the American University in Beirut. His work was selected by the Saylor Foundation’s Open Textbook Challenge for public release under a Creative Commons Attribution (CC BY) license. | 2019-08-24T18:49:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8716592788696289, "perplexity": 170.86413100813016}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027321351.87/warc/CC-MAIN-20190824172818-20190824194818-00201.warc.gz"} |
https://par.nsf.gov/biblio/10373838 | This content will become publicly available on September 28, 2023
Self-similar diffuse boundary method for phase boundary driven flow
Interactions between an evolving solid and inviscid flow can result insubstantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such interactions include melting, sublimation, and deflagration, all of which exhibit bidirectional coupling, mass/heat transfer, and topological change of the solid-fluid interface. The diffuse interface method is a powerful technique that has been used to describe a wide range of solid-phase interface-driven phenomena. The implicit treatment of the interface eliminates the need for cumbersome interface tracking, and advances in adaptive mesh refinement have provided a way to sufficiently resolve diffuse interfaces without excessive computational cost. However, the general scale-invariant coupling of these techniques to flow solvers has been relatively unexplored. In this work, a robust method is presented for treating diffuse solid-fluid interfaces with arbitrary boundary conditions. Source terms defined over the diffuse region mimic boundary conditions at the solid-fluid interface, and it is demonstrated that the diffuse length scale has no adverse effects. To show the efficacy of the method, a one-dimensional implementation is introduced and tested for three types of boundaries: mass flux through the boundary, a moving boundary, and passive interaction of the boundary with an incident acoustic wave. more »
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10373838
Journal Name:
Physics of Fluids
ISSN:
1070-6631
3. We present a quasi-incompressible Navier–Stokes–Cahn–Hilliard (q-NSCH) diffuse interface model for two-phase fluid flows with variable physical properties that maintains thermodynamic consistency. Then, we couple the diffuse domain method with this two-phase fluid model – yielding a new q-NSCH-DD model – to simulate the two-phase flows with moving contact lines in complex geometries. The original complex domain is extended to a larger regular domain, usually a cuboid, and the complex domain boundary is replaced by an interfacial region with finite thickness. A phase-field function is introduced to approximate the characteristic function of the original domain of interest. The original fluid model, q-NSCH, is reformulated on the larger domain with additional source terms that approximate the boundary conditions on the solid surface. We show that the q-NSCH-DD system converges to the q-NSCH system asymptotically as the thickness of the diffuse domain interface introduced by the phase-field function shrinks to zero ( $\epsilon \rightarrow 0$ ) with $\mathcal {O}(\epsilon )$ . Our analytic results are confirmed numerically by measuring the errors in both $L^{2}$ and $L^{\infty }$ norms. In addition, we show that the q-NSCH-DD system not only allows the contact line to move on curved boundaries, but also makes the fluid–fluid interfacemore »
5. Transition from laminar to turbulent flow occurring over a smooth surface is a particularly important route to chaos in fluid dynamics. It often occurs via sporadic inception of spatially localized patches (spots) of turbulence that grow and merge downstream to become the fully turbulent boundary layer. A long-standing question has been whether these incipient spots already contain properties of high-Reynolds-number, developed turbulence. In this study, the question is posed for geometric scaling properties of the interface separating turbulence within the spots from the outer flow. For high-Reynolds-number turbulence, such interfaces are known to display fractal scaling laws with a dimension$D≈7/3$, where the 1/3 excess exponent above 2 (smooth surfaces) follows from Kolmogorov scaling of velocity fluctuations. The data used in this study are from a direct numerical simulation, and the spot boundaries (interfaces) are determined by using an unsupervised machine-learning method that can identify such interfaces without setting arbitrary thresholds. Wide separation between small and large scales during transition is provided by the large range of spot volumes, enabling accurate measurements of the volume–area fractal scaling exponent. Measurements show a dimension of$D=2.36±0.03$over almost 5 decades of spot volume, i.e., trends fully consistent with high-Reynolds-number turbulence. Additional observations pertainingmore » | 2023-04-02T09:01:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5316229462623596, "perplexity": 1023.4716406970551}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950422.77/warc/CC-MAIN-20230402074255-20230402104255-00602.warc.gz"} |
https://pdglive.lbl.gov/DataBlock.action?node=S067D1 | #### (C) Other neutrino mixing results
The LSND collaboration reported in AGUILAR 2001 a signal which is consistent with ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ oscillations. In a three neutrino framework, this would be a measurement of $\theta _{12}$ and $\Delta \mathit m{}^{2}_{21}$. This does not appear to be consistent with most of the other neutrino data. The following listings include results from ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ , ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ appearance and ${{\mathit \nu}_{{\mu}}}$ , ${{\overline{\mathit \nu}}_{{\mu}}}$ , ${{\mathit \nu}_{{e}}}$ , and ${{\overline{\mathit \nu}}_{{e}}}$ disappearance experiments, and searches for $\mathit CPT$ violation.
#### $\Delta \mathit m{}^{2}$ for sin$^2(2{}\theta )$ = 1 ( ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ )
VALUE (eV${}^{2}$) CL% DOCUMENT ID TECN COMMENT
• • We do not use the following data for averages, fits, limits, etc. • •
$0.03\text{ to }0.55$ 90 1
2021
MBNE MiniBooNE ${{\mathit \nu}}$ ,${{\overline{\mathit \nu}}}$ combined
$0.03\text{ to }0.05$ 90 2
2018 C
MBNE MiniBooNE ${{\mathit \nu}}$ ,${{\overline{\mathit \nu}}}$ combined
$0.015\text{ to }0.050$ 90 3
2013 A
MBNE MiniBooNE
$<0.34$ 90 4
2012
MBNE MiniBooNE/SciBooNE
$<0.034$ 90
2007
MBNE MiniBooNE
$<0.0008$ 90
2004
K2K Water Cherenkov
$<0.4$ 90
2003
NOMD CERN SPS
$<2.4$ 90
2002
NTEV NUTEV FNAL
5
2001
LSND ${{\mathit \nu}}$ ${{\mathit \mu}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ osc.prob.
$0.03\text{ to }0.3$ 95 6
1998
LSND ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$
$<2.3$ 90 7
1996
CHARM/CDHS
$<0.9$ 90
1994 C
CHM2 CERN SPS
$<0.09$ 90
1986
HLBC BEBC CERN PS
1 AGUILAR-AREVALO 2021 result is based on a total of $18.75 \times 10^{20}$ POT in neutrino mode, and $11.27 \times 10^{20}$ POT in anti-neutrino mode. Best fit at 0.043 eV${}^{2}$. The allowed region does not extend to large $\Delta$m${}^{2}$. The quoted value is the entire allowed region of $\Delta$m${}^{2}$ at 90$\%$ C.L. for all values of sin$^2(2\theta )$. Supersedes AGUILAR-AREVALO 2018C.
2 AGUILAR-AREVALO 2018C result is based on ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ appearance of $460.5$ $\pm99.0$ events; The best fit value is $\Delta$m${}^{2}$ = 0.041 eV${}^{2}$. Superseded by AGUILAR-AREVALO 2021 .
3 AGUILAR-AREVALO 2013A result is based on ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ appearance of $162.0$ $\pm47.8$ events; marginally compatible with twoneutrino oscillations. The best fit value is $\Delta$m${}^{2}$ = 3.14 eV${}^{2}$.
4 MAHN 2012 is a combined spectral fit of MiniBooNE and SciBooNE neutrino data with the range of $\Delta$m${}^{2}$ up to 25 eV${}^{2}$. The best limit is 0.04 at 7 eV${}^{2}$.
5 AGUILAR 2001 is the final analysis of the LSND full data set. Search is made for the ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ oscillations using ${{\mathit \nu}_{{\mu}}}$ from ${{\mathit \pi}^{+}}$ decay in flight by observing beam-on electron events from ${{\mathit \nu}_{{e}}}$ ${}^{}\mathrm {C}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit X}}$ . Present analysis results in $8.1$ $\pm12.2$ $\pm1.7$ excess events in the 60$<\mathit E_{{{\mathit e}} }<200$ MeV energy range, corresponding to oscillation probability of $0.10$ $\pm0.16$ $\pm0.04\%$. This is consistent, though less significant, with the previous result of ATHANASSOPOULOS 1998 , which it supersedes. The present analysis uses selection criteria developed for the decay at rest region, and is less effective in removing the background above 60 MeV than ATHANASSOPOULOS 1998 .
6 ATHANASSOPOULOS 1998 is a search for the ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ oscillations using ${{\mathit \nu}_{{\mu}}}$ from ${{\mathit \pi}^{+}}$ decay in flight. The 40 observed beam-on electron events are consistent with ${{\mathit \nu}_{{e}}}$ ${}^{}\mathrm {C}$ $\rightarrow$ ${{\mathit e}^{-}}$ X; the expected background is $21.9$ $\pm2.1$. Authors interpret this excess as evidence for an oscillation signal corresponding to oscillations with probability ($0.26$ $\pm0.10$ $\pm0.05)\%$. Although the significance is only $2.3~\sigma$, this measurement is an important and consistent cross check of ATHANASSOPOULOS 1996 who reported evidence for ${{\overline{\mathit \nu}}_{{\mu}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ oscillations from ${{\mathit \mu}^{+}}$ decay at rest. See also ATHANASSOPOULOS 1998B.
7 LOVERRE 1996 uses the charged-current to neutral-current ratio from the combined CHARM (ALLABY 1986 ) and CDHS (ABRAMOWICZ 1986 ) data from 1986.
References:
AGUILAR-AREVALO 2021
PR D103 052002 Updated MiniBooNE neutrino oscillation results with increased data and new background studies
AGUILAR-AREVALO 2018C
PRL 121 221801 Significant Excess of ElectronLike Events in the MiniBooNE Short-Baseline Neutrino Experiment
AGUILAR-AREVALO 2013A
PRL 110 161801 Improved Search for ${{\overline{\mathit \nu}}_{{\mu}}}$ $\leftrightarrow{{\overline{\mathit \nu}}_{{e}}}$ Oscillations in the MiniBooNE Experiment
MAHN 2012
PR D85 032007 Dual Baseline Search for Muon Neutrino Disappearance at 0.5 eV${}^{2}$ < $\Delta$m${}^{2}$ < 40 eV${}^{2}$
AGUILAR-AREVALO 2007
PRL 98 231801 Search for Electron Neutrino Appearance at the $\Delta \mathit m{}^{2}\sim{}$1 eV${}^{2}$ Scale
AHN 2004
PRL 93 051801 Search for Electron Neutrino Appearance in 250 km Long-baseline Experiment
ASTIER 2003
PL B570 19 Search for ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ Oscillations in the NOMAD Experiment
AVVAKUMOV 2002
PRL 89 011804 A Search for ${{\mathit \nu}_{{\mu}}}$ $-{{\mathit \nu}_{{e}}}$ and ${{\overline{\mathit \nu}}_{{\mu}}}$ $-{{\overline{\mathit \nu}}_{{e}}}$ Oscillations at NUTeV
AGUILAR 2001
PR D64 112007 Evidence for Neutrino Oscillations from the Observation of ${{\overline{\mathit \nu}}_{{e}}}$ Appearance in a ${{\overline{\mathit \nu}}_{{\mu}}}$ Beam
ATHANASSOPOULOS 1998
PRL 81 1774 Evidence for ${{\mathit \nu}_{{\mu}}}$ $\leftrightarrow$ ${{\mathit \nu}_{{e}}}$ Oscillations from the LSND
LOVERRE 1996
PL B370 156 Limits on ${{\mathit \nu}_{{\mu}}}$ Oscillations from the Measurement of the Ratio of 0${{\mathit \mu}^{\pm}}$ to 1${{\mathit \mu}^{\pm}}$ Events at the CERN Narrow Band Neutrino Beam
VILAIN 1994C
ZPHY C64 539 Search for Muon to Electron Neutrino Oscillations
ANGELINI 1986
PL B179 307 New Experimental Limits on ${{\mathit \nu}_{{\mu}}}$ $\leftrightarrow$ ${{\mathit \nu}_{{e}}}$ Oscillations | 2022-12-09T13:26:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7655282616615295, "perplexity": 4274.783277667421}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711396.19/warc/CC-MAIN-20221209112528-20221209142528-00672.warc.gz"} |
http://inpa-old.lbl.gov/INPA/Abstracts/030411.html | ### Status of the KamLAND experiment
Thomas O'Donnell
LBNL
Abstract:
KamLAND is a one kiloton liquid scintillator detector which studies neutrino oscillation with reactor-antineutrinos at an average baseline of 180km. The experiment was the first to report reactor-antinuetrinodisappearance consistent with the neutrino mass splitting favored by the LMA-MSW solution to the Solar Neutrino Problem. Furthermore, KamLAND observed distortion of the reactor spectrum -- the fingerprint of mass-driven flavor oscillation -- and is uniquely sentitive to the mass splitting $\Delta m^{2}_{21}$. In this talk I will describe the experiment and present the results of the most recent data set which amounts to a total exposure of $3.49 \times 10^{32}$ proton-years and includes data collected with more favorable background conditions achieved by a detector radiopurity upgrade. Under the assumption of CPT invariance, a three-flavor analysis combining KamLAND and solar data yields best-fit values of the oscillation parameters: $\Delta m^{2}_{21} = 7.50^{+0.19}_{-0.20} \times 10^{-5} \rm{eV}^{2}$, $\tan^{2} \theta_{12} = 0.452^{+0.035}_{-0.033}$, and weak constraints on $\theta_{13}$.
Finally, as the current phase of data taking draws to an end, I will briefly describe KamLAND-Zen --- a plan to repurpose the detector to search for neutrino-less double beta decay of $^{136}$Xe. | 2017-03-25T07:49:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.759300947189331, "perplexity": 1884.5374005322064}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188891.62/warc/CC-MAIN-20170322212948-00274-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://2017-ucsc-metagenomics.readthedocs.io/en/latest/circos_tutorial.html | # Using and Installing Circos¶
Circos is a powerful visualization tool that allows for the creation of circular graphics to display complex genomic data (e.g. genome comparisons). On top of the circular ideogram generated can be layered any number of graphical information (heatmaps, scatter plots, etc.).
The goals of this tutorial are to:
• Install circos on your Ubuntu system
• Use Circos to visualize our metagenomic data
Note: Beyond this brief crash course , circos is very well-documented and has a great series of tutorials and course materials that are useful.
## Installing Circos¶
You’ll need to install one additional ubuntu package, libgd:
sudo apt-get -y install libgd-perl
cd
mkdir circos
cd circos
curl -O http://dib-training.ucdavis.edu.s3.amazonaws.com/metagenomics-scripps-2016-10-12/circos-0.69-3.tar.gz
tar -xvzf circos-0.69-3.tar.gz
Circos runs within Perl and as such does not need to be compiled to run. So, we can just add the location of circos to our path variable. (Alternatively, you can append this statement to the end of your .bashrc file.)
export PATH=~/circos/circos-0.69-3/bin:$PATH Circos does, however, require quite a few additional perl modules to operate correctly. To see what modules are missing and need to be downloaded type the following: circos -modules > modules Now, to download all of these we will be using CPAN, a package manager for perl. We are going to pick out all the missing modules and then loop over those modules and download them using cpan. grep missing modules |cut -f13 -d " " > missing_modules for mod in$(cat missing_modules);
do
sudo cpan install \$mod;
done
This will take a while to run. When it is done check that you now have all modules downloaded by typing:
circos -modules
If you got all ‘ok’ then you are good to go!
And with that, circos should be up and ready to go. Run the example by navigating to the examples folder within the circos folder.
cd ~/circos/circos-0.69-3/example
bash run
This will take a little bit to run but should generate a file called circos.png. Open it and you can get an idea of the huge variety of things that are possible with circos and a lot of patience. We will not be attempting anything that complex today, however.
## Visualizing Gene Coverage and Orientation¶
First, let’s make a directory where we will be doing all of our work for plotting:
mkdir ~/circos/plotting
cd ~/circos/plotting
Now, link in the *gff file output from prokka (which we will use to define the location of genes in each of our genomes), the genome assembly file final.contigs.fa, and the SRR*counts files that we generated with salmon:
ln -fs ~/data/prokka_annotation/*gff .
ln -fs ~/data/final.contigs.fa .
ln -fs ~/quant/*counts .
We also need to grab a set of useful scripts and config files for this plotting exercise:
curl -L -O https://github.com/ngs-docs/2016-metagenomics-sio/raw/master/circos-build.tar.gz
tar -xvzf circos-build.tar.gz
curl -L -O https://s3-us-west-1.amazonaws.com/dib-training.ucdavis.edu/metagenomics-scripps-2016-10-12/subset_assembly.fa.gz
gunzip subset_assembly.fa.gz
mv subset_assembly.fa final.contigs.fa
We are going to limit the data we are trying to visualize and get longest contigs from our assembly. We can do this using a script from the khmer package:
extract-long-sequences.py final.contigs.fa -l 24000 -o final.contigs.long.fa
cp ~/data/quant/*counts .
Next, we will run a script that processes the data from the the files that we just moved to create circos-acceptable files. This is really the crux of using circos: figuring out how to get your data into the correct format.
python parse_data_for_circos.py
If you are interested– take a look at the script and the input files to see how these data were manipulated.
Circos operates off of three main types of files: 1) a config files that dictate the style and inputs to your circos plot, 2) a karyotype file that defines the size and layout of your “chromosomes”, and 3) any data files that you call in your config file that detail attributes you want to plot.
The above script generated our karyotype file and four different data files. What are they? How are they oriented?
Now, we all that is left is actually running circos. Navigate into the circos-build directory and type circos:
cd circos-build
circos
This command should generate an circos.svg and circos.png. Check out the circos.png!
Now, let’s take a look at the file that controls this crazy figure– circos.config.
Try changing a few parameters– colors, radius, size, to see what you can do. Again, if you are into this type of visualization, do check out the extensive tutorial.
LICENSE: This documentation and all textual/graphic site content is released under Creative Commons - 0 (CC0) -- fork @ github. | 2018-03-19T06:32:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20306113362312317, "perplexity": 4019.4725952762687}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646602.39/warc/CC-MAIN-20180319062143-20180319082143-00258.warc.gz"} |
https://blog.qarnot.com/distributed_monte_carlo_simulations/ | < Back
# Distributed Monte Carlo simulations
by Paul - January 19, 2017 - Basics
CC-BY / jgilhutton
In this article, we’ll describe how to use Qarnot computing HPC platform to perform distributed Monte Carlo simulation. As a ‘hello world’ Monte Carlo workload, we’ll use a basic $\pi$ estimation.
## Estimating $\pi$ using Monte Carlo Simulation
Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to obtain numerical results. To estimate $\pi$, we randomly place $N$ points in a square of side$1$ and count $P$, the number of points that are at a distance $d<1$ from the origin as shown in the following figure.
When $N$ is large, $P/N$ converges towards $\pi/4$, the surface of the quarter circle. This being said, the following code will help you test this method.
You can notice the convergence toward $\pi$ when you increase the number of samples but also the non deterministic behaviour of the piMc function.
To make the piMc function deterministic, you can seed the random generator. Then, seeds can be used to split the computation into multiple independant sampling rounds.
As you can see, the precision increase with both the number of samples per split and the number of split.
## Let’s use Qarnot computing HPC service
First let’s save the following script in a piMc.py file.
This script simply accepts the seed and number of samples as arguments.
Now, let’s use Qarnot python SDK to launch the distributed computation. You’ll need to launch the following qPiMc.py script after replacing with the key you obtained by registering at Qarnot computing.
By executing this script, you’ll :
• connect to Qarnot API by using your API token
• create a task composed of 10 frames numbered from 1 to 10
• upload the qPiMc.py to be executed on each node
• select the right docker container to be deployed on each node (here, we use anaconda, a sledgehammer to crack a nut…)
• define the command to be launched within containers
• launch the task and print the aggregated stdout when all nodes exited (approx. 1 minute from cold boot to shutdown)
During the execution, you can follow the progress on the Qarnot console. Here is an example with 100,000,000 samples per seed :
## Next steps!
With Qarnot HPC services, you can go well beyond what could be described in this article. You will probably come up with many more interesting use cases. So, go ahead! Try it now, and share your feedback with the community, so that we can keep improving on this product.
[1] Monte Carlo method: wikipedia
[2] Parallel Pi Calculation using Python’s multiprocessing module: github
[3] Qarnot computing Developer & API documentation: qarnot | 2020-01-21T21:02:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37609100341796875, "perplexity": 1680.3940766166727}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250605075.24/warc/CC-MAIN-20200121192553-20200121221553-00264.warc.gz"} |
https://www.usgs.gov/policies-and-notices | # Policies and Notices
These information describes the principal policies and other important notices that govern information posted on USGS websites. | 2021-04-13T18:48:09 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9580733180046082, "perplexity": 8274.471217785456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038074941.13/warc/CC-MAIN-20210413183055-20210413213055-00006.warc.gz"} |
https://pos.sissa.it/294/056/ | Volume 294 - The 3rd International Symposium on “Quest for the Origin of Particles and the Universe" (KMI2017) - Poster Presentations
Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum in Run2
Y. Sano
Full text: pdf
Pre-published on: 2017 November 22
Published on: 2017 November 24
Abstract
Despite the absence of experimental evidence, weak scale supersymmetry remains one of the best motivated and studied Standard Model extensions. The recent increase in the center of mass energy of the proton-proton collisions at $\sqrt{s}=13 {\rm TeV}$ gives a unique opportunity to extend the sensitivity to production of supersymmetric particles at the Large Hadron Collider. This paper summarises the latest ATLAS result on inclusive searches for promptly decaying supersymmetric squarks and gluinos in events containing jets, missing transverse momentum and no light lepton using data of $13.3~{\rm fb^{-1}}$.
DOI: https://doi.org/10.22323/1.294.0056
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2020-06-05T00:57:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28817522525787354, "perplexity": 2349.6859859365163}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348492295.88/warc/CC-MAIN-20200604223445-20200605013445-00367.warc.gz"} |
http://www.khronos.org/registry/vulkan/specs/1.2-extensions/man/html/VkSurfaceFullScreenExclusiveWin32InfoEXT.html | ## C Specification
The VkSurfaceFullScreenExclusiveWin32InfoEXT structure is defined as:
typedef struct VkSurfaceFullScreenExclusiveWin32InfoEXT {
VkStructureType sType;
const void* pNext;
HMONITOR hmonitor;
} VkSurfaceFullScreenExclusiveWin32InfoEXT;
## Members
• sType is the type of this structure.
• pNext is NULL or a pointer to an extension-specific structure.
• hmonitor is the Win32 HMONITOR handle identifying the display to create the surface with.
## Description
Note If hmonitor is invalidated (e.g. the monitor is unplugged) during the lifetime of a swapchain created with this structure, operations on that swapchain will return VK_ERROR_OUT_OF_DATE_KHR.
Note It’s the responsibility of the application to change the display settings of the targeted Win32 display using the appropriate platform APIs. Such changes may alter the surface capabilities reported for the created surface.
Valid Usage
• hmonitor must be a valid HMONITOR
Valid Usage (Implicit)
• sType must be VK_STRUCTURE_TYPE_SURFACE_FULL_SCREEN_EXCLUSIVE_WIN32_INFO_EXT
## Document Notes
For more information, see the Vulkan Specification
This page is extracted from the Vulkan Specification. Fixes and changes should be made to the Specification, not directly.
Copyright (c) 2014-2020 Khronos Group. This work is licensed under a Creative Commons Attribution 4.0 International License. | 2020-02-27T18:17:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.248063325881958, "perplexity": 9936.728650774925}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146744.74/warc/CC-MAIN-20200227160355-20200227190355-00408.warc.gz"} |
https://par.nsf.gov/biblio/10130283-search-non-resonant-higgs-boson-pair-production-bb-final-state-atlas-detector-pp-collisions-tev | Search for non-resonant Higgs boson pair production in the bbℓνℓν final state with the ATLAS detector in pp collisions at $s=13$ TeV | 2022-12-03T03:29:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9861798286437988, "perplexity": 1180.9710971564036}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710918.58/warc/CC-MAIN-20221203011523-20221203041523-00123.warc.gz"} |
https://par.nsf.gov/biblio/10349849-dark-energy-survey-year-results-clustering-redshifts-calibration-weak-lensing-source-redshift-distributions-redmagic-boss-eboss | This content will become publicly available on December 24, 2022
Dark Energy Survey Year 3 Results: clustering redshifts – calibration of the weak lensing source redshift distributions with redMaGiC and BOSS/eBOSS
ABSTRACT We present the calibration of the Dark Energy Survey Year 3 (DES Y3) weak lensing (WL) source galaxy redshift distributions n(z) from clustering measurements. In particular, we cross-correlate the WL source galaxies sample with redMaGiC galaxies (luminous red galaxies with secure photometric redshifts) and a spectroscopic sample from BOSS/eBOSS to estimate the redshift distribution of the DES sources sample. Two distinct methods for using the clustering statistics are described. The first uses the clustering information independently to estimate the mean redshift of the source galaxies within a redshift window, as done in the DES Y1 analysis. The second method establishes a likelihood of the clustering data as a function of n(z), which can be incorporated into schemes for generating samples of n(z) subject to combined clustering and photometric constraints. Both methods incorporate marginalization over various astrophysical systematics, including magnification and redshift-dependent galaxy-matter bias. We characterize the uncertainties of the methods in simulations; the first method recovers the mean z of tomographic bins to RMS (precision) of ∼0.014. Use of the second method is shown to vastly improve the accuracy of the shape of n(z) derived from photometric data. The two methods are then applied to the DES Y3 data.
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
Award ID(s):
Publication Date:
NSF-PAR ID:
10349849
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
510
Issue:
1
Page Range or eLocation-ID:
1223 to 1247
ISSN:
0035-8711
2. ABSTRACT We develop a novel data-driven method for generating synthetic optical observations of galaxy clusters. In cluster weak lensing, the interplay between analysis choices and systematic effects related to source galaxy selection, shape measurement, and photometric redshift estimation can be best characterized in end-to-end tests going from mock observations to recovered cluster masses. To create such test scenarios, we measure and model the photometric properties of galaxy clusters and their sky environments from the Dark Energy Survey Year 3 (DES Y3) data in two bins of cluster richness $\lambda \in [30; 45)$, $\lambda \in [45; 60)$ and three bins in cluster redshift ($z\in [0.3; 0.35)$, $z\in [0.45; 0.5)$ and $z\in [0.6; 0.65)$. Using deep-field imaging data, we extrapolate galaxy populations beyond the limiting magnitude of DES Y3 and calculate the properties of cluster member galaxies via statistical background subtraction. We construct mock galaxy clusters as random draws from a distribution function, and render mock clusters and line-of-sight catalogues into synthetic images in the same format as actual survey observations. Synthetic galaxy clusters are generated from real observational data, and thus are independent from the assumptions inherent to cosmological simulations. The recipe can be straightforwardly modified to incorporate extra information, andmore »
3. ABSTRACT Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broad-band imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. A hierarchical Bayesian model has recently been developed to estimate those from the robust combination of prior information, photometry of single galaxies, and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-z’s tightens the redshift posteriors and overcomes biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of $\Deltamore » 4. ABSTRACT In this work, we present the galaxy clustering measurements of the two DES lens galaxy samples: a magnitude-limited sample optimized for the measurement of cosmological parameters, maglim, and a sample of luminous red galaxies selected with the redmagic algorithm. maglim/redmagic sample contains over 10 million/2.5 million galaxies and is divided into six/five photometric redshift bins spanning the range z ∈ [0.20, 1.05]/z ∈ [0.15, 0.90]. Both samples cover 4143$\deg ^2\$ over which we perform our analysis blind, measuring the angular correlation function with an S/N ∼ 63 for both samples. In a companion paper, these measurements of galaxy clustering are combined with the correlation functions of cosmic shear and galaxy–galaxy lensing of each sample to place cosmological constraints with a 3 × 2pt analysis. We conduct a thorough study of the mitigation of systematic effects caused by the spatially varying survey properties and we correct the measurements to remove artificial clustering signals. We employ several decontamination methods with different configurations to ensure the robustness of our corrections and to determine the systematic uncertainty that needs to be considered for the final cosmology analyses. We validate our fiducial methodology using lognormal mocks, showing that our decontamination procedure induces biases no greatermore » | 2022-11-30T04:59:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46502789855003357, "perplexity": 1644.747693074378}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710719.4/warc/CC-MAIN-20221130024541-20221130054541-00130.warc.gz"} |
https://bison.inl.gov/Documentation/source/materials/tensor_mechanics/UO2VolumetricSwellingEigenstrain.aspx | # UOvar element = document.getElementById("moose-equation-cf712ccd-f283-4539-a863-cdfee90ead9a");katex.render("_2", element, {displayMode:false,throwOnError:false}); Volumetric Swelling Eigenstrain
Calculates and sums the change in fuel pellet volume due to densification and fission product release. This class applies a volumetric strain correction before adding the strain from this class to the diagonal entries of the eigenstrain tensor.
## Description
Swelling due to solid fission products, gaseous fission products, and densification all contribute to the change in volume of a UO fuel pellet. The contributions from all three of these components are modeled in UO2VolumetricSwellingEigenstrain.
## Densification of the Fuel
Fuel densification is computed using the ESCORE empirical model (Rashid et al., 2004) given by: (1) where is the densification strain, is the total densification that can occur (given as a fraction of theoretical density), Bu is the burnup, and Bu is the burnup at which densification is complete. (2) In Eq. 2 the variable for temperature, , is defined in Celcius. Note that the parameter given in (Rashid et al., 2004) for temperatures below 750C; the values in Eq. 2 are used in Bison to eliminate the discontinuity in .
### Application to MOX Fuel
In MATPRO (Allison et al., 1993), the same model is provided for UO and MOX. Because this correlation relies on a wide database, this model is also used in Bison for MOX densification.
## Fission Product Swelling
Empirical relations from MATPRO (Allison et al., 1993) are available in Bison for calculating the swelling due to both solid and gaseous fission products. The same model is provided for both UO and MOX.
Solid fission product swelling is expressed as a simple linear function of burnup: (3) where is the volumetric solid swelling increment, Bu the burnup increment (fissions/atoms-U), and is the density (kg/m).
Swelling due to gaseous fission products is approximated by a semi-empirical model: (4) where is the volumetric gas swelling increment, and are the burnup and burnup increment (fissions/atoms-U), respectively, is the density (kg/m) and is the temperature (K).
Figure 1: UO gaseous and total swelling, as a function of temperature and burnup, based on the MATPRO correlations.
Figure 1 shows a plot of the gaseous and total fission product swelling as a function of temperature and burnup. The MATPRO correlations (Allison et al., 1993) indicate that gaseous swelling does not become significant until above 1500 K and is saturated at a burnup of 20 MWd/kgU.
Alternatively the gaseous fission product swelling can be calculated using a physics-based model that takes into account the coupling with the fission gas release (see Sifgrs ).
## Example Input Syntax
[./fuel_swelling]
type = UO2VolumetricSwellingEigenstrain
gas_swelling_model_type = MATPRO
block = '1 2 3 4 5 6 7'
temperature = temp
burnup = burnup
complete_burnup = 5
total_densification = 0.01
eigenstrain_name = swell
initial_fuel_density = 10430.0
save_densification = true
save_solid_swelling = true
[../]
(test/tests/tensor_mechanics/uo2_eigenstrains/uo2_vswelling/swelling_tm.i)
The eigenstrain_name parameter value must also be set for the strain calculator, and an example parameter setting is shown below:
[./fuel_strain]
type = ComputeFiniteStrain
block = '1 2 3 4 5 6 7'
eigenstrain_names = 'fuelthermal_strain swell'
[../]
(test/tests/tensor_mechanics/uo2_eigenstrains/uo2_vswelling/swelling_tm.i)
## Input Parameters
• temperatureCoupled Temperature in Kelvin
C++ Type:std::vector
Description:Coupled Temperature in Kelvin
• initial_fuel_densityInitial fuel density in kg-UO2/m^3
C++ Type:double
Description:Initial fuel density in kg-UO2/m^3
• eigenstrain_nameMaterial property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
C++ Type:std::string
Description:Material property name for the eigenstrain tensor computed by this model. IMPORTANT: The name of this property must also be provided to the strain calculator.
### Required Parameters
• initial_porosity0.05initial fuel porosity (dimensionless)
Default:0.05
C++ Type:double
Description:initial fuel porosity (dimensionless)
• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.
Default:True
C++ Type:bool
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.
• base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
C++ Type:std::string
Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases
• include_solid_swellingTrueShould the calculation of volumetric swelling include swelling due to solid fision products
Default:True
C++ Type:bool
Description:Should the calculation of volumetric swelling include swelling due to solid fision products
• save_solid_swellingFalseShould the solid swelling be saved in a material property
Default:False
C++ Type:bool
Description:Should the solid swelling be saved in a material property
• complete_burnup5The burnup at which densification is complete input in units of MWd/kgU
Default:5
C++ Type:double
Description:The burnup at which densification is complete input in units of MWd/kgU
• constant_dens_c_dFalseWhether to use a constant C_d (1.0)
Default:False
C++ Type:bool
Description:Whether to use a constant C_d (1.0)
• total_densification0.01The densification that will occur given as a fraction of theoretical density
Default:0.01
C++ Type:double
Description:The densification that will occur given as a fraction of theoretical density
• include_gas_swellingTrueShould the calculation of volumetric swelling include swelling due to gas fision products
Default:True
C++ Type:bool
Description:Should the calculation of volumetric swelling include swelling due to gas fision products
• blockThe list of block ids (SubdomainID) that this object will be applied
C++ Type:std::vector
Description:The list of block ids (SubdomainID) that this object will be applied
• gas_swelling_model_typeSIFGRSWhich type of model to use to calculate the gaseous swelling. Choices are SIFGRS MATPRO. If you select SIFGRS, the SIFGRS model must be included in the input file.
Default:SIFGRS
C++ Type:MooseEnum
Description:Which type of model to use to calculate the gaseous swelling. Choices are SIFGRS MATPRO. If you select SIFGRS, the SIFGRS model must be included in the input file.
• include_densificationTrueShould the calculation of volumetric swelling include volumetric changes due to densification
Default:True
C++ Type:bool
Description:Should the calculation of volumetric swelling include volumetric changes due to densification
• save_densificationFalseShould the densification be saved in a material property
Default:False
C++ Type:bool
Description:Should the densification be saved in a material property
• boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector
Description:The list of boundary IDs from the mesh where this boundary condition applies
• burnup_functionBurnup function
C++ Type:BurnupFunctionName
Description:Burnup function
• burnupCoupled Burnup
C++ Type:std::vector
Description:Coupled Burnup
### Optional Parameters
• enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Description:Set the enabled status of the MooseObject.
• use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
• control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector
Description:Adds user-defined labels for accessing object parameters via control logic.
• seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Description:The seed for the master random number generator
• implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Description:Determines whether this object is calculated using an implicit or explicit form
• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
• gaseous_swelling_scale_factor1Scale factor to be applied to the gaseous swelling strain when gas swelling model type is MATPRO. Used for calibration and sensitivity studies
Default:1
C++ Type:double
Description:Scale factor to be applied to the gaseous swelling strain when gas swelling model type is MATPRO. Used for calibration and sensitivity studies
• solid_swelling_scale_factor1Scale factor to be applied to the solid swelling strain. Used for calibration and sensitivity studies
Default:1
C++ Type:double
Description:Scale factor to be applied to the solid swelling strain. Used for calibration and sensitivity studies
• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector
Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object
## References
1. C. M. Allison, G. A. Berna, R. Chambers, E. W. Coryell, K. L. Davis, D. L. Hagrman, D. T. Hagrman, N. L. Hampton, J. K. Hohorst, R. E. Mason, M. L. McComas, K. A. McNeil, R. L. Miller, C. S. Olsen, G. A. Reymann, and L. J. Siefken. SCDAP/RELAP5/MOD3.1 code manual, volume IV: MATPRO–A library of materials properties for light-water-reactor accident analysis. Technical Report NUREG/CR-6150, EGG-2720, Idaho National Engineering Laboratory, 1993.[BibTeX]
2. Y Rashid, R Dunham, and R Montgomery. Fuel Analysis and Licensing Code: FALCON MOD01. Technical Report, Electric Power Research Institute, December 2004.[BibTeX] | 2020-11-28T02:49:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5323414206504822, "perplexity": 6640.780943052745}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141194982.45/warc/CC-MAIN-20201128011115-20201128041115-00403.warc.gz"} |
http://popflock.com/learn?s=Spinor_field | Spinor Field
Get Spinor Field essential facts below. View Videos or join the Spinor Field discussion. Add Spinor Field to your PopFlock.com topic list for future reference or share this resource on social media.
Spinor Field
In differential geometry, given a spin structure on an n-dimensional orientable Riemannian manifold (M, g), a section of the spinor bundle S is called a spinor field. A spinor bundle is the complex vector bundle ${\displaystyle \pi _{\mathbf {S} }:{\mathbf {S} }\to M\,}$ associated to the corresponding principal bundle ${\displaystyle \pi _{\mathbf {P} }:{\mathbf {P} }\to M\,}$ of spin frames over M via the spin representation of its structure group Spin(n) on the space of spinors ?n.
In particle physics, particles with spin s are described by a 2s-dimensional spinor field, where s is an integer or a half-integer. Fermions are described by spinor field, while bosons by tensor field.
## Formal definition
Let (P, FP) be a spin structure on a Riemannian manifold (M, g) that is, an equivariant lift of the oriented orthonormal frame bundle ${\displaystyle \mathrm {F} _{SO}(M)\to M}$ with respect to the double covering ${\displaystyle \rho :{\mathrm {Spin} }(n)\to {\mathrm {SO} }(n)\,.}$
One usually defines the spinor bundle[1] ${\displaystyle \pi _{\mathbf {S} }:{\mathbf {S} }\to M\,}$ to be the complex vector bundle
${\displaystyle {\mathbf {S} }={\mathbf {P} }\times _{\kappa }\Delta _{n}\,}$
associated to the spin structure P via the spin representation ${\displaystyle \kappa :{\mathrm {Spin} }(n)\to {\mathrm {U} }(\Delta _{n}),\,}$ where U(W) denotes the group of unitary operators acting on a Hilbert space W.
A spinor field is defined to be a section of the spinor bundle S, i.e., a smooth mapping ${\displaystyle \psi :M\to {\mathbf {S} }\,}$ such that ${\displaystyle \pi _{\mathbf {S} }\circ \psi :M\to M\,}$ is the identity mapping idM of M.
## Notes
1. ^ Friedrich, Thomas (2000), Dirac Operators in Riemannian Geometry, p. 53
## References
This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0. | 2021-11-28T14:04:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 9, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7937025427818298, "perplexity": 672.671398774568}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358560.75/warc/CC-MAIN-20211128134516-20211128164516-00048.warc.gz"} |
https://www.conicet.gov.ar/new_scp/detalle.php?keywords=&id=32676&congresos=yes&detalles=yes&congr_id=7497669 | In this talk we present some recent results obtained in a joint work with K. Li and J. M. Martell, about a multivariable Rubio de Francia extrapolation theorem for multilinear Muckenhoupt classes $A_{\vec{p}}$, and also some extensions to more general classes of weights.To illustrate the power of extrapolation methods we will present some applications of the beforementioned results and some mixed weak-type weighted estimates obtained in a joint work with K. Li and C. P\'erez. | 2021-04-13T12:48:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30888572335243225, "perplexity": 441.6378885484058}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038072366.31/warc/CC-MAIN-20210413122252-20210413152252-00018.warc.gz"} |
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/58664ffa472d4a82d9318775 | ### Fun With Magnets - 6.11.5:
The activity involves two bar magnets and one cylindrical magnet to find the poles of a cylindrical magnet. For instance, if one end is getting repelled by the South pole of the bar magnet, it means that end is north pole. | 2020-10-25T07:49:49 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8053121566772461, "perplexity": 498.17761864652454}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107888402.81/warc/CC-MAIN-20201025070924-20201025100924-00309.warc.gz"} |
https://lammps.sandia.gov/doc/fix_eos_table.html | # fix eos/table command
## Syntax
fix ID group-ID eos/table style file N keyword
• ID, group-ID are documented in fix command
• eos/table = style name of this fix command
• style = linear = method of interpolation
• file = filename containing the tabulated equation of state
• N = use N values in linear tables
• keyword = name of table keyword corresponding to table file
## Examples
fix 1 all eos/table linear eos.table 100000 KEYWORD
## Description
Fix eos/table applies a tabulated mesoparticle equation of state to relate the particle internal energy (u_i) to the particle internal temperature (dpdTheta_i).
Fix eos/table creates interpolation tables of length N from internal energy values listed in a file as a function of internal temperature.
The interpolation tables are created by fitting cubic splines to the file values and interpolating energy values at each of N internal temperatures, and vice versa. During a simulation, these tables are used to interpolate internal energy or temperature values as needed. The interpolation is done with the linear style.
For the linear style, the internal temperature is used to find 2 surrounding table values from which an internal energy is computed by linear interpolation, and vice versa.
The filename specifies a file containing tabulated internal temperature and internal energy values. The keyword specifies a section of the file. The format of this file is described below.
The format of a tabulated file is as follows (without the parenthesized comments):
# EOS TABLE (one or more comment or blank lines)
KEYWORD (keyword is first text on line)
N 500 (N parameter)
(blank)
1 1.00 0.000 (index, internal temperature, internal energy)
2 1.02 0.001
...
500 10.0 0.500
A section begins with a non-blank line whose first character is not a “#”; blank lines or lines starting with “#” can be used as comments between sections. The first line begins with a keyword which identifies the section. The line can contain additional text, but the initial text must match the argument specified in the fix command.
The next line lists the number of table entries. The parameter “N” is required and its value is the number of table entries that follow. Note that this may be different than the N specified in the fix eos/table command. Let Ntable = N in the fix command, and Nfile = “N” in the tabulated file. What LAMMPS does is a preliminary interpolation by creating splines using the Nfile tabulated values as nodal points. It uses these to interpolate as needed to generate energy and temperature values at Ntable different points. The resulting tables of length Ntable are then used as described above, when computing energy and temperature relationships. This means that if you want the interpolation tables of length Ntable to match exactly what is in the tabulated file (with effectively no preliminary interpolation), you should set Ntable = Nfile.
Following a blank line, the next N lines list the tabulated values. On each line, the first value is the index from 1 to N, the second value is the internal temperature (in temperature units), the third value is the internal energy (in energy units).
Note that the internal temperature and internal energy values must increase from one line to the next.
Note that one file can contain many sections, each with a tabulated potential. LAMMPS reads the file section by section until it finds one that matches the specified keyword.
## Restrictions
This command is part of the USER-DPD package. It is only enabled if LAMMPS was built with that package. See the Build package doc page for more info.
This command also requires use of the atom_style dpd command.
The equation of state must be a monotonically increasing function.
An error will occur if the internal temperature or internal energies are not within the table cutoffs.
none | 2021-01-19T13:04:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5750219225883484, "perplexity": 2080.114024168694}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703518240.40/warc/CC-MAIN-20210119103923-20210119133923-00303.warc.gz"} |
https://www.nist.gov/publications/weak-electric-field-detection-sub-1-hz-resolution-radio-frequencies-using-rydberg-atom | # Weak Electric-Field Detection with Sub-1 Hz Resolution at Radio Frequencies Using A Rydberg Atom-Based Mixer
Published: April 25, 2019
### Author(s)
Joshua A. Gordon, Christopher L. Holloway, Matthew T. Simons, Abdulaziz H. Haddab
### Abstract
Rydberg atoms have been used for measuring radio-frequency (RF) electric (E)-fields due to their strong dipole moments over the frequency range of 500 MHz-1 THz. For this, electromagnetically induced transparency (EIT) within the Autler-Townes (AT) regime is used such that the detected E-field is proportional to AT splitting. However, for weak E-fields AT peak separation becomes unresolvable thus limiting the minimum detectable field. Here, we demonstrate using the Rydberg atoms as an RF mixer for weak RF E-field detection well below the AT regime with frequency discrimination better than 1 Hz resolution. Two E-fields incident on a vapor cell full of cesium atoms are used. One E-field at 19.626000 GHz drives the 34D5=2!35P3=2 Rydberg transition and acts as a local oscillator (LO) and a second signal E-field (Sig) of interest is at 19.626090 GHz. In the presence of the LO the Rydberg atoms naturally down convert the Sig field to a 90 kHz intermediate frequency (IF) signal. This IF signal manifests as an oscillation in the probe laser intensity through the Rydberg vapor and is easily detected with a photodiode and lock-in amplifier. In the configuration used here, E-field strength down to 46 mV/m were detected. Furthermore, neighboring fields 0.1 Hz away and equal in strength to Sig could be discriminated without any leakage into the lock-in signal. For signals 1 Hz away and as high as +60 dB above Sig, leakage into the lock-in signal could be kept below 3 dB.
Citation: Applied Physics Letters
Pub Type: Journals | 2019-10-19T04:07:45 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8712158799171448, "perplexity": 4371.230455922405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986688674.52/warc/CC-MAIN-20191019013909-20191019041409-00424.warc.gz"} |
https://www.usgs.gov/media/images/a-closer-look-one-steam-sources-crack-which-st | # A closer look at one of the steam sources. The crack from which st...
## Detailed Description
A closer look at one of the steam sources. The crack from which steam is issuing is not visible through the thick vegetation.
## Details
Image Dimensions: 5184 x 3456
Date Taken: | 2021-09-25T13:11:03 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8329883813858032, "perplexity": 4185.841400404138}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057622.15/warc/CC-MAIN-20210925112158-20210925142158-00594.warc.gz"} |
https://par.nsf.gov/biblio/10278875 | The bursty origin of the Milky Way thick disc
ABSTRACT We investigate thin and thick stellar disc formation in Milky Way-mass galaxies using 12 FIRE-2 cosmological zoom-in simulations. All simulated galaxies experience an early period of bursty star formation that transitions to a late-time steady phase of near-constant star formation. Stars formed during the late-time steady phase have more circular orbits and thin-disc-like morphology at z = 0, while stars born during the bursty phase have more radial orbits and thick-disc structure. The median age of thick-disc stars at z = 0 correlates strongly with this transition time. We also find that galaxies with an earlier transition from bursty to steady star formation have a higher thin-disc fractions at z = 0. Three of our systems have minor mergers with Large Magellanic Cloud-size satellites during the thin-disc phase. These mergers trigger short starbursts but do not destroy the thin disc nor alter broad trends between the star formation transition time and thin/thick-disc properties. If our simulations are representative of the Universe, then stellar archaeological studies of the Milky Way (or M31) provide a window into past star formation modes in the Galaxy. Current age estimates of the Galactic thick disc would suggest that the Milky Way transitioned from bursty to steady phase more »
Authors:
; ; ; ; ; ; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10278875
Journal Name:
Monthly Notices of the Royal Astronomical Society
Volume:
505
Issue:
1
Page Range or eLocation-ID:
889 to 902
ISSN:
0035-8711
1. ABSTRACT We study the growth of stellar discs of Milky Way-sized galaxies using a suite of cosmological simulations. We calculate the half-mass axis lengths and axis ratios of stellar populations split by age in galaxies with stellar mass $M_{*}=10^7\!-\!10^{10}\, \mathrm{M}_{\odot }$ at redshifts z > 1.5. We find that in our simulations stars always form in relatively thin discs, and at ages below 100 Myr are contained within half-mass height z1/2 ∼ 0.1 kpc and short-to-long axial ratio z1/2/x1/2 ∼ 0.15. Disc thickness increases with the age of stellar population, reaching median z1/2 ∼ 0.8 kpc and z1/2/x1/2 ∼ 0.6 for stars older than 500 Myr. We trace the same group of stars over the simulation snapshots and show explicitly that their intrinsic shape grows more spheroidal over time. We identify a new mechanism that contributes to the observed disc thickness: rapid changes in the orientation of the galactic plane mix the configuration of young stars. The frequently mentioned ‘upside-down’ formation scenario of galactic discs, which posits that young stars form in already thick discs at high redshift, may be missing this additional mechanism of quick disc inflation. The actual formation of stars within a fairly thin plane is consistent with the correspondingly flatmore »
We use FIRE simulations to study disc formation in z ∼ 0, Milky Way-mass galaxies, and conclude that a key ingredient for the formation of thin stellar discs is the ability for accreting gas to develop an aligned angular momentum distribution via internal cancellation prior to joining the galaxy. Among galaxies with a high fraction ($\gt 70{{\ \rm per\ cent}}$) of their young stars in a thin disc (h/R ∼ 0.1), we find that: (i) hot, virial-temperature gas dominates the inflowing gas mass on halo scales (≳20 kpc), with radiative losses offset by compression heating; (ii) this hot accretion proceeds until angular momentum support slows inward motion, at which point the gas cools to $\lesssim 10^4\, {\rm K}$; (iii) prior to cooling, the accreting gas develops an angular momentum distribution that is aligned with the galaxy disc, and while cooling transitions from a quasi-spherical spatial configuration to a more-flattened, disc-like configuration. We show that the existence of this ‘rotating cooling flow’ accretion mode is strongly correlated with the fraction of stars forming in a thin disc, using a sample of 17 z ∼ 0 galaxies spanning a halo mass range of 1010.5 M⊙ ≲ Mh ≲ 1012 M⊙ and stellarmore »
3. ABSTRACT In hierarchical structure formation, metal-poor stars in and around the Milky Way (MW) originate primarily from mergers of lower mass galaxies. A common expectation is therefore that metal-poor stars should have isotropic, dispersion-dominated orbits that do not correlate strongly with the MW disc. However, recent observations of stars in the MW show that metal-poor ($\rm {[Fe/H]}\lesssim -2$) stars are preferentially on prograde orbits with respect to the disc. Using the Feedback In Realistic Environments 2 (FIRE-2) suite of cosmological zoom-in simulations of MW/M31-mass galaxies, we investigate the prevalence and origin of prograde metal-poor stars. Almost all (11 of 12) of our simulations have metal-poor stars on preferentially prograde orbits today and throughout most of their history: we thus predict that this is a generic feature of MW/M31-mass galaxies. The typical prograde-to-retrograde ratio is ∼2:1, which depends weakly on stellar metallicity at $\rm {[Fe/H]}\lesssim -1$. These trends predicted by our simulations agree well with MW observations. Prograde metal-poor stars originate largely from a single Large/Small Magellanic Cloud (LMC/SMC)-mass gas-rich merger $7\!-\!12.5\, \rm {Gyr}$ ago, which deposited existing metal-poor stars and significant gas on an orbital vector that sparked the formation of and/or shaped the orientation of a long-lived stellar disc, givingmore » | 2022-12-01T12:30:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6961564421653748, "perplexity": 3308.9551476509314}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710813.48/warc/CC-MAIN-20221201121601-20221201151601-00127.warc.gz"} |
https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/1%3A_The_Nature_of_Light/1.0%3A_Prelude_to_The_Nature_of_Light | $$\require{cancel}$$
# 1.0: Prelude to The Nature of Light
Our investigation of light revolves around two questions of fundamental importance:
1. What is the nature of light, and
2. how does light behave under various circumstances?
Answers to these questions can be found in Maxwell’s equations, which predict the existence of electromagnetic waves and their behavior. Examples of light include radio and infrared waves, visible light, ultraviolet radiation, and X-rays. Interestingly, not all light phenomena can be explained by Maxwell’s theory. Experiments performed early in the twentieth century showed that light has corpuscular, or particle-like, properties. The idea that light can display both wave and particle characteristics is called wave-particle duality, which is examined in Photons and Matter Waves.
In this chapter, we study the basic properties of light. In the next few chapters, we investigate the behavior of light when it interacts with optical devices such as mirrors, lenses, and apertures.
# Contributors
• Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0). | 2019-09-21T16:09:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42107346653938293, "perplexity": 1141.5300837920101}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574532.44/warc/CC-MAIN-20190921145904-20190921171904-00539.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=S014BET&home=sumtabM | # ${{\boldsymbol \pi}^{+}}{{\boldsymbol \pi}^{-}}{{\boldsymbol \gamma}}$ PARAMETER $\beta$ (${\boldsymbol D}{\mathrm -wave}$) INSPIRE search
Sensitive to a ${\mathit D}{\mathrm -wave}$ contribution: $\mathit dN/\mathit d$cos $\theta$ = sin$^2\theta$ ${}$ (1 + $\beta$ ${}$ cos $^2\theta$).
VALUE EVTS DOCUMENT ID TECN
$\bf{ -0.02 \pm0.07}$ OUR AVERAGE Error includes scale factor of 1.3.
$0.11$ $\pm0.11$ 35k
1974 B
OSPK
$-0.060$ $\pm0.065$ 7250
1970
WIRE
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.12$ $\pm0.06$ 1
1972
ASPK
1 The authors don't believe this indicates ${\mathit D}{\mathrm -wave}$ because the dependence of $\beta$ on the ${{\mathit \gamma}}$ energy is inconsistent with the theoretical prediction. A cos $^2\theta$ dependence can also come from $\mathit P$- and ${\mathit F}{\mathrm -wave}$ interference.
Conservation Laws:
CHARGE CONJUGATION ($\mathit C$) INVARIANCE
References:
JANE 1974B
PL 48B 265 Measurement of the Charge Asymmetry in the Decay ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$
THALER 1972
PRL 29 313 Charge Asymmetry in the Decay ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$
GORMLEY 1970
PR D2 501 Experimental Determination of the Dalitz-Plot Distribution of the Decays ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ and ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ , and the Branching ratio ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ $/$ ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ | 2020-07-14T23:45:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8921159505844116, "perplexity": 2052.1188119083017}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657151761.87/warc/CC-MAIN-20200714212401-20200715002401-00368.warc.gz"} |
https://ftp.mcs.anl.gov/pub/fathom/moab-docs/classmoab_1_1WriteCCMIO_1_1MeshInfo.html | MOAB: Mesh Oriented datABase (version 5.3.1)
moab::WriteCCMIO::MeshInfo Class Reference
contains the general information about a mesh More...
#include <WriteCCMIO.hpp>
Collaboration diagram for moab::WriteCCMIO::MeshInfo:
MeshInfo ()
## Public Attributes
unsigned int num_dim
unsigned int num_nodes
unsigned int num_elements
unsigned int num_matsets
unsigned int num_dirsets
unsigned int num_neusets
Range nodes
## Detailed Description
contains the general information about a mesh
Definition at line 77 of file WriteCCMIO.hpp.
## Constructor & Destructor Documentation
moab::WriteCCMIO::MeshInfo::MeshInfo ( ) [inline]
Definition at line 88 of file WriteCCMIO.hpp.
: num_dim( 0 ), num_nodes( 0 ), num_elements( 0 ), num_matsets( 0 ), num_dirsets( 0 ), num_neusets( 0 )
{
}
## Member Data Documentation
Definition at line 86 of file WriteCCMIO.hpp.
unsigned int moab::WriteCCMIO::MeshInfo::num_dim
Definition at line 80 of file WriteCCMIO.hpp.
unsigned int moab::WriteCCMIO::MeshInfo::num_dirsets
Definition at line 84 of file WriteCCMIO.hpp.
unsigned int moab::WriteCCMIO::MeshInfo::num_elements
Definition at line 82 of file WriteCCMIO.hpp.
unsigned int moab::WriteCCMIO::MeshInfo::num_matsets
Definition at line 83 of file WriteCCMIO.hpp.
unsigned int moab::WriteCCMIO::MeshInfo::num_neusets
Definition at line 85 of file WriteCCMIO.hpp.
unsigned int moab::WriteCCMIO::MeshInfo::num_nodes
Definition at line 81 of file WriteCCMIO.hpp.
List of all members.
The documentation for this class was generated from the following file: | 2021-12-09T00:35:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30395400524139404, "perplexity": 13767.484435434273}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363641.20/warc/CC-MAIN-20211209000407-20211209030407-00388.warc.gz"} |
https://www.itl.nist.gov/div898/handbook/prc/section2/prc231.htm | 7. Product and Process Comparisons
7.2. Comparisons based on data from one process
7.2.3. Are the data consistent with a nominal standard deviation?
## Confidence interval approach
Confidence intervals for the standard deviation Confidence intervals for the true standard deviation can be constructed using the chi-square distribution. The $$100(1-\alpha)$$ % confidence intervals that correspond to the tests of hypothesis on the previous page are given by
1. Two-sided confidence interval for $$\sigma$$ $$\frac{s\sqrt{N-1}}{\sqrt{ \chi^2_{1-\alpha/2, N-1} }} \le \sigma \le \frac{s\sqrt{N-1}}{\sqrt{ \chi^2_{\alpha/2, N-1} }} \, ,$$
2. Lower one-sided confidence interval for $$\sigma$$ $$\sigma \ge \frac{s\sqrt{N-1}}{\sqrt{ \chi^2_{1-\alpha, N-1} }} \, ,$$
3. Upper one-sided confidence interval for $$\sigma$$ $$0 \le \sigma \le \frac{s\sqrt{N-1}}{\sqrt{ \chi^2_{\alpha, N-1} }} \, .$$
For case (1), $$\chi_{\alpha/2}^2$$ is the $$\alpha/2$$ critical value from the chi-square distribution with $$N -1$$ degrees of freedom and similarly for cases (2) and (3). Critical values can be found in the chi-square table in Chapter 1.
Choice of risk level $$\alpha$$ can change the conclusion Confidence interval (1) is equivalent to a two-sided test for the standard deviation. That is, if the hypothesized or nominal value, $$\sigma_0$$, is not contained within these limits, then the hypothesis that the standard deviation is equal to the nominal value is rejected.
A dilemma of hypothesis testing A change in $$\alpha$$ can lead to a change in the conclusion. This poses a dilemma. What should $$\alpha$$ be? Unfortunately, there is no clear-cut answer that will work in all situations. The usual strategy is to set $$\alpha$$ small so as to guarantee that the null hypothesis is wrongly rejected in only a small number of cases. The risk, $$\beta$$, of failing to reject the null hypothesis when it is false depends on the size of the discrepancy, and also depends on $$\alpha$$. The discussion on the next page shows how to choose the sample size so that this risk is kept small for specific discrepancies. | 2019-11-20T22:44:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8574397563934326, "perplexity": 199.40719229994065}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670635.48/warc/CC-MAIN-20191120213017-20191121001017-00185.warc.gz"} |
https://haypikingdom.fandom.com/wiki/Speed | ## FANDOM
142 Pages
Speed is an Attribute in Haypi Kingdom
. It determines which troops attack first. The formula for this is equal to $Base Speed of Unit+(Attribute Speed+Equipment Bonus)=first attack$.
## Facts/TriviaEdit
• If the Speed of both players are equal then the player being attacked will get the first hit in battle.
• When battling a Mine or Alliance in the Alliance War feature the formula, $Base Speed of Unit+(Attribute Speed+Equipment Bonus)$, is invalid. The forumula is $Defender=First Attack$.
• Speed can have a maximum Attribute level of 100 attribute 90 gear 30 tech total 220
• Both the Horse equipment and Manual raise speed.
• Cavalry will always have first attack against non-cavalry units in range.
Community content is available under CC-BY-SA unless otherwise noted. | 2019-08-24T14:08:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43624332547187805, "perplexity": 5128.651023615476}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027321140.82/warc/CC-MAIN-20190824130424-20190824152424-00265.warc.gz"} |
https://orkfia.fandom.com/wiki/Raid | ## FANDOM
243 Pages
Storm into your enemy’s lands, capturing some easy acres, and killing up to 20% of the target citizens. Military losses are slim for the attacker and high for the defender. Attacking smaller tribes results in fewer returns.
• Kills a minimum of of 2x the target's acres as citizens. Race modifiers apply.
• You capture 35% extra land on your way to the enemy's tribe. These acres can be built on right away.
## Gains FormulaeEdit
Land Gained = $\frac{0.039\cdot AttLand}{\left(1+0.5\cdot e^{-8\cdot\left(\tfrac{DefLand}{AttLand}-0.8\right)}\right)^2}$
## LossesEdit
• Attacking tribe loses 0.6% of the amount of offense required to break the defender's defenses.
• Defending tribe loses 1% of defensive military units, as well as up to 20% citizens.
Community content is available under CC-BY-SA unless otherwise noted. | 2020-08-07T08:58:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4205023944377899, "perplexity": 10784.120880127484}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737172.50/warc/CC-MAIN-20200807083754-20200807113754-00124.warc.gz"} |
https://tjyj.stats.gov.cn/CN/10.19343/j.cnki.11-1302/c.2016.08.014 | • 论文 •
整数值时间序列模型单位根检验问题研究
• 出版日期:2016-08-15 发布日期:2016-08-11
Research on Unit Root Test for Integer-valued Time Series Models
Wang Zeyu et al.
• Online:2016-08-15 Published:2016-08-11
Abstract:
The unit root test research about the integer-valued time series is just getting started, compared with the non-integer-valued time series. In this paper, the Monte Carlo simulation would be ushered to check the DF statistic and the statistic in INAR (1) models with unit root process. Based on the research, DF statistic asymptotically conforms to the standard normal distribution, meanwhile the actual distribution of this statistic has been impacted by the sample size and the mean of the disturbance term in the finite sample. In addition, the DF statistic does not have the property of any level distortion. That is, the DF can well control the probability of type I error. Because of the data generation feature, the statistic’s probability of committing type I error is zero. Furthermore, the test powers of DF statistic and statistic are influenced by the sample size, autoregressive coefficient and the mean of the error term. In most cases, the test power of statistic is much better than the DF statistic. | 2022-07-01T00:11:04 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5532605648040771, "perplexity": 872.797160686506}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103915196.47/warc/CC-MAIN-20220630213820-20220701003820-00540.warc.gz"} |
https://www.federalreserve.gov/econresdata/notes/ifdp-notes/2016/low-for-long-interest-rates-and-net-interest-margins-of-banks-in-advanced-foreign-economies-20160411.html | ## IFDP Notes
### "Low-for-long" interest rates and net interest margins of banks in Advanced Foreign Economies
Stijn Claessens (FRB), Nicholas Coleman (FRB), and Michael Donnelly (FRB)1
1. Introduction
Since the global financial crisis (GFC), interest rates in many advanced economies have been low and in many cases are expected to remain low for some time. Low interest rates help economies recover and can enhance banks' balance sheets and performance by supporting asset prices and reducing non-performing loans. But persistently low interest rates may also erode the profitability of banks as low rates are typically associated with lower net interest margins -- NIMs, typically measured as net interest income divided by interest earning assets. While overall advanced economies' bank profitability, measured by return on assets, has recovered from the worst of the GFC, it remains low and many advanced economies' banks are facing profitability challenges, related to low net interest margins as well as weak loan and non-interest income growth. And while NIMs across many advanced economy banks have been trending down on a longer-term basis, they have fallen more sharply since the GFC, in part, as appears so, on account of lower interest rates.
But how strong is the link between interest rates and NIMs, and is this relationship different in low interest rate environments? This note explores the empirical evidence between changes in interest rates and NIMs for different interest rate environments to discover the potential adverse effects of a low interest rate on bank NIMs. Using cross-country evidence can be insightful to assess a situation that is not so common in any individual country. Overall, the new empirical analysis shows that low rates are contributing to weaker NIMs and identifies an adverse effect that is materially larger when interest rates are low. It suggests that these effects can be material for banks in some key advanced foreign economies (AFEs).2
2. Literature on the effects of low interest rates on banks' NIMs
In many ways, banks, of course, may benefit from low interest rates, directly (e.g., through valuation gains on securities they hold) and indirectly (e.g., as non-performing loans will be lower as borrowers' debt service will be less burdensome). The focus here is on the narrower question of the effects of low interest rates on banks' NIMs. Analytics and existing empirical findings suggest that, controlling for other factors, banks' NIMs are lower when interest rates are low. We briefly review the reasoning and this literature.
Low short-term interest rates can depress bank margins because for many types of deposits, banks are reluctant to lower deposit rates, especially below zero (while there is anecdotal evidence that some banks are passing negative rates onto corporate customers in select cases, banks have been reluctant to pass on negative policy rates to retail depositors). As a result, when interest rates decline, bank margins compress, since banks must pass on lower rates on assets based on contractual repricing terms (e.g., floating rate loans) and have an incentive to do so to those borrowers that have other financing choices (e.g., from corporate bond markets). Moreover, low long-term interest rates can depress NIMs by flattening the yield curve. Because banks transform short-dated liabilities into longer-dated assets, their NIMs are negatively affected by shallower yield curves. Modeling (see Appendix I) further suggests that, ceteris paribus, the effects are larger in a low-yield environment since, besides the reluctance to lower deposit rates below zero, spreads on loans over deposit rates can be expected to be lower.
Cross-country empirical evidence and studies for various individual countries support the negative effects of lower interest rates on net interest margins, with effects often found to be greater in low interest rate environments. Analyzing a sample of 108 relatively large international banks, many from Europe and Japan, and 16 from the United States, Borio, Gambacorta and Hofmann (2015) document the non-linear relationships between the interest rate level and the slope of the yield curve on one hand and banks' NIMs and profitability, i.e., return on assets, on the other hand. They confirm that effects on NIMs are stronger at lower levels of interest rates (50 basis points for a 1 percentage point change at a rate of 1% vs. 20 basis points at a rate of 6%) and when there is an unusually flat term structure.
Evidence for the United States (e.g., Genay and Podjasek, 2014) also finds that banks are adversely affected by interest rates that are low for an extended period of time through a narrower NIM. They also note, however, that the direct effects of low rates are small relative to the economic benefits, including through better support for asset quality.3 Analysis for Germany (Busch and Memmel, 2015) suggests that in normal interest rate environments the long-run effect of a 100 basis points change in the interest rate on NIMs is very small, close to 7 basis points. In the recent, low-interest rate environment, however, they find that banks' interest margins for retail deposits, especially for term deposits, have declined by up to 97 basis points. The Bundesbank's Financial Stability Review of September 2015, analyzing 1,500 banks, also finds that a persistently low interest rate is one of the main risk factors weighting on German banks' profitability. For Japan, analysis (Deutsche Bank, 2013) shows that the low-for-long interest rate there also contributed to the declining NIMs of Japanese banks. Over time, however, portfolio shifts towards investment in securities, a greater reliance on non-interest income, and a holding down of costs allowed Japanese banks' profitability to remain mostly positive. Evidence for other countries on the effects of (low) interest rates on NIMs and profitability is scarcer.
The literature has found that the direct effects of changes in interest rates on margins and profitability can vary by bank size. Analysis for U.S. banks suggests that in general rate changes have greater, short-run impact on small banks as they depend more on traditional intermediation of retail deposits, which are stickier in price, into loans, many of which are priced off floating rates. Large banks typically have greater ability to manage interest rate risks through the use of derivatives and the repricing of managed liabilities, and are thus less affected by low interest rates. Also, large banks, with their greater international reach, have more potential to increase lending abroad, and their more diversified business models can allow them to more easily expand non-interest income to offset lower margins. Since the GFC, however, large U.S. banks have seen their funding cost advantage erode and NIMs decline more than small banks, but this seems at least in part due to recent regulatory changes (Covas, Rezende and Voitech, 2015).
Capital markets seem to acknowledge some of the effects of low interest rate on banks' profitability. In their analysis, English, Van den Heuvel, and Zakrajsek (2012) find that while equity prices of U.S. banks fall following unanticipated increases in interest rates or a steepening of the yield curve, a large maturity gap weakens this effect, suggesting that on account of their maturity transformation function, banks gain relatively from a higher interest rate or a steeper yield curve. This shows that, conversely, a lower interest rate or a shallower yield curve hurts those banks that are more engaged in maturity transformation, at least relative to other banks.
3. New analysis
New cross-country analysis we conduct confirms and expands on these findings. We first describe below the data and sample of commercial banks we use, as well as some raw statistics. We then provide the methodology and empirical findings.
Data sample and raw comparisons. To investigate the impact of the short-term interest rate on banks' NIMs, a database was assembled with (yearly averages of) three-month and ten-year sovereign yields from Bloomberg and of bank balance sheet and income statement data from Bankscope at an annual frequency.4 The final sample contains 3,418 banks from 47 countries for 2005-2013.5 Unconsolidated data are used, where available, to isolate the effect of a country's interest rate on only the bank's operations in that country. Observations are only trimmed in cases where the data is logically inconsistent, for example when assets are below zero or when deposits are greater than liabilities. We additionally ignore observations where the NIM for a bank changes by more than ten percentage points from one year to the next.
To explore differential impacts, countries were classified each year as being in a low- or high-rate environment based on whether the interest rate on their 3-month sovereign bond was below or above 1.25 percent (other cutoffs were also tested and yielded similar results). Figure 1 shows the sample of countries covered and the range and median of the short-term yields in each. The variations in rates are large for many countries, and many countries are both in the high- and low-yield environment for some time (the median provides a sense of how long each country has been in each environment). Appendix Figure 1 shows the exact classification of countries in the low- and high-yield environments for 2005, 2009, and 2013. It is notable that many more countries, especially advanced economies, are in the low-yield environment post-GFC: 19 in 2009 vs. only two in 2005. These shifts help to estimate the differential impact of low interest rates on banks' NIM and profitability, and whether effects are greater the longer banks are in a low interest rate environment.
Figure 2 compares the broad composition of bank balance sheets in low- and high-rate environments. Overall, there do not appear to be major shifts in asset compositions or liability structures in low- versus high-rate environments that could be expected to drive differences in how net interest margins respond to interest rates. Banks have roughly the same loan-to-deposit and loan-to-asset ratios in the high-rate environment (the orange bars) as in the low-rate environment (the blue bars) at about 125 and 60 percent, respectively. Banks in the high-rate environment have slightly higher leverage ratios, while deposits-to-total liabilities and securities-over-assets are slightly higher in the low-rate environment, possibly because low rates are associated with lower economic and loan growth, less non-deposit borrowing, greater investment in safer securities, and lower profits and capital.
Figure 1: Range of 3-Month Sovereign Yield by Country (2005-2013)
Note: The figure shows the range of the three-month sovereign yield for each country from 2005-2013. Values used are yearly averages of the implied three-month rate published daily by Bloomberg.
Sources: Bloomberg, staff calculations.
Accessible version
Figure 2: Balance Sheet Composition
Source: Bankscope, staff analysis.
Accessible version
Figure 3 shows that average NIMs are higher in the high-rate environment (the orange bars) than in the low-rate environment (the blue bars). Profitability, measured by return on assets, is higher too in the high-rate environment, likely reflecting both higher NIMs and concurrent better overall economic and financial environments.
Figure 3: Banks' NIM and Profitability
Source: Bankscope, staff analysis.
Accessible version
Methodology and findings. To isolate the direct effects of changes in interest rates on NIMs in low- and high-rate environments, we perform an econometric analysis that holds other factors constant, including any correlations that interest rates might have with economic growth, demand for loans, or supply of deposits. We regress a bank's NIM for each year on the average level of the three-month sovereign rate in that year, a common proxy for banks' marginal funding costs, controlling for the bank's own lagged NIM, other time-varying bank characteristics, and a bank fixed effect, as well as GDP growth and the spread between the three-month and ten-year sovereign rates. The sample is then split by banks in low- and high-interest rate environments Specifically, the regressions use the following empirical specification:
$$y_{ijt}=\beta _{0}+\beta _{1}y_{ijt-1}+\theta _{1}3MonthRate_{jt}+\theta_{2}RateSpread_{jt}+\theta _{3}Low_{jt}+y_{1}GDPgrowth_{jt}+y_{2}X_{it}+\delta _{i}+\varepsilon _{ijt}$$
Where:
• $y_{ijt}$ is the NIM of bank $i$ in country $j$ in year $t$,
• 3Month$Rate_{jt}$ is the yearly average 3-month government bond yield,
• $Rat{eSpread}_{jt}$ is the spread between the 10-year government bond yield and 3-month government bond yield,
• $Low_{jt}$ is a dummy equal to 1 if the country is in a "low rate environment" which we define to be under 1.25% on the 3-month rate.
• ${GDPgrowth_{jt}}_{it}$ controls for the country's economic growth6
• $X_{it}$ are bank level controls, specifically total securities over total assets, deposits over total liabilities, and total equity capital over total assets
• $\delta _{i}$ is a bank fixed effect and $\varepsilon_{ijt }$ is an error term
Because the regressions control for each bank's average NIM and its country's general economic conditions, results can be interpreted as the direct effects of a change in the short-term interest rate on banks' NIMs.7
The baseline regression results show that a decrease in the short-term interest rate lowers NIMs in both a low- and high-rate rate environment, with effects symmetric for an interest rate increase. But other things equal, effects are statistically significantly larger in a low-rate environment. Figure 4 summarizes the regression results. For a representative bank, a one percentage-point decrease in the short-term rate is associated with a 9 basis-point decrease in NIM in the high-rate environment (the orange bars) versus a 17 basis-point decrease in NIM in the low-rate environment (the blue bars). Similar magnitudes and comparisons are found when using overall samples composed of different banks and countries.8 Even so, when conducting the analysis for individual countries, there is significant heterogeneity in effects. For example, a one percentage point decline in the 3-month sovereign rate leads to a 6 basis-point decline in NIMs in Austria, compared to a 27 basis-point decrease in Italy.
Figure 4: Effect of 1 p.p. Decrease in 3-Month Yield
Note. The figure above reflects average differences among banks and estimated effects of a decrease in the three-month sovereign yield, respectively, for banks in a "low" rate environment and a "high" rate environment.
Accessible version
We next run regressions analyzing separately the effects of changes in interest rate on changes in interest expenses and on changes in interest income. The greater effects on NIMs in the low-rate environment is largely driven by the greater pass-through of low interest rates on interest income than on interest expense. Specifically, a one percentage point decrease in the short-term rate is associated with a 63 basis-point decrease in the ratio of interest income to earning assets in the low-rate environment and only a 35 basis-point decrease in the high-rate environment, a 28 basis-point difference. The equivalent difference is about 20 basis points for the ratio of interest expense to liabilities. In other words, at low rates, banks have greater difficulty reducing their funding rates, while they have to pass the lower rates to a greater degree on to their borrowers, likely due to greater competition, including from non-bank lenders, and lower demand for loans -- as economic activity is less in times of low interest rates, leading NIMs to decline more.
We also analyzed if effects differ by banks' maturity mismatches. We defined a bank as having a "long" maturity (asset and liabilities separately) if it has an average balance sheet maturity over the sample period greater than the median maturity for banks in its country and as having a "short" maturity otherwise. We then analyze using the same methodology, for a smaller sample of banks, the impact of a one percentage point increase in the short-term interest rate on the same period interest income ratio (the interest expense ratio) differentiating by the maturity of the banks' assets (liabilities).9 Consistent with a priori expectations, the analysis shows that the highest contemporaneous pass-through from a decrease in interest rates to interest income is for banks with short asset maturities in the low interest rate environment. Banks with longer maturity assets see statistically significantly less pass-through, 64 basis points vs. 92 basis points (Figure 5). Similarly, although somewhat lower, the pass-through to interest expenses is significantly higher in the low interest rate environment than in the high environment for banks with short liability maturities.
Figure 5: Effect of 1 p.p. Decrease in 3-Month Sovereign Yield, by Duration
Note. The figure shows the estimated effect of a 1 percentage point decrease in the three-month sovereign yield on a bank's net interest income margin and interest expense margin adjusted for interest rate environment and a bank's balance sheet maturity. A bank is classified as having a "long" maturity if it has an average balance sheet maturity over the sample period greater than the median maturity for banks in its country, and is classified as having a "short" maturity otherwise. Assets are used to determine maturity for the interest income margin, while liabilities are used for the interest expense margin. This figure only includes those countries with over 100 banks reporting maturity information.
Sources: Bankscope, staff calculations.
Accessible version
4. Overall Effects for AFE Banking Systems and Conclusions
The cross-country analysis conducted suggests that low interest rates negatively affect many AFE banks' NIMs, which is consistent with several studies on individual countries. We can summarize our results by considering the situations of banking systems in four key AFEs, the euro area, Canada, Japan, and the UK, and comparing these to U.S. banks (Table 1). Wide differences remain between the relatively strong profitability reported by Canadian, U.K. and U.S. banks, and the weaker profitability reported by euro area and Japanese banks.10 These differences in profitability partially reflect differences in NIMs, which are typically lower in the AFEs than in the United States, as many AFE banks have higher shares of typically lower-yielding mortgages and sovereign debt. And the lower NIMs in the later period in turn likely reflect the large declines in sovereign yields in these economies.
Table 1: Advanced Economy Bank Profitability
Median Return on Assets - 2007 Median Return on Assets - 2013 Median Net Interest Margin - 2007 Median Net Interest Margin - 2013 3-Month Sovereign Yield - 2007 3-Month Sovereign Yield - 2014
Euro Area 33 24 253 235 398 14
Canada 54 56 229 214 425 92
Japan 23 18 181 139 45 3
United Kingdom 84 66 195 128 535 31
Advanced Foreign Economies 30 22 236 213 277 10
United States 96 81 391 382 450 5
Sources: Bankscope, staff analysis.
Using our regression results, our estimates suggest that the NIMs in these four banking systems declined by roughly 26 basis points due to the actual decreases in interest rates between 2007 and 2013 (Table 2), or roughly 82 percent of the median decline in NIMs observed over this period, which was 32 basis points. These impacts vary by interest rate declines and are between 3 basis points for Japan and 46 basis points for the U.K. If already in a low-rate environment, e.g., Japan and the euro area today, estimates suggest a NIM contraction of 17 basis points for every 1 percentage point further decline in the 3 month rate.
Table 2: Predicted and Observed Changes in Net Interest Margins from 2007-2013
Change in 3-Month Rate (b.p.) Predicted Change in Net Interest Margin (b.p.) Observed Change in Net Interest Margin (b.p.) Percent of Net Interest Margin Change Explained
Euro Area -373 -33 -34 97%
Japan -38 -3 -39 8%
United Kingdom -526 -46 -28 168%
Advanced Foreign Economies -297 -26 -32 82%
Note. Change in the 3-month rate is the change in the 3-month sovereign yield from 2007-2013. We predict a change of 8.8 basis points in a bank's net interest margin for every 100 basis point change in the sovereign's 3-month yield. Observed change is shown as the median change in net interest margins for banks in that sample.
There are caveats to this analysis, related to appropriate lags and potential other non-linearities between changes in interest rates and NIMs. First, there may be important non-linearities in the impact of interest rate changes in a low-yield environment compared to the high-yield environment not captured with our specification. Second, while we included one lag for the dependent variable, which was statistically significant with a coefficient of about 0.5, there are likely additional lags in the relationship between changes in interest rates and NIMs that are not captured (for example, as long-term loans are repriced over time at higher or lower interest rates, affecting NIMs many years after an interest rate change). Analysis using German banks, Memmel (2011), suggests for example that the full effects of repricing take place over a period of 1-1.5 years. This is consistent with the pattern in NIMs which seems to progressively decline as the banks are longer in a low interest rate environment (Figure 6). Third, the analysis only looks at the effect on current margins assuming no shifts in behavior, while changes in interest rates and the full effect on banks' NIMs (and profitability, capital adequacy and franchise values over time) may vary as banks adjust their funding structures, lending and investment portfolios and their non-interest activities. These adjustments have been found to be important in the case of Japan (see Deutsche Bank, 2013). Lastly, there have been many regulatory changes since the GFC that could also have affected banks' NIMs, as has been found for large U.S. banks (see Covas, Rezende and Voitech, 2015).
Figure 6: Change in NIM in a Low Rate Environment
Note. The figure above reflects the average change in net interest margins between the year prior to entering the low interest rate environment and each successive year after entering a low rate environment, t=1 through t=4.
Sources: Bankscope, staff analysis.
Accessible version
While there are these and other caveats to the analysis, nevertheless, the findings suggest strongly that when NIMs are low -- due to persistently low rates or otherwise -- the important issue is how banks can adjust their activities and cost structures so as to offset low rates' adverse effects on profitability and capital. Similar regressions of the effects of low interest rates on bank ROA show no consistent results, however, likely as the direct effects of changes in interest rates on NIMs are confounded by the volatility in other sources of income and costs, including gains on security holdings and provisioning, especially since the GFC, and possibly because banks are taking actions to offset the effects on ROAs of changes in NIMs due to interest rate declines (as well as in light of recent regulatory changes, heightened market pressures, and changed opportunities). Although institutions are making adjustments, such efforts take time, as Japan's experience shows, with limited immediate payoffs when facing weak cyclical conditions and deleveraging pressures. As such, banking systems in many low interest rate countries will face challenges. Until lost income can be offset through other actions, lower profitability will reduce financial institutions' ability to build and attract capital, increasing their vulnerability to shocks and declines in market confidence and undermining their ability to support the real economy.
Appendix I: Effects of low interest rates: Analytics and Modelling
Analytics
At the individual institution level, exposures to fluctuations in interest rates can vary significantly. Relevant factors determining this variation include the amount held of fixed income assets (e.g., (government) bonds), the maturity and repricing nature of liabilities and assets, and the related degree of maturity mismatches. The degree to which fluctuations in short-term interest rates impact banks' NIMs and profitability (and bank's equity market valuation) depends importantly on the maturity and repricing structure of banks' assets and liabilities, accounting for the use of hedging tools, and the degree to which banks can and do alter their balance sheets and activities in response to the changes in interest rates. Banks with shorter-term and frequently repriced assets (or liabilities) will experience a larger decrease in interest income (or interest expense) as the short-term interest rate falls compared to banks with longer-term and infrequently repriced assets (or liabilities). In addition to asset-liability mismatches, the impact of interest rate changes on banks' NIMs depends on banks' relative ability to pass on changes in the interest rate to depositors and borrowers.
Typically though, as they transform short-dated liabilities in longer-dated assets, banks are negatively affected by shallower yield curves which act to lower their NIMs and overall profitability. The NIM is effectively the mark-up that banks charge on their liabilities to fund their assets and reflects the liquidity transformation that banks perform, borrowing liquid deposits and funding themselves more generally with short-term liabilities and making illiquid loans and investing in longer-dated securities. Ceteris paribus, bank margins increase as the steepness of the yield curve increases as then the difference between bank (short-term) borrowing and (long-term) lending rates increases. Controlling for the steepness of the spread, the level of the short-term interest rate may be important as well for bank margins (see modelling). Especially when interest rates are close to zero, the de-facto lower bound for at least retail deposits, banks may see their margins compress as they have greater difficulty adjusting deposit rates down, while they still have to pass on the lower rate to their borrowers.
Effects of changes in interest rates on NIMs and profitability may vary by bank size. Large banks may be able to more effectively hedge interest rate risk so a change in the short-term interest rate could have a smaller short-run effect on changes in interest income than for small banks. At the same time, borrowers from large banks have greater opportunities to switch banks, forcing large banks to pass on low interest rate to a greater degree to their borrowers. Smaller banks may rely more on retail deposits, so a low interest rate could have a relatively less beneficial impact on their expenses.
While lower interest rates need not adversely affect banks, and the overall literature finds ambiguous results, pass-through of low interest rate can be expected to be even less to deposit rates at lower rates/ZLB. As a consequence, NIMs can decline. Institutions, notably those with more long-dated and fixed-price liabilities (i.e., insurance and pension funds), will typically see their net worth fall. Different than banks, contractual savings institutions have some time and scope though to adjust premiums and benefits. Distributional/adverse effects arise when some types of banks and other institutions (small, large, other) are more affected.
The impact of interest rate changes on overall bank profitability and capital adequacy positions is more ambiguous as it will vary on the state of the economy. For example, if low interest rate environments tend to happen in a period where demand for loans is low as well, or where banks are (capital or otherwise) constrained and otherwise deleveraging after a financial crisis, this may (further) suppress NIMs and overall profitability, especially when banks are also facing balance sheets problems and deleveraging, say in the wake of a crisis. The net impact on asset quality and non-performing loans, which feed into profitability, is more ambiguous as low rates make on one hand loan payments easier for borrowers but also may be associated with poorer quality borrowers getting loans. More generally, the state of the economy will importantly both influence the scope for profitable banking business and the level of interest rates. Related, effects of decreases in interest rates on the equity valuation of banks are often found to be positive, re?ecting the net effect of a combination of capital gains on longer-term assets and lower discount rates on future earnings, and expectations of higher future pro?ts, the latter as changes in interest rates (in part due to monetary policy actions) relate to expected economic growth and thereby loan demand and asset quality. When interest rates adversely affect banks' profitability and valuations, they can also impede banks' ability to raise new capital.
Besides the direct effects on banks' NIMs and profitability, banks may also alter their activities in responses to changes in interest rates. If short-term interest rates or spreads are not high enough to allow banks to reach their profit goals, banks may switch out of lending to opportunities to earn non-interest income, such as fee income from underwriting or asset management. This ability to engage in other activities will vary across countries depending on financial system structures, e.g., bank vs. market-based, and regulations. It may also vary across banks in ways related to bank size. Large banks are for example more likely to be able to engage in non-interest earning activities, such as investment banking or wealth management.
Theoretical Interpretation of NIM
Empirically, we find that the NIMs are higher when interest rates are higher, but NIMs are more sensitive to interest rates fluctuations when the level of interest rates is lower. This empirical result is consistent with a theoretical breakdown of the components of NIM.
First, consider the definition of the NIM:
$$Net\ Interest\ Margin=\frac{Interest\ Income-Interest\ Expense}{Average\ Earning\ Assets}$$
By definition, interest income can be written as the product of the bank's earning assets and the interest rate on lending, r, while interest expense can be written as the product of the bank's interest bearing liabilities and the interest rate on borrowing, r'.
$$Net\ Interest\ Margin=\frac{Avg.\ Earing\ Assets*r-Int.\ Bearing\ Liab.\ *r'}{Avg.\ Earning\ Assets}$$
We can write interest bearing liabilities as a ratio of average earning assets, so
$$Int.\ Bearing\ Liab.=\lambda *Avg.\ Earnign\ Assets, where\ \lambda =\frac{Int.\ Bearing\ Liabilities}{Avg.\ Earning\ Assets}$$
Likewise, we can define the ratio of the interest rate on borrowing and lending as: $r^{\prime }=\phi \ast r, where\ \phi =\frac{borrowing rate}{lending rate}$
Therefore,
$$Net\ Interest\ Margin=\frac{Avg.\ Earning\ Assets*r-Avg.\ Earning\ Assets*\ \lambda *\ \phi *r}{Average\ Earning\ Assets}$$
Taken together this becomes $\mathrm{NIM=r(1-\ }\mathrm{\lambda }\mathrm{\phi }\mathrm{)}$. In order to model how NIMs change as the interest rate level changes, it is easiest to assume a static balance sheet, i.e. that $\lambda$ is a fixed constant which yields three cases to consider how the borrowing rate relates to the lending rate.
Case 1: $\phi$ is static (e.g., the deposit rate is an unchanging proportion of the loan rate).
If this were the case then the rate of change of NIM in relation to r would be $\frac{dNIM}{dr}=1-\ \lambda \phi$
Because $\lambda$ and $\phi$ are both constants, the change in NIM would also be constant as r changes.
Case 2: $\phi =\frac{r-a}{r}$ (e.g., the deposit rate is a fixed spread below the loan rate).
If this were the case then we can substitute in $\frac{r-a}{r}$ for $\phi$ and we find that
$$NIM=\ r\left(1-\ \lambda \phi \right)=r\left[1-\ \lambda \left(\frac{r-a}{r}\right)\right]=r\left(1-\ \lambda \right) \ \lambda a$$
Then the rate of change of NIM in relation to r would be $\frac{dNIM}{dr}=1-\ \lambda$
Because we assume $\lambda$ to be a constant, the change in NIM would also be constant as r changes.
Case 3: $\phi =r^{\alpha -1}$, for $\alpha >1$ and $r>0$ and (e.g. the deposit rate grows as a proportion of the loan rate).
If this were the case then we can substitute in $r^{\alpha -1}$ for $\phi$ and we find that
$$NIM=\ r\left(1-\ \lambda \phi \right)=r\left(1-\lambda r^{\alpha -1}\right)=r-\lambda r^{\alpha }$$
Then the rate of change of NIM in relation to r would be $\frac{dNIM}{dr}=1-\ \lambda \alpha r^{\alpha -1}$
Because we assume $\lambda$ and $\alpha$ to be constant, the change in NIM would shrink as r increases, and would be greater when r is lower. In other words, the NIM would be more sensitive to changes in the interest rate when the interest rate is closer to zero.
Conclusion: Given our empirical results, we reject cases 1 and 2 as our tests are consistent with case 3. This result implies that there is an important non-linearity in the mapping of the short-term interest rate to the lending and borrowing interest rates.
Appendix Figure 1: Country Assignments by "Low" vs "High" 3-Month Sovereign Rate
Note: The figure shows how countries were classified for three years in the sample from 2005-2013. A country was classified as being in the "low" rate environment if its average three-month implied sovereign yield for that year was less than or equal to 1.25 percent and was classified as being in a "high" rate environment otherwise.
Sources: Bloomberg, staff calculations.
Accessible version
References
Adrian, Tobias, and Nellie Liang, 2014, "Monetary Policy, Financial Conditions, and Financial Stability," Federal Reserve Bank of New York Staff Reports, no. 690 September.
Borio, Claudio E. V. and Gambacorta, Leonardo and Hofmann, Boris, 2015, "The Influence of Monetary Policy on Bank Profitability," (October), BIS Working Paper No. 514.
Busch, Ramona and Christoph Memmel, 2015, "Banks' net interest margin and the level of interest rates," Discussion Papers 16/2015, Deutsche Bundesbank, Research Centre.
Bundesbank, 2015, "Financial Stability Review," September.
Covas, Francisco B. Marcelo Rezende, and Cindy M. Vojtech, 2015, "Why Are Net Interest Margins of Large Banks So Compressed?", FEDS Notes, October.
Dell'Ariccia, Giovanni, and Robert Marquez, 2013, "Interest Rates and the Bank Risk taking Channel," Annual Review of Financial Economics 5(1), 123--141.
Deutsche Bank, 2013, "Ultra-low interest rate: How Japanese banks have coped," June.
English, William B., Skander J. Van den Heuvel, and Egon Zakrajsek, 2012, "Interest Rate Risk and Bank Equity Valuations," FEDS Working Paper 2012-26.
ECB 2015, "Financial Stability Review," May, Frankfurt.
Genay, Hesna and Rich Podjasek, 2014, "What is the impact of a low interest rate environment on bank profitability?," Chicago Fed Letter, 324, July.
Memmel, Christoph, 2011, "Banks' exposure to interest rate risk, their earnings from term transformation, and the dynamics of the term structure," Journal of Banking and Finance, 35, 282--289.
1. We would like to thank William English and other Federal Reserve System colleagues for extensive comments. The views expressed in this note are those of the authors and should not be attributed to the Board of Governors of Federal Reserve System. Return to text
2. An overall assessment of how low interest rates may affect banks is beyond the scope of this note. For example, low interest rates can lead to valuation gains on securities, affect the quality of loans and related changes in loan-loss provisioning, etc. We also do not review whether low interest rates may lead to unhealthy reach for yield by banks (see Adrian and Liang (2014) and Dell'Ariccia and Marquez (2014) for (literature) reviews of the links between risk taking and interest rates). Return to text
3. Similarly, a study of 98 EU banks (ECB 2015) finds that macroeconomic factors, and not interest rates, have had the most importance for bank health since the global financial crisis. Return to text
4. Implied yields on currently outstanding three-month and ten-year bonds are used since not every country has at all points in time bonds maturing exactly three months or ten years later. These daily rates are then averaged over each year. Return to text
5. A limitation of Bankscope is that it focuses on relatively large banks within countries so results may be biased. That said, many smaller (and unlisted) banks are still included. Return to text
6. We also included in regressions commercial real estate prices, house prices, unemployment rates, and stock market performances. Because these data are not available for many countries and longer periods, it decreased coverage to such a degree that we preferred to use a more parsimonious specification. For those countries where we had these data, however, regression results were robust. Return to text
7. We additionally studied the impact of changes in the interest rate on banks' return on assets and of changes in the slope of the yield curve on NIMs and on return on assets. Here less consistent patterns emerged, as was also the case for Genay and Podjasek (2014). We suspect that over this period, which includes the global financial crisis, non-interest income and expense items, such as provisioning for non-performing loans, and large valuation gains and losses led to (even) greater volatility in banks' profitability, obscuring the direct effects of changes in interest rates. Return to text
8. Results hold for unbalanced or balanced samples, samples with or without U.S. banks, and trimming observations differently. Return to text
9. The sample was split into "long" versus "short" maturity of bank by first taking the average maturity for each bank over the sample period and then calculating the median average duration by country. Banks above the median average duration within each country were then classified to have a "long" and below a "short" duration. Besides differences in maturity structure, there can also be differences in the frequency of repricing of claims with the same final maturity, as for example, in fixed vs. variable rate mortgages. Consistent data on such differences across banks and countries is not available, however. Return to text
10. Accounting differences across countries can limit direct comparability of U.S. and AFE financial statements. For example, derivatives are reported to some extent at net values for U.S. banks but are largely at gross values under International Financial Reporting Standards, which has the effect of inflating assets and reducing return on asset figures for AFE banks. Gross derivatives represent roughly 15 percent for a representative European bank sample assets on a weighted basis, a material share, but not one that would substantially affect the profitability and NIM comparisons. Return to text | 2019-03-22T04:27:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4915870726108551, "perplexity": 3419.290521936726}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202628.42/warc/CC-MAIN-20190322034516-20190322060516-00290.warc.gz"} |
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# Snowmass Community Planning Meeting - Virtual
5-8 October 2020
Virtual
US/Central timezone
Captions are available at https://us.ai-live.com/CaptionViewer/Join/thirdparty?sessionId=USFERM0810B . Default meeting times are in US Central Daylight Time (UTC-5). Zoom connection information has been sent to registered participants.
## Gas TPCs with directional sensitivity to dark matter, neutrinos, and BSM physics
Not scheduled
3m
Virtual
### Speaker
Sven Vahsen (University of Hawaii)
### Description
There is an opportunity to develop a long-term, diverse, and cost-effective US experimental program based on directional detection of nuclear recoils in gas TPCs.
Smaller, 1 m$^3$ scale detectors could detect and demonstrate directional sensitivity to Coherent Elastic Neutrino-Nucleus Scattering (CEνNS) at either NuMI or DUNE. This technology is also sensitive to beyond the Standard Model (BSM) physics in the form of low-mass dark matter, heavy sterile neutrinos, and axion-like particles. For every factor ten increase in exposure, new measurements are possible. A 10 m$^3$ detector could produce the strongest SD WIMP-proton cross section limits of any experiment across all WIMP masses. A 1000 m$^3$ detector would detect between 13 and 37 solar CEνNS events over six years. Larger volumes would bring sensitivity to neutrinos from an even wider range of sources, including galactic supernovae, nuclear reactors, and geological processes. An ambitious DUNE-scale detector, but operating at room temperature and atmospheric pressure, would have non-directional WIMP sensitivity comparable to any proposed experiment, and would, in addition, allow us to utilize directionality to penetrate deep into the neutrino floor.
If a dark matter signal is observed, this would mark the beginning of a new era in physics. A large directional detector would then hold the key to first establishing the galactic origin of the signal, and to subsequently map the local WIMP velocity distribution and explore the particle phenomenology of dark matter.
To understand and fully maximize the physics reach of gas TPCs as envisioned here, further phenomenological work on dark matter and neutrinos, improved micro-pattern gaseous detectors (MPGDs), customized front end electronics and novel region-of-interest triggers are needed. We encourage the wider dark matter, neutrino, and instrumentation communities participating in Snowmass to come together and help evaluate and improve this proposal.
Primary frontier topic Cosmic Frontier
### Primary authors
Diego Aristizabal Sierra (Universidad Tecnica Federico Santa Mar\'{i}a) Connor Awe (Duke University) Elisabetta Baracchini (INFN, GSSI) Phillip Barbeau (Duke University) Bhaskar Dutta (Texas A&M University) Warren Lynch (University of Sheffield) Neil Spooner (University of Sheffield) James Battat (Wellesley College) Cosmin Deaconu (UChicago / KICP) Callum Eldridge (University of Sheffield) Majd Ghrear (University of Haawaii) Peter Lewis (University of Bonn) Dinesh Loomba (University of New Mexico) Katie J. Mack (North Carolina State University) Diane Markoff Markoff (North Carolina Central University) Hans Muller (University of Bonn) Kentaro Miuchi (Kobe University) Ciaran O'Hare (University of Sydney) Nguyen Phan (Los Alamos National Laboratory) Kate Scholberg (Duke University) Daniel Snowden-Ifft (Occidental College) Louis Strigari (Texas A&M University) Thomas Thorpe (GSSI) Sven Vahsen (University of Hawaii)
### Presentation Materials
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https://math.wikia.org/wiki/Incircle_and_excircles_of_a_triangle | ## FANDOM
1,168 Pages
In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is called the triangle's incenter.
An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two.
Every triangle has three distinct excircles, each tangent to one of the triangle's sides.
The center of the incircle can be found as the intersection of the three internal angle bisectors
The center of an excircle is the intersection of the internal bisector of one angle and the external bisectors of the other two. Because the internal bisector of an angle is perpendicular to its external bisector, it follows that the center of the incircle together with the three excircle centers form an orthocentric system.
## Relation to area of the triangle
The radii of the incircles and excircles are closely related to the area of the triangle. Suppose $\triangle ABC$ has an incircle with radius r and center I.
Let a be the length of BC, b the length of AC, and c the length of AB.
Now, the incircle is tangent to AB at some point C′, and so
$\angle AC'I$ is right.
Thus the radius C'I is an altitude of
$\triangle IAB$
Therefore
$\triangle IAB$
has base length c and height r, and so has area
$\tfrac{1}{2}cr$.
Similarly,
$\triangle IAC$
has area
$\tfrac{1}{2}br$
and
$\triangle IBC$
has area $\tfrac{1}{2}ar$.
Since these three triangles decompose $\triangle ABC$, we see that
$\Delta = \frac{1}{2} (a+b+c) r = s r,$
where $\Delta$ is the area of $\triangle ABC$ and $s= \frac{1}{2}(a+b+c)$ is its semiperimeter.
The radii in the excircles are called the exradii. Let the excircle at side AB touch at side AC extended at G, and let this excircle's
radius be $r_c$ and its center be $I_c$. Then $I_c G$ is an altitude of $\triangle ACI_c$,
so $\triangle ACI_c$ has area $\tfrac{1}{2}br_c$. By a similar argument,
$\triangle BCI_c$
has area
$\tfrac{1}{2}ar_c$
and $\triangle ABI_c$
has area
$\tfrac{1}{2}cr_c$.
Thus
$\Delta = \frac{1}{2}(a+b-c)r_c = (s-c)r_c$.
So, by symmetry,
$\Delta = sr = (s-a)r_a = (s-b)r_b = (s-c)r_c$.
By the law of cosines, we have
$\cos A = \frac{b^2 + c^2 - a^2}{2bc}$
Combining this with the identity $\sin^2 A + \cos^2 A = 1$, we have
$\sin A = \frac{\sqrt{-a^4 - b^4 - c^4 + 2a^2b^2 + 2b^2 c^2 + 2 a^2 c^2}}{2bc}$
But $\Delta = \tfrac{1}{2}bc \sin A$, and so
\begin{align} \Delta &= \frac{1}{4} \sqrt{-a^4 - b^4 - c^4 + 2a^2b^2 + 2b^2 c^2 + 2 a^2 c^2} \\ &= \frac{1}{4} \sqrt{ (a+b+c) (-a+b+c) (a-b+c) (a+b-c) }\\ & = \sqrt{s(s-a)(s-b)(s-c)}, \end{align}
[/itex]
which is Heron's formula.
Combining this with $sr=\Delta$, we have
$r^2 = \frac{\Delta^2}{s^2} = \frac{(s-a)(s-b)(s-c)}{s}$.
Similarly, $(s-a)r_a = \Delta$ gives
$r_a^2 = \frac{s(s-b)(s-c)}{s-a}$.
From these formulas one can see that the excircles are always larger than the incircle and that the largest excircle is the one tangent to the longest side and the smallest excircle is tangent to the shortest side. Further, combining these formulas formula yields:
$\Delta=\sqrt{rr_ar_br_c}.$
The ratio of the area of the incircle to the area of the triangle is less than or equal to $\frac{\pi}{3\sqrt{3}}$, with equality holding only for equilateral triangles.
## Nine-point circle and Feuerbach point
The circle tangent to all three of the excircles as well as the incircle is known as the nine-point circle. The point where the nine-point circle touches the incircle is known as the Feuerbach point.
## Gergonne triangle and point
The Gergonne triangle(of ABC) is defined by the 3 touchpoints of the incircle on the 3 sides.
Those vertices are denoted as TA, etc.
The point that TA denotes, lies opposite to A.
This Gergonne triangle TATBTC is also known as the contact triangle or intouch triangle of ABC.
The three lines ATA, BTB and CTC intersect in a single point called Gergonne point, denoted as Ge - X(7).
Interestingly, the Gergonne point of a triangle is the symmedian point of the Gergonne triangle.
The touchpoints of the three excircles with segments BC,CA and AB are the vertices of the extouch triangle. The points of intersection of the interior angle bisectors of ABC with the segments BC,CA,AB are the vertices of the incentral triangle.
## Nagel triangle and point
The Nagel triangle of ABC is denoted by the vertices XA, XB and XC that are the three points where the excircles touch the reference triangle ABC and where XA is opposite of A, etc. This triangle XAXBXC is also known as the extouch triangle of ABC. The circumcircle of the extouch triangle XAXBXC is called the Mandart circle. The three lines AXA, BXB and CXC are called the splitters of the triangle; they each bisect the perimeter of the triangle, and they intersect in a single point, the triangle's Nagel point Na - X(8).
Trilinear coordinates for the vertices of the intouch triangle are given by
• $A-\text{vertex}= 0 : \sec^2 \left(\frac{B}{2}\right) :\sec^2\left(\frac{C}{2}\right)$
• $B-\text{vertex}= \sec^2 \left(\frac{A}{2}\right):0:\sec^2\left(\frac{C}{2}\right)$
• $C-\text{vertex}= \sec^2 \left(\frac{A}{2}\right) :\sec^2\left(\frac{B}{2}\right):0$
Trilinear coordinates for the vertices of the extouch triangle are given by
• $A-\text{vertex} = 0 : \csc^2\left(\frac{B}{2}\right) : \csc^2\left(\frac{C}{2}\right)$
• $B-\text{vertex} = \csc^2\left(\frac{A}{2}\right) : 0 : \csc^2\left(\frac{C}{2}\right)$
• $C-\text{vertex} = \csc^2\left(\frac{A}{2}\right) : \csc^2\left(\frac{B}{2}\right) : 0$
Trilinear coordinates for the vertices of the incentral triangle are given by
• $\ A-\text{vertex} = 0 : 1 : 1$
• $\ B-\text{vertex} = 1 : 0 : 1$
• $\ C-\text{vertex} = 1 : 1 : 0$
Trilinear coordinates for the vertices of the excentral triangle are given by
• $\ A-\text{vertex}= -1 : 1 : 1$
• $\ B-\text{vertex}= 1 : -1 : 1$
• $\ C-\text{vertex}= 1 : -1 : -1$
Trilinear coordinates for the Gergonne point are given by
$\sec^2\left(\frac{A}{2}\right) : \sec^2 \left(\frac{B}{2}\right) : \sec^2\left(\frac{C}{2}\right)$,
or, equivalently, by the Law of Sines,
$\frac{bc}{b+ c - a} : \frac{ca}{c + a-b} : \frac{ab}{a+b-c}$.
Trilinear coordinates for the Nagel point are given by
$\csc^2\left(\frac{A}{2}\right) : \csc^2 \left(\frac{B}{2}\right) : \csc^2\left(\frac{C}{2}\right)$,
or, equivalently, by the Law of Sines,
$\frac{b+ c - a}{a} : \frac{c + a-b}{b} : \frac{a+b-c}{c}$.
It is the isotomic conjugate of the Gergonne point.
## Coordinates of the incenter
The Cartesian coordinates of the incenter are a weighted average of the coordinates of the three vertices using the side lengths of the triangle as weights. (The weights are positive so the incenter lies inside the triangle as stated above.) If the three vertices are located at $(x_a,y_a)$, $(x_b,y_b)$, and $(x_c,y_c)$, and the sides opposite these vertices have corresponding lengths $a$, $b$, and $c$, then the incenter is at
$\bigg(\frac{a x_a+b x_b+c x_c}{P},\frac{a y_a+b y_b+c y_c}{P}\bigg) = \frac{a(x_a,y_a)+b(x_b,y_b)+c(x_c,y_c)}{P}$
where $\ P = a + b + c.$
Trilinear coordinates for the incenter are given by
$\ 1 : 1 : 1.$
Barycentric coordinates for the incenter are given by
$\ a : b : c$
or equivalently
$\sin(A):\sin(B):\sin(C).$
## Equations for four circles
Let x : y : z be a variable point in trilinear coordinates, and let u = cos2(A/2), v = cos2(B/2), w = cos2(C/2). The four circles described above are given by these equations:
• Incircle:
$\ u^2x^2+v^2y^2+w^2z^2-2vwyz-2wuzx-2uvxy=0$
• A-excircle:
$\ u^2x^2+v^2y^2+w^2z^2-2vwyz+2wuzx+2uvxy=0$
• B-excircle:
$\ u^2x^2+v^2y^2+w^2z^2+2vwyz-2wuzx+2uvxy=0$
• C-excircle:
$\ u^2x^2+v^2y^2+w^2z^2+2vwyz+2wuzx-2uvxy=0$
## Euler's theorem
Euler's theorem states that in a triangle:
$(R-r_{in})^2=d^2+r_{in}^2,$
where R and rin are the circumradius and inradius respectively, and d is the distance between the circumcenter and the incenter.
For excircles the equation is similar:
$(R+r_{ex})^2=d^2+r_{ex}^2,$
where rex is the radius of one of the excircles, and d is the distance between the circumcenter and this excircle's center.
## Other incircle properties
Suppose the tangency points of the incircle divide the sides into lengths of x and y, y and z, and z and x. Then the incircle has the radius
$r = \sqrt{\frac{xyz}{x+y+z}}$
and the area of the triangle is
$K=\sqrt{xyz(x+y+z)}.$
If the altitudes from sides of lengths a, b, and c are ha, hb, and hc then the inradius r is one-third of the harmonic mean of these altitudes, i.e.
$r = \frac{1}{h_a^{-1}+h_b^{-1}+h_c^{-1}}.$
The product of the incircle radius r and the circumcircle radius R of a triangle with sides a, b, and c is
$rR=\frac{abc}{2(a+b+c)}.$
$ab+bc+ca=s^2+(4R+r)r,$
$a^2+b^2+c^2=2s^2-2(4R+r)r.$
Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its incircle). There are either one, two, or three of these for any given triangle.
The distance from the incenter to the centroid is less than one third the length of the longest median of the triangle.
Denoting the distance from the incenter to the Euler line as d, the length of the longest median as v, the length of the longest side as u, and the semiperimeter as s, the following inequalities hold:
$\frac{d}{s} < \frac{d}{u} < \frac{d}{v} < \frac{1}{3}.$
Denoting the center of the incircle of triangle ABC as I, we have
$\frac{\overline{IA} \cdot \overline{IA}}{\overline{CA} \cdot \overline{AB}} + \frac{\overline{IB} \cdot \overline{IB}}{\overline{AB} \cdot \overline{BC}} + \frac{\overline{IC} \cdot \overline{IC}}{\overline{BC} \cdot \overline{CA}} = 1.$
## Other excircle properties
The circular hull of the excircles is internally tangent to each of the excircles, and thus is an Apollonius circle. The radius of this Apollonius circle is $\frac{r^2+s^2}{4r}$ where r is the incircle radius and s is the semiperimeter of the triangle.
The following relations hold among the inradius r, the circumradius R, the semiperimeter s, and the excircle radii r'a, rb, rc:
$r_a+r_b+r_c=4R+r,$
$r_a r_b+r_br_c+r_cr_a = s^2,$
$r_a^2 + r_b^2 + r_c^2 = (4R+r)^2 -2s^2,$
The circle through the centers of the three excircles has radius 2R.
If H is the orthocenter of triangle ABC, then
$r_a+r_b+r_c+r=AH+BH+CH+2R,$
$r_a^2+r_b^2+r_c^2+r^2=AH^2+BH^2+CH^2+(2R)^2.$
Some (but not all) quadrilaterals have an incircle. These are called tangential quadrilaterals. Among their many properties perhaps the most important is that their opposite sides have equal sums. This is called the Pitot theorem.
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https://zbmath.org/authors/?q=ai%3Ahajek.jaroslav | # zbMATH — the first resource for mathematics
## Hájek, Jaroslav
Compute Distance To:
Author ID: hajek.jaroslav Published as: Hajek, J.; Hajek, Jaroslav; Hájek, J.; Hájek, Jaroslav External Links: MGP · Math-Net.Ru · Wikidata · GND · MacTutor
Documents Indexed: 54 Publications since 1955, including 7 Books Biographic References: 7 Publications
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#### Co-Authors
45 single-authored 2 Dupac, Vaclav 2 Šidák, Zbyněk 1 Dalenius, Tore 1 Fabian, František 1 Fischer, Otto F. 1 Kimeldorf, George S. 1 Koutník, Václav 1 Novotný, Miroslav 1 Rényi, Alfréd 1 Sekanina, Milan 1 Sen, Pranab Kumar 1 Zubrzycki, Stefan
all top 5
#### Serials
6 Časopis Pro Pěstování Matematiky 6 Czechoslovak Mathematical Journal 6 Selected Translations in Mathematical Statistics and Probability 5 Annals of Mathematical Statistics 3 Aplikace Matematiky 2 The Annals of Statistics 2 Bulletin de l’Institut International de Statistique 1 Acta Mathematica Academiae Scientiarum Hungaricae 1 Zastosowania Matematyki 1 Theory of Probability and its Applications 1 Colloquium Mathematicum 1 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 1 Proceedings of the National Academy of Sciences of the United States of America 1 Publications of the Mathematical Institute of the Hungarian Academy of Sciences, Series A 1 Statistics: Textbooks and Monographs 1 Wiley Series in Probability and Statistics
#### Fields
19 Statistics (62-XX) 5 Probability theory and stochastic processes (60-XX) 2 History and biography (01-XX) 1 General and overarching topics; collections (00-XX) 1 Geometry (51-XX)
#### Citations contained in zbMATH
34 Publications have been cited 1,296 times in 1,099 Documents Cited by Year
Theory of rank tests. Zbl 0161.38102
Hájek, Jaroslav; Šidák, Zbyněk
1967
Theory of rank tests. 2nd ed. Zbl 0944.62045
Hájek, Jaroslav; Šidák, Zbyněk; Sen, Pranab K.
1999
Asymptotic normality of simple linear rank statistics under alternatives. Zbl 0187.16401
Hájek, Jaroslav
1968
A characterization of limiting distributions of regular estimates. Zbl 0193.18001
Hajek, J.
1970
Asymptotic normality of linear rank statistics under alternatives. Zbl 0162.50503
Hajek, J.
1967
Asymptotic theory of rejective sampling with varying probabilities from a finite population. Zbl 0138.13303
Hájek, Jaroslav
1964
Some extensions of the Wald-Wolfowitz-Noether theorem. Zbl 0107.13404
Hajek, J.
1961
Generalization of an inequality of Kolmogorov. Zbl 0067.10701
Hájek, J.; Rényi, Alfréd
1955
Asymptotically most powerful rank-order tests. Zbl 0133.42001
Hajek, J.
1962
Limiting distributions in simple random sampling from a finite population. Zbl 0102.15001
Hajek, Jaroslav
1960
Local asymptotic minimax and admissibility in estimation. Zbl 0281.62010
Hajek, Jaroslav
1972
Sampling from a finite population. Ed. by Václav Dupač. Zbl 0494.62008
Hájek, Jaroslav
1981
A course in nonparametric statistics. Zbl 0193.16901
Hajek, J.
1969
Optimum strategy and other problems in probability sampling. Zbl 0138.13301
Hajek, J.
1959
On linear statistical problems in stochastic processes. Zbl 0114.34504
Hajek, J.
1962
On a property of normal distributions of any stochastic process. Zbl 0086.33503
Hájek, Jaroslav
1958
Asymptotic sufficiency of the vector of ranks in the Bahadur sense. Zbl 0286.62026
Hajek, Jaroslav
1974
Asymptotic normality of simple linear rank statistics under alternatives. II. Zbl 0193.17401
Dupač, Václav; Hájek, Jaroslav
1969
A property of $$J$$-divergences of marginal probability distributions. Zbl 0082.34103
Hájek, Jaroslav
1958
Asymptotic theory of rejective sampling from a finite population. Zbl 0156.40103
Hajek, J.
1965
Inequalities for the generalized Student’s distribution and their applications. Zbl 0111.34107
Hajek, J.
1962
On plane sampling and related geometrical problems. Zbl 0213.43803
Dalenius, Tore; Hájek, Jaroslav; Zubrzycki, Stefan
1961
Extension of the Kolmogorov-Smirnov test to regression alternatives. Zbl 0142.15802
Hajek, Jaroslav
1965
Predicting a stationary process when the correlation function is convex. Zbl 0080.13003
Hájek, Jaroslav
1958
Collected works of Jaroslav Hájek. With commentary. Zbl 0903.01017
Hájek, Jaroslav
1998
Regression designs in autoregressive stochastic processes. Zbl 0282.62067
Hajek, Jaroslav; Kimeldorf, George
1974
On basic concepts of statistics. Zbl 0214.45704
Hájek, J.
1967
On linear estimation theory for an infinite number of observations. Zbl 0114.35504
Hajek, J.
1962
On a property of normal distributions of any stochastic process. Zbl 0112.09702
Hájek, Jaroslav
1961
Asymptotic normality of the Wilcoxon statistic under divergent alternatives. Zbl 0237.62039
Dupac, V.; Hajek, J.
1969
Locally most powerful rank tests of independence. Zbl 0187.16103
Hajek, J.
1968
Theorie der Wahrscheinlichkeitsstichproben mit Anwendungen auf Stichprobenuntersuchungen. [Teorie pravděpodobnostního výběru s aplikacemi na výběrová šetření.]. Zbl 0097.34203
Hájek, Jaroslav
1960
Some contributions to the théory of probability sampling. Zbl 0091.14804
Hájek, Jaroslav
1959
Linear estimation of the mean value of a stationary random process with convex correlation function. Zbl 0112.09701
Hájek, Jaroslav
1956
Theory of rank tests. 2nd ed. Zbl 0944.62045
Hájek, Jaroslav; Šidák, Zbyněk; Sen, Pranab K.
1999
Collected works of Jaroslav Hájek. With commentary. Zbl 0903.01017
Hájek, Jaroslav
1998
Sampling from a finite population. Ed. by Václav Dupač. Zbl 0494.62008
Hájek, Jaroslav
1981
Asymptotic sufficiency of the vector of ranks in the Bahadur sense. Zbl 0286.62026
Hajek, Jaroslav
1974
Regression designs in autoregressive stochastic processes. Zbl 0282.62067
Hajek, Jaroslav; Kimeldorf, George
1974
Local asymptotic minimax and admissibility in estimation. Zbl 0281.62010
Hajek, Jaroslav
1972
A characterization of limiting distributions of regular estimates. Zbl 0193.18001
Hajek, J.
1970
A course in nonparametric statistics. Zbl 0193.16901
Hajek, J.
1969
Asymptotic normality of simple linear rank statistics under alternatives. II. Zbl 0193.17401
Dupač, Václav; Hájek, Jaroslav
1969
Asymptotic normality of the Wilcoxon statistic under divergent alternatives. Zbl 0237.62039
Dupac, V.; Hajek, J.
1969
Asymptotic normality of simple linear rank statistics under alternatives. Zbl 0187.16401
Hájek, Jaroslav
1968
Locally most powerful rank tests of independence. Zbl 0187.16103
Hajek, J.
1968
Theory of rank tests. Zbl 0161.38102
Hájek, Jaroslav; Šidák, Zbyněk
1967
Asymptotic normality of linear rank statistics under alternatives. Zbl 0162.50503
Hajek, J.
1967
On basic concepts of statistics. Zbl 0214.45704
Hájek, J.
1967
Asymptotic theory of rejective sampling from a finite population. Zbl 0156.40103
Hajek, J.
1965
Extension of the Kolmogorov-Smirnov test to regression alternatives. Zbl 0142.15802
Hajek, Jaroslav
1965
Asymptotic theory of rejective sampling with varying probabilities from a finite population. Zbl 0138.13303
Hájek, Jaroslav
1964
Asymptotically most powerful rank-order tests. Zbl 0133.42001
Hajek, J.
1962
On linear statistical problems in stochastic processes. Zbl 0114.34504
Hajek, J.
1962
Inequalities for the generalized Student’s distribution and their applications. Zbl 0111.34107
Hajek, J.
1962
On linear estimation theory for an infinite number of observations. Zbl 0114.35504
Hajek, J.
1962
Some extensions of the Wald-Wolfowitz-Noether theorem. Zbl 0107.13404
Hajek, J.
1961
On plane sampling and related geometrical problems. Zbl 0213.43803
Dalenius, Tore; Hájek, Jaroslav; Zubrzycki, Stefan
1961
On a property of normal distributions of any stochastic process. Zbl 0112.09702
Hájek, Jaroslav
1961
Limiting distributions in simple random sampling from a finite population. Zbl 0102.15001
Hajek, Jaroslav
1960
Theorie der Wahrscheinlichkeitsstichproben mit Anwendungen auf Stichprobenuntersuchungen. [Teorie pravděpodobnostního výběru s aplikacemi na výběrová šetření.]. Zbl 0097.34203
Hájek, Jaroslav
1960
Optimum strategy and other problems in probability sampling. Zbl 0138.13301
Hajek, J.
1959
Some contributions to the théory of probability sampling. Zbl 0091.14804
Hájek, Jaroslav
1959
On a property of normal distributions of any stochastic process. Zbl 0086.33503
Hájek, Jaroslav
1958
A property of $$J$$-divergences of marginal probability distributions. Zbl 0082.34103
Hájek, Jaroslav
1958
Predicting a stationary process when the correlation function is convex. Zbl 0080.13003
Hájek, Jaroslav
1958
Linear estimation of the mean value of a stationary random process with convex correlation function. Zbl 0112.09701
Hájek, Jaroslav
1956
Generalization of an inequality of Kolmogorov. Zbl 0067.10701
Hájek, J.; Rényi, Alfréd
1955
all top 5
#### Cited by 1,229 Authors
34 Sen, Pranab Kumar 21 Hallin, Marc 17 Puri, Madan Lal 16 Janssen, Arnold 14 Hušková, Marie 13 Bandyopadhyay, Uttam 10 Berger, Yves G. 10 Jurečková, Jana 10 Schick, Anton 9 Kössler, Wolfgang 9 Koziol, James A. 9 Shiraishi, Taka-aki 9 Wefelmeyer, Wolfgang 8 Akritas, Michael G. 8 Biswas, Atanu 8 Koul, Hira Lal 7 Hettmansperger, Thomas P. 7 Höpfner, Reinhard 7 Mukherjee, Amitava 7 Paindaveine, Davy 7 Tardif, Serge 6 Bertail, Patrice 6 Clémençon, Stéphan 6 Müller, Ursula U. 6 Neuhaus, Georg 6 Ruymgaart, Frits H. 6 Seoh, Munsup 6 Tillé, Yves 6 van Eeden, Constance 5 Alvo, Mayer 5 Bindele, Huybrechts F. 5 Brunner, Edgar 5 Chauvet, Guillaume 5 Conti, Pier Luigi 5 Ghosh, Malay 5 Johnson, Richard A. 5 Klaassen, Chris A. J. 5 Milbrodt, Hartmut 5 Murakami, Hidetoshi 5 Quessy, Jean-François 5 Roussas, George Gregory 5 Rublík, František 5 Šidák, Zbyněk 5 Strasser, Helmut 5 Werker, Bas J. M. 4 Albers, Willem 4 Allal, Jelloul 4 Antille, Andre 4 Behnen, Konrad 4 Beran, Rudolf J. 4 Bickel, Peter John 4 Büning, Herbert 4 Chautru, Emilie 4 Csörgő, Miklós 4 Das, Radhakanta 4 Denker, Manfred 4 Dufour, Jean-Marie 4 Fligner, Michael A. 4 Genest, Christian 4 Haux, Reinhold 4 Horváth, Lajos 4 Janssen, Paul 4 Ledwina, Teresa 4 Mansouri, Hossein 4 Merzougui, M. 4 Nadarajah, Saralees 4 Nikitin, Yakov Yu. 4 Oja, Hannu 4 Rieder, Helmut 4 Withers, Christopher Stroude 4 Wu, Tieejian 3 Abd-Elfattah, Ehab F. 3 Antoch, Jaromír 3 Bagkavos, Dimitrios 3 Baker, Charles R. 3 Balakrishnan, Narayanaswamy 3 Bening, Vladimir E. 3 Bentarzi, Mohamed 3 Bhattacharya, Debasis 3 Bhattacharyya, Gouri K. 3 Borroni, Claudio Giovanni 3 Burger, Hans Ulrich 3 Cabaña, Alejandra 3 Cabaña, Enrique M. 3 Cardot, Hervé 3 Chatterjee, Shoutir Kishore 3 Chattopadhyay, Gopaldeb 3 del Barrio, Eustasio 3 Deville, Jean-Claude 3 Ding, Peng 3 Duran, Benjamin S. 3 Froda, Sorana M. 3 Gombay, Edit 3 Govindarajulu, Zakkula 3 Grafström, Anton 3 Greenwood, Priscilla E. 3 Hájek, Jaroslav 3 Hothorn, Torsten 3 Hwang, Tea-Yuan 3 Jammalamadaka, Sreenivasa Rao ...and 1,129 more Authors
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#### Cited in 137 Serials
128 Journal of Statistical Planning and Inference 101 Communications in Statistics. Theory and Methods 77 Statistics & Probability Letters 53 Journal of Nonparametric Statistics 44 Journal of Multivariate Analysis 43 Annals of the Institute of Statistical Mathematics 41 The Annals of Statistics 36 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 32 Journal of Econometrics 29 The Canadian Journal of Statistics 25 Journal of Statistical Computation and Simulation 25 Computational Statistics and Data Analysis 24 Statistica Neerlandica 23 Metrika 20 Stochastic Processes and their Applications 19 Statistics 18 Communications in Statistics. Simulation and Computation 17 Kybernetika 16 Aplikace Matematiky 12 Biometrical Journal 11 Probability Theory and Related Fields 11 Journal of Mathematical Sciences (New York) 11 Bernoulli 10 Sequential Analysis 10 Electronic Journal of Statistics 9 Scandinavian Journal of Statistics 8 Journal of Soviet Mathematics 8 Statistical Papers 7 Biometrics 7 Statistical Science 7 Journal of Applied Statistics 6 Journal of the American Statistical Association 6 Computational Statistics 6 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 6 Journal of Statistical Theory and Practice 5 Lithuanian Mathematical Journal 5 Journal of Time Series Analysis 5 Stochastic Analysis and Applications 5 Applications of Mathematics 5 Econometric Theory 4 Journal of Mathematical Analysis and Applications 4 Proceedings of the American Mathematical Society 4 Acta Applicandae Mathematicae 4 Test 4 Mathematical Methods of Statistics 4 Statistical Methods and Applications 4 Statistical Methodology 3 Acta Mathematica Academiae Scientiarum Hungaricae 3 Periodica Mathematica Hungarica 3 Theory of Probability and its Applications 3 The Annals of Probability 3 Applied Mathematics and Computation 3 Czechoslovak Mathematical Journal 3 Statistical Inference for Stochastic Processes 3 Brazilian Journal of Probability and Statistics 3 AStA. Advances in Statistical Analysis 2 Mathematical Notes 2 Psychometrika 2 Journal of Approximation Theory 2 Mathematica Slovaca 2 Metron 2 Notre Dame Journal of Formal Logic 2 Trabajos de Estadistica y de Investigacion Operativa 2 American Journal of Mathematical and Management Sciences 2 Acta Mathematicae Applicatae Sinica. English Series 2 Journal of Theoretical Probability 2 MCSS. Mathematics of Control, Signals, and Systems 2 Annales de l’Institut Henri Poincaré. Nouvelle Série. Section B. Calcul des Probabilités et Statistique 2 ZOR. Zeitschrift für Operations Research 2 Lifetime Data Analysis 2 Journal of Inequalities and Applications 2 Methodology and Computing in Applied Probability 2 Decisions in Economics and Finance 2 Journal of the Korean Statistical Society 2 Sankhyā. Series A 2 Statistics and Computing 1 Computers & Mathematics with Applications 1 Communications in Mathematical Physics 1 International Journal of Systems Science 1 Journal of the Franklin Institute 1 Rocky Mountain Journal of Mathematics 1 Arkiv för Matematik 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques 1 Fuzzy Sets and Systems 1 Journal of Combinatorial Theory. Series A 1 Journal of Computational and Applied Mathematics 1 Journal of Economic Theory 1 Journal of Mathematical Economics 1 Journal of Mathematical Psychology 1 Mathematics and Computers in Simulation 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Numerische Mathematik 1 Scandinavian Actuarial Journal 1 Transactions of the American Mathematical Society 1 Moscow University Computational Mathematics and Cybernetics 1 Advances in Applied Mathematics 1 Insurance Mathematics & Economics 1 Optimization 1 Journal of Complexity ...and 37 more Serials
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#### Cited in 25 Fields
988 Statistics (62-XX) 224 Probability theory and stochastic processes (60-XX) 86 Numerical analysis (65-XX) 17 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Information and communication theory, circuits (94-XX) 8 History and biography (01-XX) 7 Functional analysis (46-XX) 6 Operations research, mathematical programming (90-XX) 4 Measure and integration (28-XX) 4 Computer science (68-XX) 4 Biology and other natural sciences (92-XX) 4 Systems theory; control (93-XX) 3 Mathematical logic and foundations (03-XX) 3 Combinatorics (05-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Quantum theory (81-XX) 1 Geophysics (86-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-03-08T23:14:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35499510169029236, "perplexity": 6865.872514127702}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178385529.97/warc/CC-MAIN-20210308205020-20210308235020-00153.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Azener.clarence | # zbMATH — the first resource for mathematics
## Zener, Clarence
Compute Distance To:
Author ID: zener.clarence Published as: Zener, C.; Zener, Clarence External Links: Wikidata · GND
Documents Indexed: 46 Publications since 1929, including 4 Books
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#### Co-Authors
33 single-authored 3 Duffin, Richard James 3 Guillemin, V. jun. 2 Peterson, Elmor L. 1 Heikes, R. R. 1 Kemble, Edwin C. 1 Mott, Nevill Francis 1 Nuckolls, R. 1 Otis, W. 1 Rosen, Nathan
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#### Serials
22 Physical Review, II. Series 8 Proceedings of the National Academy of Sciences of the United States of America 7 Proceedings of the Royal Society of London. Series A 3 Proceedings of the Cambridge Philosophical Society 1 Reviews of Modern Physics 1 Zeitschrift für Physik
#### Fields
3 Operations research, mathematical programming (90-XX)
#### Citations contained in zbMATH Open
32 Publications have been cited 530 times in 460 Documents Cited by Year
Geometric programming. Theory and application. Zbl 0171.17601
Duffin, Richard J.; Peterson, Elmor L.; Zener, Clarence
1967
Non-adiabatic crossing of energy levels. Zbl 0005.18605
Zener, Clarence
1932
Internal friction in solids. I: Theory of internal friction reeds. JFM 63.1341.03
Zener, C.
1937
Elasticity and unelasticity of metals. Zbl 0032.22202
Zener, Clarence
1948
Non-adiabatic crossing of energy levels. JFM 58.1356.02
Zener, C.
1932
Internal friction in solids. II. General theory of thermoelastic internal friction. JFM 64.1420.03
Zener, C.
1938
A theory of the electrical breakdown of solid dielectrics. Zbl 0009.27605
Zener, Clarence
1934
Double Stern-Gerlach experiment and related collision phenomena. Zbl 0004.42704
Rosen, N.; Zener, C.
1932
Analytic atomic wave functions. JFM 56.1313.01
Zener, C.
1930
A mathematical aid in optimizing engineering designs. Zbl 0094.36701
Zener, Clarence
1961
The intrinsic inelasticity of large plates. Zbl 0026.36701
Zener, Clarence
1941
Interaction between the $$d$$ shells in the transition metals. Zbl 0042.23502
Zener, C.
1951
Interchange of translational, rotational and vibrational energy in molecular collisions. Zbl 0001.17703
Zener, Clarence
1931
A theory of the electrical breakdown of solid dielectrics. JFM 60.0781.04
Zener, C.
1934
A further mathematical aid in optimizing engineering designs. Zbl 0105.33901
Zener, C.
1962
Internal friction in solids. III. Experimental demonstration of thermoelastic internal friction. JFM 64.1421.01
Zener, C.; Otis, W.; Nuckolls, R.
1938
The $$B$$-state of the hydrogen molecule. JFM 55.0540.01
Zener, C.; Guillemin, V. jun.
1929
The two quantum excited states of the hydrogen molecule. JFM 55.0539.05
Kemble, E. C.; Zener, C.
1929
Low velocity inelastic collisions. Zbl 0002.23101
Zener, Clarence
1931
A general proof of certain fundamental equations in the theory of metallic conduction. Zbl 0008.42304
Jones, H.; Zener, C.
1934
Hydrogen-ion wave function. JFM 55.0540.02
Guillemin, V. jun.; Zener, C.
1929
The theory of the change in resistance in a magnetic field. Zbl 0009.14005
Jones, H.; Zener, C.
1934
Theory of strain interaction of solute atoms. Zbl 0032.14103
Zener, C.
1948
Exchange interactions. Zbl 0050.23807
Zener, C.; Heikes, R. R.
1953
Interaction between the $$d$$-shells in the transition metals. IV. The intrinsic antiferromagnetic character of iron. Zbl 0046.45604
Zener, C.
1952
The intrinsic inelasticity of large plates. JFM 67.0828.01
Zener, C.
1941
Internal friction in solids. IV. Relation between cold work and internal friction. JFM 64.1421.02
Zener, C.
1938
Geometric programming, chemical equilibrium, and the antientropy function. Zbl 0182.53103
Duffin, R. J.; Zener, C.
1969
Geometric programming – theory and application. Übersetzung aus dem Englischen von D. A. Babaev. (Геометрическое программирование.) Zbl 0236.90062
Duffin, Richard J.; Peterson, Elmor L.; Zener, Clarence
1972
Dissociation of excited diatomic molecules by external perturbations. Zbl 0007.08901
Zener, Clarence
1933
Elastic reflection of atoms from crystal. JFM 58.0947.07
Zener, C.
1932
Redesign overcompensation. Zbl 0128.39503
Zener, C.
1965
Geometric programming – theory and application. Übersetzung aus dem Englischen von D. A. Babaev. (Геометрическое программирование.) Zbl 0236.90062
Duffin, Richard J.; Peterson, Elmor L.; Zener, Clarence
1972
Geometric programming, chemical equilibrium, and the antientropy function. Zbl 0182.53103
Duffin, R. J.; Zener, C.
1969
Geometric programming. Theory and application. Zbl 0171.17601
Duffin, Richard J.; Peterson, Elmor L.; Zener, Clarence
1967
Redesign overcompensation. Zbl 0128.39503
Zener, C.
1965
A further mathematical aid in optimizing engineering designs. Zbl 0105.33901
Zener, C.
1962
A mathematical aid in optimizing engineering designs. Zbl 0094.36701
Zener, Clarence
1961
Exchange interactions. Zbl 0050.23807
Zener, C.; Heikes, R. R.
1953
Interaction between the $$d$$-shells in the transition metals. IV. The intrinsic antiferromagnetic character of iron. Zbl 0046.45604
Zener, C.
1952
Interaction between the $$d$$ shells in the transition metals. Zbl 0042.23502
Zener, C.
1951
Elasticity and unelasticity of metals. Zbl 0032.22202
Zener, Clarence
1948
Theory of strain interaction of solute atoms. Zbl 0032.14103
Zener, C.
1948
The intrinsic inelasticity of large plates. Zbl 0026.36701
Zener, Clarence
1941
The intrinsic inelasticity of large plates. JFM 67.0828.01
Zener, C.
1941
Internal friction in solids. II. General theory of thermoelastic internal friction. JFM 64.1420.03
Zener, C.
1938
Internal friction in solids. III. Experimental demonstration of thermoelastic internal friction. JFM 64.1421.01
Zener, C.; Otis, W.; Nuckolls, R.
1938
Internal friction in solids. IV. Relation between cold work and internal friction. JFM 64.1421.02
Zener, C.
1938
Internal friction in solids. I: Theory of internal friction reeds. JFM 63.1341.03
Zener, C.
1937
A theory of the electrical breakdown of solid dielectrics. Zbl 0009.27605
Zener, Clarence
1934
A theory of the electrical breakdown of solid dielectrics. JFM 60.0781.04
Zener, C.
1934
A general proof of certain fundamental equations in the theory of metallic conduction. Zbl 0008.42304
Jones, H.; Zener, C.
1934
The theory of the change in resistance in a magnetic field. Zbl 0009.14005
Jones, H.; Zener, C.
1934
Dissociation of excited diatomic molecules by external perturbations. Zbl 0007.08901
Zener, Clarence
1933
Non-adiabatic crossing of energy levels. Zbl 0005.18605
Zener, Clarence
1932
Non-adiabatic crossing of energy levels. JFM 58.1356.02
Zener, C.
1932
Double Stern-Gerlach experiment and related collision phenomena. Zbl 0004.42704
Rosen, N.; Zener, C.
1932
Elastic reflection of atoms from crystal. JFM 58.0947.07
Zener, C.
1932
Interchange of translational, rotational and vibrational energy in molecular collisions. Zbl 0001.17703
Zener, Clarence
1931
Low velocity inelastic collisions. Zbl 0002.23101
Zener, Clarence
1931
Analytic atomic wave functions. JFM 56.1313.01
Zener, C.
1930
The $$B$$-state of the hydrogen molecule. JFM 55.0540.01
Zener, C.; Guillemin, V. jun.
1929
The two quantum excited states of the hydrogen molecule. JFM 55.0539.05
Kemble, E. C.; Zener, C.
1929
Hydrogen-ion wave function. JFM 55.0540.02
Guillemin, V. jun.; Zener, C.
1929
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#### Cited by 685 Authors
11 Dinkel, John J. 9 Fang, Shu-Cherng 8 Ecker, Joseph G. 8 Kochenberger, Gary A. 7 Jefferson, Thomas R. 7 Kumar Roy, Tapan 7 Peterson, Elmor L. 7 Scott, Carlton H. 6 Bricker, Dennis L. 6 Rajasekera, J. R. 6 Zener, Clarence 5 Fermanian-Kammerer, Clotilde 5 Mandal, Nirmal Kumar 5 Passy, Ury 4 Dembo, Ron S. 4 Eleuch, Hichem 4 Hagedorn, George A. 4 Islam, Sahidul 4 Maiti, Manoranjan 4 Rice, Oscar Knefler 4 Slater, John Clarke 4 Tupholme, G. E. 4 Van Vleck, John Hasbrouck 3 Avriel, Mordecai 3 Ben-Israel, Adi 3 Boyd, Stephen Poythress 3 Cao, Bingyuan 3 Do Nascimento, Roberto Quirino 3 Dutta, Amit Kumar 3 Elster, Karl-Heinz 3 Elster, Rosalind 3 Gochet, Willy F. 3 Joye, Alain 3 Jung, Hoon 3 Klein, Cerry M. 3 Knowles, Kevin M. 3 Kortanek, Kenneth O. 3 Rajgopal, Jayant 3 Rezazadeh, Ghader 3 Rosen, Nathan 3 Rostovtsev, Yuri V. 3 Rotter, Ingrid 3 Smeers, Yves 2 Allueva, Ana Isabel 2 Aryanezhad, Mir-Bahador-Qoli 2 Berman, Gennady P. 2 Biswal, Mahendra Prasad 2 Bloch, Leon 2 Castro, Pedro M. 2 Chandrasekaran, Venkat 2 Chen, Zhiping 2 Cheng, Hao 2 Cheng, Tai-Chiu Edwin 2 Colin de Verdière, Yves 2 Coolidge, Albert Sprague 2 De Oliveira Santos, Rubia Mara 2 de Wolff, Timo 2 Demeio, Lucio 2 Dressler, Mareike 2 Duffin, Richard James 2 Figueiredo Lima, Edson jun. 2 Fraas, Martin 2 Grover, Dhruv 2 Guseinov, I. I. 2 Iliman, Sadik 2 James, Hubert M. 2 Kelly, Donald W. 2 Kim, Seung-Jean 2 Korsch, Hans Jürgen 2 Kupferschmid, Michael 2 Lavery, John E. 2 Lisser, Abdel 2 Liu, Jia 2 Lu, Jianfeng 2 Luptacik, Mikulas 2 Lyra, Marcelo L. 2 Mahapatra, Ghanshaym Singha 2 Matos, Henrique A. 2 McCarl, Bruce A. 2 Nesterov, Alexander I. 2 Panda, Debdulal 2 Phillips, Andrew T. 2 Pratt, George W. jun. 2 Rosen, J. Ben 2 Rossikhin, Yury A. 2 Sadjadi, Seyed Jafar 2 Schwieger, Horst 2 Segall, Richard S. 2 Seitz, Frederick 2 Sengupta, Jati K. 2 Shah, Parikshit 2 Shitikova, Marina V. 2 Stark, Robert M. 2 Teles, João P. 2 Vahdat, Armin Saeedi 2 Vakakis, Alexander F. 2 Verma, Rakesh Kumar 2 Watanabe, Takuya 2 Wiebking, Rolf D. 2 Wilde, Douglass J. ...and 585 more Authors
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#### Cited in 147 Serials
40 Physical Review, II. Series 34 Journal of Optimization Theory and Applications 31 European Journal of Operational Research 17 Mathematical Programming 16 Acta Mechanica 13 Applied Mathematical Modelling 12 Journal of Mathematical Physics 11 Journal of Mathematical Analysis and Applications 11 Applied Mathematics and Computation 9 New Journal of Physics 7 Journal of Mathematical Chemistry 6 Optimization 6 Journal of Modern Optics 5 International Journal of Modern Physics B 5 Journal of Engineering Mathematics 5 Reviews of Modern Physics 5 Journal of Elasticity 5 Optimization and Engineering 4 Computers & Mathematics with Applications 4 Communications in Mathematical Physics 4 International Journal of Theoretical Physics 4 Journal of Computational Physics 4 Fuzzy Sets and Systems 4 Meccanica 4 Operations Research Letters 4 Mathematical and Computer Modelling 4 The Journal of Chemical Physics 3 Computer Methods in Applied Mechanics and Engineering 3 Discrete Applied Mathematics 3 Journal of Statistical Physics 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Information Sciences 3 International Journal for Numerical Methods in Engineering 3 International Journal of Production Research 3 Computers & Operations Research 3 Journal of Global Optimization 3 Zeitschrift für Operations Research. Serie A: Theorie 3 Mathematical Programming. Series A. Series B 3 Computational Optimization and Applications 3 Nonlinear Dynamics 3 Annales Henri Poincaré 3 Quantum Information Processing 3 Journal of Statistical Mechanics: Theory and Experiment 3 Bulletin of the Russian Academy of Sciences: Physics 3 Physical Review A, Third Series 2 Archive for Rational Mechanics and Analysis 2 European Journal of Physics 2 International Journal of Plasticity 2 International Journal of Solids and Structures 2 International Journal of Systems Science 2 Journal of the Franklin Institute 2 Journal of the Mechanics and Physics of Solids 2 Physics Letters. A 2 Physics Reports 2 Theoretical and Mathematical Physics 2 Fortschritte der Physik 2 Journal of Computational and Applied Mathematics 2 Physica D 2 Annals of Operations Research 2 Physics of Fluids 2 Mathematical Problems in Engineering 2 Journal of Vibration and Control 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Fuzzy Optimization and Decision Making 2 Journal of Applied Physics 2 Annales de l’Institut Henri Poincaré 2 Unternehmensforschung 2 Studies in History and Philosophy of Science. Part B. Studies in History and Philosophy of Modern Physics 2 Fuzzy Information and Engineering 2 SIAM Journal on Applied Algebra and Geometry 1 Modern Physics Letters B 1 General Relativity and Gravitation 1 Ingenieur-Archiv 1 International Journal of Control 1 International Journal of Engineering Science 1 International Journal of Heat and Mass Transfer 1 Journal d’Analyse Mathématique 1 Mathematical Biosciences 1 Transport Theory and Statistical Physics 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 Mathematics of Computation 1 Reviews in Mathematical Physics 1 Annales de l’Institut Fourier 1 The Annals of Statistics 1 Automatica 1 Computing 1 Journal of Pure and Applied Algebra 1 Journal of Soviet Mathematics 1 Kybernetika 1 Mathematics and Computers in Simulation 1 Mathematika 1 Opsearch 1 SIAM Journal on Computing 1 Advances in Applied Mathematics 1 OR Spektrum 1 Insurance Mathematics & Economics 1 Applied Numerical Mathematics 1 Journal of Symbolic Computation 1 Computational Mechanics 1 International Journal of Approximate Reasoning ...and 47 more Serials
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#### Cited in 42 Fields
199 Operations research, mathematical programming (90-XX) 84 Quantum theory (81-XX) 71 Mechanics of deformable solids (74-XX) 45 Statistical mechanics, structure of matter (82-XX) 43 Numerical analysis (65-XX) 31 Partial differential equations (35-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Ordinary differential equations (34-XX) 11 Classical thermodynamics, heat transfer (80-XX) 10 Fluid mechanics (76-XX) 8 Computer science (68-XX) 8 Information and communication theory, circuits (94-XX) 7 Optics, electromagnetic theory (78-XX) 7 Biology and other natural sciences (92-XX) 6 Statistics (62-XX) 6 Systems theory; control (93-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Real functions (26-XX) 5 Probability theory and stochastic processes (60-XX) 5 Mechanics of particles and systems (70-XX) 4 Algebraic geometry (14-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Operator theory (47-XX) 4 Convex and discrete geometry (52-XX) 3 Field theory and polynomials (12-XX) 3 Measure and integration (28-XX) 3 Special functions (33-XX) 3 Approximations and expansions (41-XX) 2 General and overarching topics; collections (00-XX) 2 Mathematical logic and foundations (03-XX) 2 Combinatorics (05-XX) 1 History and biography (01-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)
#### Wikidata Timeline
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https://zbmath.org/authors/?q=Christian+P%C3%B6tzsche | zbMATH — the first resource for mathematics
Pötzsche, Christian
Compute Distance To:
Author ID: potzsche.christian Published as: Poetzsche, Christian; Pötzsche, C.; Pötzsche, Ch.; Pötzsche, Christian External Links: MGP · Wikidata
Documents Indexed: 85 Publications since 2001, including 6 Books
all top 5
Co-Authors
43 single-authored 8 Rasmussen, Martin 6 Kloeden, Peter Eris 6 Siegmund, Stefan 3 Aulbach, Bernd 3 Pituk, Mihály 3 Russ, Evamaria 3 Skiba, Robert 2 Elaydi, Saber Nasr 2 Garab, Ábel 2 Heuberger, Clemens 2 Kaltenbacher, Barbara 2 Müller, Johannes 2 Rendl, Franz 1 Aarset, Christian 1 Duan, Jinqiao 1 Ey, Kristine 1 Fuchs, Thilo M. 1 Hamaya, Yoshihiro 1 Henkel, A. 1 Hense, Burkhard A. 1 Hüls, Thorsten 1 Keller, Stefan 1 Liz, Eduardo 1 Matsunaga, Hideaki 1 Palmer, Kenneth James 1 Sasu, Adina Luminiţa 1 Utz, Margarete 1 Wirth, Fabian Roger
all top 5
Serials
7 Journal of Difference Equations and Applications 5 Internationale Mathematische Nachrichten 4 Journal of Dynamics and Differential Equations 3 Journal of Mathematical Analysis and Applications 3 Journal of Differential Equations 3 Mathematische Nachrichten 3 Discrete and Continuous Dynamical Systems 3 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Computational and Applied Mathematics 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Physica D 2 Communications on Pure and Applied Analysis 2 Advances in Difference Equations 2 Lecture Notes in Mathematics 2 Springer Proceedings in Mathematics & Statistics 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 IMA Journal of Numerical Analysis 1 Journal of Mathematical Biology 1 Mathematical Methods in the Applied Sciences 1 Applied Mathematics and Computation 1 Integral Equations and Operator Theory 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 SIAM Journal on Numerical Analysis 1 Zeitschrift für Analysis und ihre Anwendungen 1 Applied Mathematics Letters 1 Dynamic Systems and Applications 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Topological Methods in Nonlinear Analysis 1 Electronic Journal of Differential Equations (EJDE) 1 Functional Differential Equations 1 Differential Equations and Dynamical Systems 1 Positivity 1 Electronic Journal of Qualitative Theory of Differential Equations 1 Nonlinear Analysis. Real World Applications 1 Dynamical Systems 1 Stochastics and Dynamics 1 SIAM Journal on Applied Dynamical Systems 1 Discrete and Continuous Dynamical Systems. Series S 1 IFIP Advances in Information and Communication Technology 1 Journal of Theoretical Biology
all top 5
Fields
55 Dynamical systems and ergodic theory (37-XX) 53 Difference and functional equations (39-XX) 32 Ordinary differential equations (34-XX) 13 Biology and other natural sciences (92-XX) 12 Numerical analysis (65-XX) 11 Operator theory (47-XX) 10 General and overarching topics; collections (00-XX) 5 Systems theory; control (93-XX) 3 Partial differential equations (35-XX) 3 Integral equations (45-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX)
Citations contained in zbMATH
57 Publications have been cited 394 times in 274 Documents Cited by Year
A spectral characterization of exponential stability for linear time-invariant systems on time scales. Zbl 1054.34086
Pötzsche, Christian; Siegmund, Stefan; Wirth, Fabian
2003
Geometric theory of discrete nonautonomous dynamical systems. Zbl 1247.37003
Pötzsche, Christian
2010
Chain rule and invariance principle on measure chains. Zbl 1011.34045
Pötzsche, Christian
2002
Discrete-time nonautonomous dynamical systems. Zbl 1310.37011
Kloeden, P. E.; Pötzsche, C.; Rasmussen, M.
2013
Exponential dichotomies of linear dynamic equations on measure chains under slowly varying coefficients. Zbl 1046.34076
Pötzsche, Christian
2004
Nonautonomous bifurcation of bounded solutions. I: a Lyapunov-Schmidt approach. Zbl 1215.37017
Pötzsche, Christian
2010
Fine structure of the dichotomy spectrum. Zbl 06087704
Pötzsche, Christian
2012
Limitations of pullback attractors for processes. Zbl 1241.39004
Kloeden, Peter E.; Pötzsche, Christian; Rasmussen, Martin
2012
Topological decoupling, linearization and perturbation on inhomogeneous time scales. Zbl 1190.34120
Pötzsche, Christian
2008
Slow fiber bundles of dynamic equations on measure chains. Zbl 1198.37024
Pötzsche, Christian
2002
Exponential dichotomies for dynamic equations on measure chains. Zbl 1042.34510
Pötzsche, Christian
2001
Dichotomy spectra of triangular equations. Zbl 1364.39016
Pötzsche, Christian
2016
Taylor approximation of integral manifolds. Zbl 1106.34029
Pötzsche, Christian; Rasmussen, Martin
2006
A smoothness theorem for invariant fiber bundles. Zbl 1037.37013
Aulbach, Bernd; Pötzsche, Christian; Siegmund, Stefan
2002
Nonautonomous dynamical systems in the life sciences. Zbl 1311.37075
Kloeden, Peter E.; Pötzsche, Christian
2013
Asymptotic behavior of recursions via fixed point theory. Zbl 1138.39007
Ey, Kristine; Pötzsche, Christian
2008
$$C^m$$-smoothness of invariant fiber bundles. Zbl 1075.39014
Pötzsche, Christian; Siegmund, Stefan
2004
Bet-hedging in stochastically switching environments. Zbl 1411.92219
Müller, Johannes; Hense, Burkhard A.; Fuchs, Thilo M.; Utz, M.; Pötzsche, Christian
2013
Computation of nonautonomous invariant and inertial manifolds. Zbl 1169.65116
Pötzsche, Christian; Rasmussen, Martin
2009
Taylor approximation of invariant fiber bundles for nonautonomous difference equations. Zbl 1070.39023
Pötzsche, Christian; Rasmussen, Martin
2005
Nonautonomous continuation of bounded solutions. Zbl 1237.39005
Pötzsche, Christian
2011
Nonautonomous bifurcation of bounded solutions. II: A shovel-bifurcation pattern. Zbl 1258.37029
Pötzsche, Christian
2011
A note on the dichotomy spectrum. Zbl 1180.39030
Pötzsche, Christian
2009
Reducibility of linear dynamic equations on measure chains. Zbl 1032.39008
Aulbach, Bernd; Pötzsche, Christian
2002
PBC-based pulse stabilization of periodic orbits. Zbl 1286.39008
Liz, Eduardo; Pötzsche, Christian
2014
Computation of integral manifolds for Carathéodory differential equations. Zbl 1201.65218
Pötzsche, Christian; Rasmussen, Martin
2010
Continuity and invariance of the Sacker-Sell spectrum. Zbl 1366.39013
Pötzsche, Christian; Russ, Evamaria
2016
Qualitative analysis of a nonautonomous Beverton-Holt Ricker model. Zbl 1326.37017
Hüls, Thorsten; Pötzsche, Christian
2014
Modeling the spread of Phytophthora. Zbl 1271.92036
Henkel, A.; Müller, J.; Pötzsche, C.
2012
Bifurcations in nonautonomous dynamical systems: results and tools in discrete time. Zbl 1242.39026
Pötzsche, Christian
2011
Nonautonomous bifurcation scenarios in SIR models. Zbl 1357.37090
Kloeden, P. E.; Pötzsche, C.
2015
Bifurcations in a periodic discrete-time environment. Zbl 1278.39023
Pötzsche, Christian
2013
Dynamics of modified predator-prey models. Zbl 1202.34086
Kloeden, P. E.; Pötzsche, C.
2010
A functional-analytical approach to the asymptotics of recursions. Zbl 1180.39019
Pötzsche, Christian
2009
Invariant foliations and stability in critical cases. Zbl 1139.39034
Pötzsche, Christian
2006
Integral manifolds under explicit variable time-step discretization. Zbl 1104.34037
Keller, Stefan; Pötzsche, Christian
2006
$$\mathcal{C}^m$$-smoothness of invariant fiber bundles for dynamic equations on measure chains. Zbl 1086.37016
Pötzsche, Christian; Siegmund, Stefan
2004
Slow and fast variables in non-autonomous difference equations. Zbl 1044.39011
Pötzsche, Christian
2003
Morse decompositions for delay-difference equations. Zbl 1414.39002
Garab, Ábel; Pötzsche, Christian
2019
Order-preserving nonautonomous discrete dynamics: attractors and entire solutions. Zbl 1327.39004
Pötzsche, Christian
2015
Persistence and imperfection of nonautonomous bifurcation patterns. Zbl 1218.37035
Pötzsche, Christian
2011
Delay equations on measure chains: basics and linearized stability. Zbl 1117.39324
Pötzsche, Christian
2005
Stability of center fiber bundles for nonautonomous difference equations. Zbl 1074.37018
Pötzsche, Christian
2004
Pseudo-stable and pseudo-unstable fiber bundles for dynamic equations on measure chains. Zbl 1046.39011
Pötzsche, Christian
2003
Numerical dynamics of integrodifference equations: basics and discretization errors in a $$C^0$$-setting. Zbl 1429.65322
Pötzsche, Christian
2019
Smooth roughness of exponential dichotomies, revisited. Zbl 1334.39021
Pötzsche, Christian
2015
Book review of: K. Nipp and D. Stoffer, Invariant manifolds in discrete and continuous dynamical systems. Zbl 1335.00072
Pötzsche, C.
2014
Nonautonomous dynamical systems in the life sciences. Zbl 1282.37004
Kloeden, Peter E. (ed.); Pötzsche, Christian (ed.)
2013
Corrigendum on: “A note on the dichotomy spectrum”. Zbl 1257.39016
Pötzsche, Christian
2012
Nonautonomous bifurcation of bounded solutions: crossing curve situations. Zbl 1284.37024
Pötzsche, Christian
2012
Extended hierarchies of invariant fiber bundles for dynamic equations on measure chains. Zbl 1213.37048
Pötzsche, Christian
2010
Robustness of hyperbolic solutions under parametric perturbations. Zbl 1207.39017
Pötzsche, Christian
2009
Discrete inertial manifolds. Zbl 1146.39030
Pötzsche, Christian
2008
Attractive invariant fiber bundles. Zbl 1127.37023
Pötzsche, Christian
2007
Local approximation of invariant fiber bundles: an algorithmic approach. Zbl 1094.65128
Pötzsche, Christian; Rasmussen, Martin
2005
On periodic dynamic equations on measure chains. Zbl 1089.34035
Pötzsche, Christian
2004
Invariant manifolds with asymptotic phase for nonautonomous difference equations. Zbl 1067.39031
Aulbach, B.; Pötzsche, C.
2003
Morse decompositions for delay-difference equations. Zbl 1414.39002
Garab, Ábel; Pötzsche, Christian
2019
Numerical dynamics of integrodifference equations: basics and discretization errors in a $$C^0$$-setting. Zbl 1429.65322
Pötzsche, Christian
2019
Dichotomy spectra of triangular equations. Zbl 1364.39016
Pötzsche, Christian
2016
Continuity and invariance of the Sacker-Sell spectrum. Zbl 1366.39013
Pötzsche, Christian; Russ, Evamaria
2016
Nonautonomous bifurcation scenarios in SIR models. Zbl 1357.37090
Kloeden, P. E.; Pötzsche, C.
2015
Order-preserving nonautonomous discrete dynamics: attractors and entire solutions. Zbl 1327.39004
Pötzsche, Christian
2015
Smooth roughness of exponential dichotomies, revisited. Zbl 1334.39021
Pötzsche, Christian
2015
PBC-based pulse stabilization of periodic orbits. Zbl 1286.39008
Liz, Eduardo; Pötzsche, Christian
2014
Qualitative analysis of a nonautonomous Beverton-Holt Ricker model. Zbl 1326.37017
Hüls, Thorsten; Pötzsche, Christian
2014
Book review of: K. Nipp and D. Stoffer, Invariant manifolds in discrete and continuous dynamical systems. Zbl 1335.00072
Pötzsche, C.
2014
Discrete-time nonautonomous dynamical systems. Zbl 1310.37011
Kloeden, P. E.; Pötzsche, C.; Rasmussen, M.
2013
Nonautonomous dynamical systems in the life sciences. Zbl 1311.37075
Kloeden, Peter E.; Pötzsche, Christian
2013
Bet-hedging in stochastically switching environments. Zbl 1411.92219
Müller, Johannes; Hense, Burkhard A.; Fuchs, Thilo M.; Utz, M.; Pötzsche, Christian
2013
Bifurcations in a periodic discrete-time environment. Zbl 1278.39023
Pötzsche, Christian
2013
Nonautonomous dynamical systems in the life sciences. Zbl 1282.37004
Kloeden, Peter E. (ed.); Pötzsche, Christian (ed.)
2013
Fine structure of the dichotomy spectrum. Zbl 06087704
Pötzsche, Christian
2012
Limitations of pullback attractors for processes. Zbl 1241.39004
Kloeden, Peter E.; Pötzsche, Christian; Rasmussen, Martin
2012
Modeling the spread of Phytophthora. Zbl 1271.92036
Henkel, A.; Müller, J.; Pötzsche, C.
2012
Corrigendum on: “A note on the dichotomy spectrum”. Zbl 1257.39016
Pötzsche, Christian
2012
Nonautonomous bifurcation of bounded solutions: crossing curve situations. Zbl 1284.37024
Pötzsche, Christian
2012
Nonautonomous continuation of bounded solutions. Zbl 1237.39005
Pötzsche, Christian
2011
Nonautonomous bifurcation of bounded solutions. II: A shovel-bifurcation pattern. Zbl 1258.37029
Pötzsche, Christian
2011
Bifurcations in nonautonomous dynamical systems: results and tools in discrete time. Zbl 1242.39026
Pötzsche, Christian
2011
Persistence and imperfection of nonautonomous bifurcation patterns. Zbl 1218.37035
Pötzsche, Christian
2011
Geometric theory of discrete nonautonomous dynamical systems. Zbl 1247.37003
Pötzsche, Christian
2010
Nonautonomous bifurcation of bounded solutions. I: a Lyapunov-Schmidt approach. Zbl 1215.37017
Pötzsche, Christian
2010
Computation of integral manifolds for Carathéodory differential equations. Zbl 1201.65218
Pötzsche, Christian; Rasmussen, Martin
2010
Dynamics of modified predator-prey models. Zbl 1202.34086
Kloeden, P. E.; Pötzsche, C.
2010
Extended hierarchies of invariant fiber bundles for dynamic equations on measure chains. Zbl 1213.37048
Pötzsche, Christian
2010
Computation of nonautonomous invariant and inertial manifolds. Zbl 1169.65116
Pötzsche, Christian; Rasmussen, Martin
2009
A note on the dichotomy spectrum. Zbl 1180.39030
Pötzsche, Christian
2009
A functional-analytical approach to the asymptotics of recursions. Zbl 1180.39019
Pötzsche, Christian
2009
Robustness of hyperbolic solutions under parametric perturbations. Zbl 1207.39017
Pötzsche, Christian
2009
Topological decoupling, linearization and perturbation on inhomogeneous time scales. Zbl 1190.34120
Pötzsche, Christian
2008
Asymptotic behavior of recursions via fixed point theory. Zbl 1138.39007
Ey, Kristine; Pötzsche, Christian
2008
Discrete inertial manifolds. Zbl 1146.39030
Pötzsche, Christian
2008
Attractive invariant fiber bundles. Zbl 1127.37023
Pötzsche, Christian
2007
Taylor approximation of integral manifolds. Zbl 1106.34029
Pötzsche, Christian; Rasmussen, Martin
2006
Invariant foliations and stability in critical cases. Zbl 1139.39034
Pötzsche, Christian
2006
Integral manifolds under explicit variable time-step discretization. Zbl 1104.34037
Keller, Stefan; Pötzsche, Christian
2006
Taylor approximation of invariant fiber bundles for nonautonomous difference equations. Zbl 1070.39023
Pötzsche, Christian; Rasmussen, Martin
2005
Delay equations on measure chains: basics and linearized stability. Zbl 1117.39324
Pötzsche, Christian
2005
Local approximation of invariant fiber bundles: an algorithmic approach. Zbl 1094.65128
Pötzsche, Christian; Rasmussen, Martin
2005
Exponential dichotomies of linear dynamic equations on measure chains under slowly varying coefficients. Zbl 1046.34076
Pötzsche, Christian
2004
$$C^m$$-smoothness of invariant fiber bundles. Zbl 1075.39014
Pötzsche, Christian; Siegmund, Stefan
2004
$$\mathcal{C}^m$$-smoothness of invariant fiber bundles for dynamic equations on measure chains. Zbl 1086.37016
Pötzsche, Christian; Siegmund, Stefan
2004
Stability of center fiber bundles for nonautonomous difference equations. Zbl 1074.37018
Pötzsche, Christian
2004
On periodic dynamic equations on measure chains. Zbl 1089.34035
Pötzsche, Christian
2004
A spectral characterization of exponential stability for linear time-invariant systems on time scales. Zbl 1054.34086
Pötzsche, Christian; Siegmund, Stefan; Wirth, Fabian
2003
Slow and fast variables in non-autonomous difference equations. Zbl 1044.39011
Pötzsche, Christian
2003
Pseudo-stable and pseudo-unstable fiber bundles for dynamic equations on measure chains. Zbl 1046.39011
Pötzsche, Christian
2003
Invariant manifolds with asymptotic phase for nonautonomous difference equations. Zbl 1067.39031
Aulbach, B.; Pötzsche, C.
2003
Chain rule and invariance principle on measure chains. Zbl 1011.34045
Pötzsche, Christian
2002
Slow fiber bundles of dynamic equations on measure chains. Zbl 1198.37024
Pötzsche, Christian
2002
A smoothness theorem for invariant fiber bundles. Zbl 1037.37013
Aulbach, Bernd; Pötzsche, Christian; Siegmund, Stefan
2002
Reducibility of linear dynamic equations on measure chains. Zbl 1032.39008
Aulbach, Bernd; Pötzsche, Christian
2002
Exponential dichotomies for dynamic equations on measure chains. Zbl 1042.34510
Pötzsche, Christian
2001
all top 5
Cited by 368 Authors
32 Pötzsche, Christian 14 Kloeden, Peter Eris 8 Davis, John M. 8 Rasmussen, Martin 8 Xia, Yonghui 7 Caraballo Garrido, Tomás 7 Defoort, Michael 7 Djemai, Mohamed 6 Braverman, Elena 6 Gravagne, Ian A. 6 Hüls, Thorsten 6 Langa, Jose’ Antonio 6 Sasu, Adina Luminiţa 6 Sasu, Bogdan 5 DaCunha, Jeffrey J. 5 Koo, Namjip 5 Lorenz, Thomas 5 Nguyen Huu Du 5 Robledo, Gonzalo 5 Shah, Syed Omar 5 Siegmund, Stefan 5 Zada, Akbar 5 Zhang, Jimin 4 Bartosiewicz, Zbigniew 4 Castañeda, Alvaro 4 Choi, Sungkyu 4 Cui, Hongyong 4 Doan, Thai Son 4 Erbe, Lynn Harry 4 Han, Xiaoying 4 Megan, Mihail 4 Nolasco de Carvalho, Alexandre 4 Palmer, Kenneth James 4 Sacker, Robert J. 4 Taousser, Fatima Zohra 3 Babuţia, Mihai Gabriel 3 Bortolan, Matheus Cheque 3 Fan, Meng 3 Garab, Ábel 3 Hamza, Alaa E. 3 Karpuz, Başak 3 Li, Yangrong 3 Liem, Nguyen Chi 3 Liz, Eduardo 3 Obaya, Rafael 3 O’Regan, Donal 3 Peterson, Allan C. 3 Poulsen, Dylan 3 Roberts, Anthony John 3 Rodkina, Alexandra 3 Silva, César M. 3 Stehlík, Petr 3 Steyer, Andrew J. 3 Tisdell, Christopher C. 3 Van Vleck, Erik S. 3 Yang, Meihua 3 Yin, Jinyan 2 Agarwal, Ravi P. 2 Aulbach, Bernd 2 Bai, Yuzhen 2 Battelli, Flaviano 2 Bento, António J. G. 2 Bohner, Martin J. 2 Bouin, Emeric 2 Chang, Xiaoyuan 2 Chekroun, Mickaël D. 2 Cui, Yinhua 2 Do Duc Thuan 2 Girod, Alina 2 Gyori, Istvan 2 Hense, Burkhard A. 2 Hilger, Stefan 2 Horváth, László 2 Jackson, Billy J. 2 Kelly, Cónall 2 Kurbatov, Vitaliĭ Gennad’evich 2 Kurbatova, Irina Vital’evna 2 Kuttler, Christina 2 Li, Ming-Chia 2 Liu, Ping 2 Liu, Xinzhi 2 Longo, Iacopo P. 2 Lupa, Nicolae 2 Lyu, Ming-Jiea 2 Mert, Raziye 2 Müller, Johannes 2 Novo, Sylvia 2 Oganesyan, Gro R. 2 Oraby, Karima M. 2 Petropoulou, Eugenia N. 2 Pinto, Manuel 2 Piotrowska, Ewa 2 Russ, Evamaria 2 Shi, Yuming 2 Skiba, Robert 2 Slavík, Antonín 2 Smith, Hal Leslie 2 Volek, Jonáš 2 Wang, Chao 2 Wang, Yuwen ...and 268 more Authors
all top 5
Cited in 99 Serials
22 Journal of Difference Equations and Applications 19 Journal of Differential Equations 17 Journal of Mathematical Analysis and Applications 14 Discrete and Continuous Dynamical Systems. Series B 9 Journal of Dynamics and Differential Equations 9 Advances in Difference Equations 8 Applied Mathematics and Computation 7 Computers & Mathematics with Applications 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Discrete and Continuous Dynamical Systems 6 Nonlinear Analysis. Hybrid Systems 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Abstract and Applied Analysis 5 Qualitative Theory of Dynamical Systems 5 Communications on Pure and Applied Analysis 4 Journal of Computational and Applied Mathematics 4 Proceedings of the American Mathematical Society 4 Systems & Control Letters 4 Physica D 3 Journal of Mathematical Biology 3 Chaos, Solitons and Fractals 3 Bulletin des Sciences Mathématiques 3 Differential Equations and Dynamical Systems 2 International Journal of Control 2 Journal of the Franklin Institute 2 Journal of Statistical Physics 2 Mathematical Biosciences 2 Mathematical Methods in the Applied Sciences 2 Nonlinearity 2 Physica A 2 Bulletin of Mathematical Biology 2 Automatica 2 BIT 2 Numerische Mathematik 2 Mathematical and Computer Modelling 2 Discrete Dynamics in Nature and Society 2 Communications in Nonlinear Science and Numerical Simulation 2 Nonlinear Analysis. Real World Applications 2 Dynamical Systems 2 SIAM Journal on Applied Dynamical Systems 2 Mediterranean Journal of Mathematics 2 Journal of Biological Dynamics 2 Journal of Nonlinear Science and Applications 2 Journal of Theoretical Biology 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Discrete Applied Mathematics 1 General Relativity and Gravitation 1 Inverse Problems 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Engineering Mathematics 1 Rocky Mountain Journal of Mathematics 1 Mathematics of Computation 1 Acta Mathematica Vietnamica 1 Fuzzy Sets and Systems 1 Integral Equations and Operator Theory 1 Journal of Functional Analysis 1 Mathematische Nachrichten 1 SIAM Journal on Numerical Analysis 1 Note di Matematica 1 Stochastic Analysis and Applications 1 Applied Numerical Mathematics 1 Applied Mathematics Letters 1 MCSS. Mathematics of Control, Signals, and Systems 1 Neural Computation 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Set-Valued Analysis 1 International Applied Mechanics 1 Combinatorics, Probability and Computing 1 Journal of Mathematical Sciences (New York) 1 Turkish Journal of Mathematics 1 Integral Transforms and Special Functions 1 Complexity 1 Nonlinear Dynamics 1 Positivity 1 Journal of Inequalities and Applications 1 Chaos 1 Communications of the Korean Mathematical Society 1 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 1 Computational Methods in Applied Mathematics 1 Journal of Applied Mathematics 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Stochastics and Dynamics 1 Central European Journal of Mathematics 1 Journal of Function Spaces and Applications 1 Communications in Mathematical Analysis 1 Journal of Physics A: Mathematical and Theoretical 1 European Journal of Pure and Applied Mathematics 1 Discrete and Continuous Dynamical Systems. Series S 1 Kinetic and Related Models 1 Proceedings of the Estonian Academy of Sciences 1 Asian-European Journal of Mathematics 1 International Journal of Differential Equations 1 Advances in Nonlinear Analysis 1 International Journal of Analysis and Applications
all top 5
Cited in 37 Fields
124 Ordinary differential equations (34-XX) 106 Dynamical systems and ergodic theory (37-XX) 82 Difference and functional equations (39-XX) 37 Systems theory; control (93-XX) 36 Biology and other natural sciences (92-XX) 31 Partial differential equations (35-XX) 26 Operator theory (47-XX) 24 Numerical analysis (65-XX) 11 Probability theory and stochastic processes (60-XX) 7 Real functions (26-XX) 6 Integral equations (45-XX) 5 Mechanics of particles and systems (70-XX) 4 Combinatorics (05-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Functional analysis (46-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Integral transforms, operational calculus (44-XX) 2 General topology (54-XX) 2 Computer science (68-XX) 2 Fluid mechanics (76-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 History and biography (01-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 $$K$$-theory (19-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Information and communication theory, circuits (94-XX)
Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-02-27T09:32:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4270813763141632, "perplexity": 6664.010656950883}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358798.23/warc/CC-MAIN-20210227084805-20210227114805-00074.warc.gz"} |
https://nroer.gov.in/55ab34ff81fccb4f1d806025/file/560a5a3081fccb5282ea79bd | Can you See the Pattern?:
Next
Chapter 07 of Math - Magic, the Mathematics textbook for class 05
License:[Source NCERT ] May 24, 2016, 10:30 p.m. | 2021-04-17T21:36:32 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8411030769348145, "perplexity": 3728.0846782985436}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038464045.54/warc/CC-MAIN-20210417192821-20210417222821-00608.warc.gz"} |
https://par.nsf.gov/biblio/10219983-periodicity-random-walks-dynamic-networks | On the Periodicity of Random Walks in Dynamic Networks
We investigate random walks in graphs whose edges change over time as a function of the current probability distribution of the walk. We show that such systems can be chaotic and can exhibit hyper-torpid" mixing. Our main result is that, if each graph is strongly connected, then the dynamics is asymptotically periodic almost surely.
Authors:
Editors:
Award ID(s):
Publication Date:
NSF-PAR ID:
10219983
Journal Name:
IEEE transactions on network science and engineering
Volume:
7
Issue:
3
Page Range or eLocation-ID:
1337 - 1343
ISSN:
2327-4697 | 2023-02-08T11:40:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7623668313026428, "perplexity": 951.6363829623966}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500758.20/warc/CC-MAIN-20230208092053-20230208122053-00095.warc.gz"} |
https://par.nsf.gov/biblio/10227249-measurement-tt-production-cross-section-lepton+jets-channel-tev-atlas-experiment | Measurement of the $tt¯$ production cross-section in the lepton+jets channel at $s=13$ TeV with the ATLAS experiment | 2022-09-29T18:30:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9546537399291992, "perplexity": 1780.3461003121263}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335362.18/warc/CC-MAIN-20220929163117-20220929193117-00643.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/proc.2015.0185 | Article Contents
Article Contents
# Construction of highly stable implicit-explicit general linear methods
• This paper deals with the numerical solution of systems of differential equations with a stiff part and a non-stiff one, typically arising from the semi-discretization of certain partial differential equations models. It is illustrated the construction and analysis of highly stable and high-stage order implicit-explicit (IMEX) methods based on diagonally implicit multistage integration methods (DIMSIMs), a subclass of general linear methods (GLMs). Some examples of methods with optimal stability properties are given. Finally numerical experiments confirm the theoretical expectations.
Mathematics Subject Classification: Primary: 65L05; Secondary: 65L20.
Citation:
• [1] U. M. Ascher, S. J. Ruuth and R. J. Spiteri, Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations, Appl. Numer. Math, 25 (1997), 151-167. [2] U. M. Ascher, S. J. Ruuth and B. T. R. Wetton, Implicit-explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal., 32 (1995), 797-823. [3] S. Boscarino, Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems, SIAM Journal on Numerical Analysis, 45 (2007), 1600-1621. [4] S. Boscarino and G. Russo, On a class of uniformly accurate IMEX Runge-Kutta schemes and applications to hyperbolic systems with relaxation, SIAM J. Sci. Comput., 31 (2009), 1926-1945. [5] M. Braś and A. Cardone, Construction of efficient general linear methods for non-stiff differential systems, Math. Model. Anal., 17 (2012), 171-189. [6] M. Braś, A. Cardone and R. D'Ambrosio, Implementation of explicit nordsieck methods with inherent quadratic stability, Math. Model. Anal., 18 (2013), 289-307. [7] J. C. Butcher, Diagonally-implicit multi-stage integration methods, Appl. Numer. Math., 11 (1993), 347-363. [8] M. P. Calvo, J. de Frutos and J. Novo, Linearly implicit Runge-Kutta methods for advection-reaction-diffusion equations, Appl. Numer. Math., 37 (2001), 535-549. [9] A. Cardone and Z. Jackiewicz, Explicit Nordsieck methods with quadratic stability, Numer. Algorithms, 60 (2012), 1-25. [10] A. Cardone, Z. Jackiewicz and H. Mittelmann, Optimization-based search for Nordsieck methods of high order with quadratic stability, Math. Model. Anal., 17 (2012), 293-308. [11] A. Cardone, Z. Jackiewicz, A. Sandu and H. Zhang, Extrapolated implicit-explicit Runge-Kutta methods, Math. Model. Anal., 19 (2014), 18-43. [12] A. Cardone, Z. Jackiewicz, A. Sandu and H. Zhang, Extrapolation-based implicit-explicit general linear methods, Numer. Algorithms, 65 (2014), 377-399. [13] J. Frank, W. Hundsdorfer and J. G. Verwer, On the stability of implicit-explicit linear multistep methods, Appl. Numer. Math., 25 (1997), 193-205. [14] W. Hundsdorfer and S. J. Ruuth, IMEX extensions of linear multistep methods with general monotonicity and boundedness properties, J. Comput. Phys., 225 (2007), 2016-2042. [15] W. Hundsdorfer and J. Verwer, Numerical solution of time-dependent advection-diffusion-reaction equations, vol. 33 of Springer Series in Comput. Mathematics, Springer-Verlag, 2003. [16] Z. Jackiewicz, General linear methods for ordinary differential equations, John Wiley & Sons Inc., Hoboken, NJ, 2009. [17] C. A. Kennedy and M. H. Carpenter, Additive Runge-Kutta schemes for convection-diffusion-reaction equations, Appl. Numer. Math., 44 (2003), 139-181. [18] L. Pareschi and G. Russo, Implicit-explicit Runge-Kutta schemes for stiff systems of differential equations, in Recent trends in numerical analysis, vol. 3 of Adv. Theory Comput. Math., Nova Sci. Publ., Huntington, NY, 2001, 269-288. [19] L. Pareschi and G. Russo, Implicit-Explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation, J. Sci. Comput., 25 (2005), 129-155. [20] W. M. Wright, The construction of order 4 DIMSIMs for ordinary differential equations, Numer. Algorithms, 26 (2001), 123-130. [21] H. Zhang and A. Sandu, A second-order diagonally-implicit-explicit multi-stage integration method, Procedia CS, 9 (2012), 1039-1046. [22] H. Zhang, A. Sandu and S. Blaise, High order implicit-explicit general linear methods with optimized stability regions, arXiv preprint, URL http://arxiv.org/abs/1407.2337. [23] H. Zhang, A. Sandu and S. Blaise, Partitioned and Implicit-Explicit General Linear Methods for ordinary differential equations, J. Sci. Comput., 61 (2014), 119-144. [24] E. Zharovski, A. Sandu and H. Zhang, A class of implicit-explicit two-step Runge-Kutta methods, SIAM J. Numer. Anal., 53 (2015), no. 1, 321-341.
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https://par.nsf.gov/biblio/10159346 | Absorbing–active transition in a multi-cellular system regulated by a dynamic force network
Collective cell migration in 3D extracellular matrix (ECM) is crucial to many physiological and pathological processes. Migrating cells can generate active pulling forces via actin filament contraction, which are transmitted to the ECM fibers and lead to a dynamically evolving force network in the system. Here, we elucidate the role of this force network in regulating collective cell behaviors using a minimal active-particle-on-network (APN) model, in which active particles can pull the fibers and hop between neighboring nodes of the network following local durotaxis. Our model reveals a dynamic transition as the particle number density approaches a critical value, from an “absorbing” state containing isolated stationary small particle clusters, to an “active” state containing a single large cluster undergoing constant dynamic reorganization. This reorganization is dominated by a subset of highly dynamic “radical” particles in the cluster, whose number also exhibits a transition at the same critical density. The transition is underlaid by the percolation of “influence spheres” due to the particle pulling forces. Our results suggest a robust mechanism based on ECM-mediated mechanical coupling for collective cell behaviors in 3D ECM.
Authors:
; ; ; ; ; ; ; ;
Award ID(s):
Publication Date:
NSF-PAR ID:
10159346
Journal Name:
Soft Matter
Volume:
15
Issue:
35
Page Range or eLocation-ID:
6938 to 6945
ISSN:
1744-683X
National Science Foundation
##### More Like this
1. Cells interacting over an extracellular matrix (ECM) exhibit emergent behaviors, which are often observably different from single-cell dynamics. Fibroblasts embedded in a 3-D ECM, for example, compact the surrounding gel and generate an anisotropic strain field, which cannot be observed in single cellinduced gel compaction. This emergent matrix behavior results from collective intracellular mechanical interaction and is crucial to explain the large deformations and mechanical tensions that occur during embryogenesis, tissue development and wound healing. Prediction of multi-cellular interactions entails nonlinear dynamic simulation, which is prohibitively complex to compute using first principles especially as the number of cells increase. Here, we introduce a new methodology for predicting nonlinear behaviors of multiple cells interacting mechanically through a 3D ECM. In the proposed method, we first apply Dual- Faceted Linearization to nonlinear dynamic systems describing cell/matrix behavior. Using this unique linearization method, the original nonlinear state equations can be expressed with a pair of linear dynamic equations by augmenting the independent state variables with auxiliary variables which are nonlinearly dependent on the original states. Furthermore, we can find a reduced order latent space representation of the dynamic equations by orthogonal projection onto the basis of a lower dimensional linear manifold within themore »
2. Many-body interactions in systems of active matter can cause particles to move collectively and self-organize into dynamic structures with long-range order. In cells, the self-assembly of cytoskeletal filaments is critical for cellular motility, structure, intracellular transport, and division. Semiflexible cytoskeletal filaments driven by polymerization or motor-protein interactions on a two-dimensional substrate, such as the cell cortex, can induce filament bending and curvature leading to interesting collective behavior. For example, the bacterial cell-division filament FtsZ is known to have intrinsic curvature that causes it to self-organize into rings and vortices, and recent experiments reconstituting the collective motion of microtubules driven by motor proteins on a surface have observed chiral symmetry breaking of the collective behavior due to motor-induced curvature of the filaments. Previous work on the self-organization of driven filament systems have not studied the effects of curvature and filament structure on collective behavior. In this work, we present Brownian dynamics simulation results of driven semiflexible filaments with intrinsic curvature and investigate how the interplay between filament rigidity and radius of curvature can tune the self-organization behavior in homochiral systems and heterochiral mixtures. We find a curvature-induced reorganization from polar flocks to self-sorted chiral clusters, which is modified by filament flexibility.more »
3. Abstract
The transport of particles and fluids through multichannel microfluidic networks is influenced by details of the channels. Because channels have micro-scale textures and macro-scale geometries, this transport can differ from the case of ideally smooth channels. Surfaces of real channels have irregular boundary conditions to which streamlines adapt and with which particle interact. In low-Reynolds number flows, particles may experience inertial forces that result in trans-streamline movement and the reorganization of particle distributions. Such transport is intrinsically 3D and an accurate measurement must capture movement in all directions. To measure the effects of non-ideal surface textures on particle transport through complex networks, we developed an extended field-of-view 3D macroscope for high-resolution tracking across large volumes ($$25\,\hbox {mm} \times 25\,\hbox {mm} \times 2\,\hbox {mm}$$$25\phantom{\rule{0ex}{0ex}}\text{mm}×25\phantom{\rule{0ex}{0ex}}\text{mm}×2\phantom{\rule{0ex}{0ex}}\text{mm}$) and investigated a model multichannel microfluidic network. A topographical profile of the microfluidic surfaces provided lattice Boltzmann simulations with a detailed feature map to precisely reconstruct the experimental environment. Particle distributions from simulations closely reproduced those observed experimentally and both measurements were sensitive to the effects of surface roughness. Under the conditions studied, inertial focusing organized large particles into an annular distribution that limited their transport throughout the network while small particles were transported uniformly tomore »
4. Abstract
Active particle systems can vary greatly from one-component systems of spheres to mixtures of particle shapes at different composition ratios. We investigate computationally the combined effect of anisotropy and stoichiometry on the collective behavior of two-dimensional active colloidal mixtures of polygons. We uncover three emergent phenomena not yet reported in active Brownian particle systems. First, we find that mixtures containing hexagons exhibit micro-phase separation with large grains of hexagonal symmetry. We quantify a measurable, implicit ‘steric attraction’ between the active particles as a result of shape anisotropy and activity. This calculation provides further evidence that implicit interactions in active systems, even without explicit attraction, can lead to an effective preferential attraction between particles. Next, we report stable fluid clusters in mixtures containing one triangle or square component. We attribute the fluidization of the dense cluster to the interplay of cluster destabilizing particles, which introduce grain boundaries and slip planes into the system, causing solid-like clusters to break up into fluid clusters. Third, we show that fluid clusters can coexist with solid clusters within a sparse gas of particles in a steady state of three coexisting phases. Our results highlight the potential for a wide variety of behavior to bemore »
5. Abstract
Vasculogenesis is thede novoformation of a vascular network from individual endothelial progenitor cells occurring during embryonic development, organogenesis, and adult neovascularization. Vasculogenesis can be mimicked and studiedin vitrousing network formation assays, in which endothelial cells (ECs) spontaneously form capillary-like structures when seeded in the appropriate microenvironment. While the biochemical regulators of network formation have been well studied using these assays, the role of mechanical and topographical properties of the extracellular matrix (ECM) is less understood. Here, we utilized both natural and synthetic fibrous materials to better understand how physical attributes of the ECM influence the assembly of EC networks. Our results reveal that active cell-mediated matrix recruitment through actomyosin force generation occurs concurrently with network formation on Matrigel, a reconstituted basement membrane matrix regularly used to promote EC networks, and on synthetic matrices composed of electrospun dextran methacrylate (DexMA) fibers. Furthermore, modulating physical attributes of DexMA matrices that impair matrix recruitment consequently inhibited the formation of cellular networks. These results suggest an iterative process in which dynamic cell-induced changes to the physical microenvironment reciprocally modulate cell behavior to guide the formation and stabilization of multicellular networks. | 2023-02-08T23:55:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38101741671562195, "perplexity": 3162.3579247289626}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500983.76/warc/CC-MAIN-20230208222635-20230209012635-00348.warc.gz"} |
http://quantum.lanl.gov/qlunch/2008_qlunch/smerzi.shtml | ## CONTACTS
• Coordinator
Diego Dalvit
• Quantum Lunch Location:
T-Division Conference Room, TA-3,
Building 123, Room 121
# Quantum Institute: Visitor Schedule
The Quantum Lunch is regularly held on Thursdays in the Theoretical Division Conference Room, TA-3, Building 123, Room 121.
Thursday, August 21, 2008
12:30 PM to 2 PM
Speaker: Augusto Smerzi, BEC CNR-INFM and Dipartimento di Fisica, Universita' di Trento, Italy
### TOPIC: Entanglement and Heisenberg Limit in Quantum Interferometry
Abstract
The quantum Fisher information provides a sufficient condition to recognize multi-particle entanglement in a N quibit state. The same criterion gives a necessary and sufficient condition for sub shot-noise phase sensitivity in the estimation of a collective rotation angle $\theta$. The analysis therefore singles out the class of entangled states which are "useful" to overcome classical phase sensitivity in metrology and sensors. We will discuss the creation of such useful entangled states by the non-linear dynamical evolution of a Bose-Einstein condensates trapped in a double-well potential.
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy's NNSA | 2014-07-30T15:08:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31007513403892517, "perplexity": 3969.482594497586}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510270577.0/warc/CC-MAIN-20140728011750-00465-ip-10-146-231-18.ec2.internal.warc.gz"} |
https://wikimho.com/us/q/security/48022 | ### What kinds of encryption are _not_ breakable via Quantum Computers?
• There's the recent article NSA seeks to build quantum computer that could crack most types of encryption. Now I'm not surprised by the NSA trying anything1, but what slightly baffles me is the word "most" - so, what encryption algorithms are known and sufficiently field-tested that are not severely vulnerable to Quantum Computing?
1) Yup, I wouldn't even be surprised if they had a secret department of fortune telling...
Best to use OTP -in real world and for the virtual world use symmetric algorithms + 256bit keys. look at this http://www.theguardian.com/world/2013/sep/05/nsa-how-to-remain-secure-surveillance
Quantum computers are still a ways off. The concept relies on using bits, that when unobserved, are both 1 and 0 and so able to calculate with all the values that can be represented in the given space -- with one calculation. As romantic as this sounds, I have yet to hear of a way to calculate with this bits while leaving them unobserved.
Don't assume that just because an organization the size of the NSA is trying to build something that they expect to successfully deploy one anytime soon. Because arms-races are races, often an organization will research something because they don't want to be just starting out when their competitors are deploying one. If the NSA builds up a brain-trust of people who know about quantum computing then they might be able to deploy one ahead of their competitors, and are less likely to be caught flat-footed.
My concern is not the NSA, who might just as well use some less pleasant meatworld methods to obtain one's secrets, but rather the implications of QC in general
Why wouldn't quantum computers also enable correspondingly stronger encryption?
@mirimir Who claimed that? Of course there's Quantum Cryptography, but even once available not everyone will be able to afford it I assume, so it's still important to know what classical encryption one can rely upon even if potential eavesdroppers have Quantum Computers
@November Slightly modifying this nice Gedankenexperiment, assume a friend of yours went outside before it got cold. Neither you or they know how many gloves (if any) they took with them, but both know where the remaining ones would be; and that, due to the severe cold, your friend would return home for the remaining glove(s) once they noticed some were missing. Assume the same for a friend your friend wanted to meet outside. Now observe whether some of their gloves are at home - and voilà you can determine whether they met outside or come home
@November Your knowledge is outdated. Computations on qbits *have* been performed. Just not very many. But there’s nothing “romantic” about this concept, it’s been demonstrated in practice.
Thanks for correcting me. This is very exciting, do you have a link that explains this more in-depth?
@November This just came out: http://arxiv.org/pdf/1512.02206v1.pdf It is a bit technical and requires a quite a bit of knowledge to be usable, but I guess most people here are :-)
• As usual, journalism talking about technical subjects tends to be fuzzy about details...
Assuming that a true Quantum Computer can be built, then:
• RSA, and other algorithms which rely on the hardness of integer factorization (e.g. Rabin), are toast. Shor's algorithm factors big integers very efficiently.
• DSA, Diffie-Hellman ElGamal, and other algorithms which rely on the hardness of discrete logarithm, are equally broken. A variant of Shor's algorithm also applies. Note that this is true for every group, so elliptic curve variants of these algorithms fare no better.
• Symmetric encryption is weakened; namely, a quantum computer can search through a space of size 2n in time 2n/2. This means that a 128-bit AES key would be demoted back to the strength of a 64-bit key -- however, note that these are 264 quantum-computing operations; you cannot apply figures from studies with FPGA and GPU and blindly assume that if a quantum computer can be built at all, it can be built and operated cheaply.
• Similarly, hash function resistance to various kind of attacks would be similarly reduced. Roughly speaking, a hash function with an output of n bits would resist preimages with strength 2n/2 and collisions up to 2n/3 (figures with classical computers being 2n and 2n/2, respectively). SHA-256 would still be as strong against collisions as a 170-bit hash function nowadays, i.e. better than a "perfect SHA-1".
So symmetric cryptography would not be severely damaged if a quantum computer turned out to be built. Even if it could be built very cheaply actual symmetric encryption and hash function algorithms would still offer a very fair bit of resistance. For asymmetric encryption, though, that would mean trouble. We nonetheless know of several asymmetric algorithms for which no efficient QC-based attack is known, in particular algorithms based on lattice reduction (e.g. NTRU), and the venerable McEliece encryption. These algorithms are not very popular nowadays, for a variety of reasons (early versions of NTRU turned out to be weak; there are patents; McEliece's public keys are huge; and so on), but some would still be acceptable.
Study of cryptography under the assumption that efficient quantum computers can be built is called post-quantum cryptography.
Personally I don't believe that a meagre 80 millions dollars budget would get the NSA far. IBM has been working on that subject for decades and spent a lot more than that, and their best prototypes are not amazing. It is highly plausible that NSA has spent some dollars on the idea of quantum computing; after all, that's their job, and it would be a scandal if taxpayer money did not go into that kind of research. But there is a difference between searching and finding...
+1, and wish I could give you +10 just for the last two sentences. With all the scandals about their abuses it's sometimes easy to forget that when all's said and done being able to spy on people is their *job* and what we're objecting to is their lack of restraint when doing it...
+1 - Of course you might consider that with 80 million dollars, the NSA could just hire goons to beat private keys out of most targets... Then again they could have forced IBM and others to "volunteer" in providing their most secret research progress so far
@Thomas Pornin Is the complexity of searching a space decreased due to the uncertainty principle? I might be way off.....
@Rell3oT: the idea is that a qubit is a superposition of several states, and thus, _to some extent_, with one operation, several computations are done simultaneously. The uncertainty principle is another, rather unrelated expression of the fact that at the quantum level, what we think of as "matter" actually behaves like a probability distribution.
Okay Thank you @ThomasPornin . What you described is what I thought the uncertainty principle was. Apparently I need to brush up...
Don't all this mean that if RSA can be broken that all TLS sessions with certificates are essentially broken as RSA is used to negotiate a symmetric key at the beginning of the session? Can we still have PFS?
@Rell3oT Uncertainty boils down to that it is not sufficient to exploit the superposition of states but that you have to do it in a way that you can afterwards measure the entire result without changing the already measured part of it - e.g. if one bit were encoded in the x-coordinate and another one in that direction's momentum, you might still be screwed since measuring momentum (sufficiently precise) will _retroactively_ change the x-coordinate (maximum possible precision) you just measured and vice versa. Btw, check out http://physics.stackexchange.com ;)
@Matrix RSA (or DSA) is used for the server to identify itself, the key negotiation uses Diffie-Hellman. But since that relies on the discrete logarithm just as DSA does, I guess it is just as vulnerable to Quantum Computing. However I'd be surprised if there weren't a way to use/modify the less QC-vulnerable methods for PFS
And what if the encryption was done on a quantum computer as well?
@Jojo01: I think some encryption algorithms designed to run on quantum computers have been defined (I don't recall the details at the moment). They should resist attackers with quantum computers, but they also require a quantum computer to be used at all, and given the lack of availability of quantum computers right now, we cannot test them. Let's say they are an interesting intellectual construction that _might_ be useful in a future world where every single computer and smartphone is a quantum computer.
@ThomasPornin Yeah, i think that quantum computing will improve account security, because the big companies will most likely be using quantum computers, that your typical hacker doesn't have. Of course when quantum computing gets to consumer lever, that advantage is lost and the situation goes back to zero.
What about Serpent? I've read it won't be affected either.
@skan: Serpent is a symmetric encryption algorithm; what I say about AES applies equally well to Serpent. In effect, it means that Serpent encryption with a 128-bit key could be broken with about 2^64 operations on a quantum computer (2^64 is already a very substantial amount on a classical computer).
Having dealt with IBM a lot, it's my suspicion that they developed a quantum computer decades ago, but nobody can find the link for it on their website.
"note that these are $2^64$ quantum-computing operations": also these operations must be sequential, meaning that your quantum computer has to be really fast ($2^64$ nanoseconds > 500 years). With $K$ parallel quantum computers you get a small speed up, but you still need time $\frac{2^64}{\sqrt{K}}$. See https://quantumcomputing.stackexchange.com/a/4538/5047
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Content dated before 7/24/2021 11:53 AM
• {{ error }} | 2021-12-03T06:48:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4742790460586548, "perplexity": 1198.6595170317587}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362605.52/warc/CC-MAIN-20211203060849-20211203090849-00452.warc.gz"} |
http://itl.nist.gov/div898/handbook/prc/section4/prc433.htm | 7. Product and Process Comparisons
7.4. Comparisons based on data from more than two processes
7.4.3. Are the means equal?
## The ANOVA table and tests of hypotheses about means
Sums of Squares help us compute the variance estimates displayed in ANOVA Tables The sums of squares SST and SSE previously computed for the one-way ANOVA are used to form two mean squares, one for treatments and the second for error. These mean squares are denoted by $$MST$$ and $$MSE$$, respectively. These are typically displayed in a tabular form, known as an ANOVA Table. The ANOVA table also shows the statistics used to test hypotheses about the population means.
Ratio of $$MST$$ and $$MSE$$ When the null hypothesis of equal means is true, the two mean squares estimate the same quantity (error variance), and should be of approximately equal magnitude. In other words, their ratio should be close to 1. If the null hypothesis is false, $$MST$$ should be larger than $$MSE$$.
Divide sum of squares by degrees of freedom to obtain mean squares The mean squares are formed by dividing the sum of squares by the associated degrees of freedom.
Let $$N = \sum n_i$$. Then, the degrees of freedom for treatment are $$DFT = k - 1 \, ,$$ and the degrees of freedom for error are $$DFE = N - k \, .$$
The corresponding mean squares are:
$$MST = SST / DFT$$
$$MSE = SSE / DFE$$.
The F-test The test statistic, used in testing the equality of treatment means is: $$F = MST / MSE$$.
The critical value is the tabular value of the $$F$$ distribution, based on the chosen $$\alpha$$ level and the degrees of freedom $$DFT$$ and $$DFE$$.
The calculations are displayed in an ANOVA table, as follows:
ANOVA table
Source SS DF MS F Treatments $$SST$$ $$k-1$$ $$SST / (k-1)$$ $$MST/MSE$$ Error $$SSE$$ $$N-k$$ $$\,\,\, SSE / (N-k) \,\,\,$$ Total (corrected) $$SS$$ $$N-1$$
The word "source" stands for source of variation. Some authors prefer to use "between" and "within" instead of "treatments" and "error", respectively.
ANOVA Table Example
A numerical example The data below resulted from measuring the difference in resistance resulting from subjecting identical resistors to three different temperatures for a period of 24 hours. The sample size of each group was 5. In the language of design of experiments, we have an experiment in which each of three treatments was replicated 5 times.
Level 1 Level 2 Level 3 6.9 8.3 8.0 5.4 6.8 10.5 5.8 7.8 8.1 4.6 9.2 6.9 4.0 6.5 9.3 means 5.34 7.72 8.56
The resulting ANOVA table is
Example ANOVA table
Source SS DF MS F Treatments 27.897 2 13.949 9.59 Error 17.452 12 1.454 Total (corrected) 45.349 14 Correction Factor 779.041 1
Interpretation of the ANOVA table The test statistic is the $$F$$ value of 9.59. Using an $$\alpha$$ of 0.05, we have $$F_{0.05; \, 2, \, 12}$$ = 3.89 (see the F distribution table in Chapter 1). Since the test statistic is much larger than the critical value, we reject the null hypothesis of equal population means and conclude that there is a (statistically) significant difference among the population means. The $$p$$-value for 9.59 is 0.00325, so the test statistic is significant at that level.
Techniques for further analysis The populations here are resistor readings while operating under the three different temperatures. What we do not know at this point is whether the three means are all different or which of the three means is different from the other two, and by how much.
There are several techniques we might use to further analyze the differences. These are: | 2017-01-23T12:33:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8255650401115417, "perplexity": 472.4832144663588}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560282926.64/warc/CC-MAIN-20170116095122-00333-ip-10-171-10-70.ec2.internal.warc.gz"} |
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Call number: 9783319393391:ONLINE Show nearby items on shelf Title: Singularities in Geometry, Topology, Foliations and Dynamics A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014 Author(s): Date: 2017 Size: 1 online resource (XVII, 231 p. 15 illus., 10 illus. in color p.) Contents: Extending the action of Schottky groups on the complex anti-de Sitter space to the projective space -- Puiseux Parametric Equations via the Amoeba of the Discriminant -- Some open questions on arithmetic Zariski pairs -- Logarithmic vector fields and the Severi strata in the discriminant -- Classification of Isolated Polar Weighted Homogeneous Singularities -- Rational and iterated maps, degeneracy loci, and the generalized Riemann-Hurwitz formula -- On singular varieties with smooth subvarieties -- On Polars of Plane Branches -- Singular Intersections of Quadrics I -- A New Conjecture, a New Invariant, and a New Non-splitting Result -- Lipschitz geometry does not determine embedded topological type -- Projective transverse structures for some foliations -- Chern classes and transversality for singular spaces ISBN: 9783319393391 Series: eBooks Series: Springer eBooks Series: Springer 2017 package Keywords: Mathematics , Algebraic geometry , Global analysis (Mathematics) , Manifolds (Mathematics) , Functions of complex variables , Mathematics , Several Complex Variables and Analytic Spaces , Algebraic Geometry , Global Analysis and Analysis on Manifolds Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: 9783319297347:ONLINE Show nearby items on shelf Title: Geometrodynamics of Gauge Fields On the Geometry of Yang-Mills and Gravitational Gauge Theories Author(s): Eckehard W Mielke Date: 2017 Edition: 2nd ed. 2017 Size: 1 online resource (XVII, 373 p. 18 illus., 8 illus. in color p.) Contents: Preface -- 1 Historical background -- 2 Geometry of gauge fields -- 3 Maxwell and Yang-Mills theory -- 4 Gravitation as a gauge theory -- 5 Einstein-Cartan theory -- 6 Teleparallelism -- 7 Yang’s theory of gravity -- 8 BRST quantization of gravity -- 9 Gravitational instantons -- 10 Three-dimensional gravity -- 11 Spinor bundles -- 12 Chiral anomalies -- 13 Topological SL(5R) gauge invariant action -- 14 Geometrodynamics and its extensions -- 15 Color Geometrodynamics -- 16 Geometrodynamical model of quark confinement?- Appendix A Notation and mathematical terms -- Appendix B Calculus of exterior forms -- Appendix C Lie groups ISBN: 9783319297347 Series: eBooks Series: Springer eBooks Series: Springer 2017 package Keywords: Physics , Mathematical physics , Gravitation , Elementary particles (Physics) , Quantum field theory , Physics , Classical and Quantum Gravitation, Relativity Theory , Mathematical Physics , Elementary Particles, Quantum Field Theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2016-9783658106331:ONLINE Show nearby items on shelf Title: Manifolds, Sheaves, and Cohomology Author(s): Torsten Wedhorn Date: 2016 Size: 1 online resource (354 p.) Note: 10.1007/978-3-658-10633-1 Contents: Topological Preliminaries -- Algebraic Topological Preliminaries -- Sheaves -- Manifolds -- Local Theory of Manifolds -- Lie Groups -- Torsors and Non-abelian Cech Cohomology -- Bundles -- Soft Sheaves -- Cohomology of Complexes of Sheaves -- Cohom ology of Sheaves of Locally Constant Functions -- Appendix: Basic Topology, The Language of Categories, Basic Algebra, Homological Algebra, Local Analysis ISBN: 9783658106331 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Keywords: Mathematics , Category theory (Mathematics) , Homological algebra , Topological groups , Lie groups , Global analysis (Mathematics) , Manifolds (Mathematics) , Differential geometry , Mathematics , Category Theory, Homological Algebra , Topological Groups, Lie Groups , Differential Geometry , Global Analysis and Analysis on Manifolds Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2016-9783319397801:ONLINE Show nearby items on shelf Title: Extensions of Positive Definite Functions Applications and Their Harmonic Analysis Author(s): Palle Jorgensen Date: 2016 Size: 1 online resource (9 p.) Note: 10.1007/978-3-319-39780-1 ISBN: 9783319397801 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Lecture Notes in Mathematics: 2160 Keywords: Mathematics , Topological groups , Lie groups , Harmonic analysis , Fourier analysis , Functional analysis , Probabilities , Mathematical physics , Mathematics , Abstract Harmonic Analysis , Topological Groups, Lie Groups , Fourier Analysis , Functional Analysis , Mathematical Physics , Probability Theory and Stochastic Processes Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2016-9783319392868:ONLINE Show nearby items on shelf Title: Operator Algebras and Applications The Abel Symposium 2015 Author(s): Date: 2016 Size: 1 online resource (2 p.) Note: 10.1007/978-3-319-39286-8 Contents: C*-tensor categories and subfactors for totally disconnected groups: Y. Arano and S. Vaes -- Decomposable approximations revisited: N.P. Brown, J.R. Carrión and S. White -- Exotic crossed products: A. Buss, S. Echterhoff, and R. Willett -- On Hong and Szymanski’s description of the primitive-ideal space of a graph algebra: T. M. Carlsen and A. Sims -- Commutator inequalities via Schur products: E. Christensen -- C*-algebras associated with algebraic actions: J. Cuntz -- A new look at C*-simplicit y and the unique trace property of a group: U. Haagerup -- Equilibrium states on graph algebras: A. an Huef and I. Raeburn -- Semigroup C_-algebras: X. Li -- Topological full groups of étale groupoids: H. Matui -- Towards a classification of compact quan tum groups of Lie type: S. Neshveyev and M. Yamashita -- A homology theory for Smale spaces: a summary: I.F. Putnam -- On the positive eigenvalues and eigenvectors of a non-negative matrix: K. Thomsen -- Classification of graph algebras: a selective survey: M. Tomforde -- QDQ vs. UCT: W. Winter ISBN: 9783319392868 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Abel Symposia: 12 Keywords: Mathematics , K-theory , Dynamics , Ergodic theory , Functional analysis , Mathematical physics , Mathematics , Functional Analysis , Dynamical Systems and Ergodic Theory , K-Theory , Mathematical Physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2016-9783319304519:ONLINE Show nearby items on shelf Title: Symmetries in Graphs, Maps, and Polytopes 5th SIGMAP Workshop, West Malvern, UK, July 2014 Author(s): Date: 2016 Edition: 1st ed. 2016 Size: 1 online resource (332 p.) Note: 10.1007/978-3-319-30451-9 ISBN: 9783319304519 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Springer Proceedings in Mathematics & Statistics: 159 Keywords: Mathematics , Algebra , Field theory (Physics) , Topological groups , Lie groups , Graph theory , Mathematics , Graph Theory , Field Theory and Polynomials , Topological Groups, Lie Groups Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2016-9783319295589:ONLINE Show nearby items on shelf Title: Quantization on Nilpotent Lie Groups Author(s): Veronique Fischer Date: 2016 Edition: 1st ed. 2016 Size: 1 online resource (557 p.) Note: 10.1007/978-3-319-29558-9 Contents: Preface -- Introduction -- Notation and conventions -- 1 Preliminaries on Lie groups -- 2 Quantization on compact Lie groups -- 3 Homogeneous Lie groups -- 4 Rockland operators and Sobolev spaces -- 5 Quantization on graded Lie groups -- 6 Pseudo-d ifferential operators on the Heisenberg group -- A Miscellaneous -- B Group C* and von Neumann algebras -- Schrödinger representations and Weyl quantization -- Explicit symbolic calculus on the Heisenberg group -- List of quantizations -- Bibliography -- Index ISBN: 9783319295589 Series: eBooks Series: SpringerLink (Online service) Series: Springer eBooks Series: Progress in Mathematics: 314 Keywords: Mathematics , Topological groups , Lie groups , Harmonic analysis , Functional analysis , Mathematical physics , Mathematics , Topological Groups, Lie Groups , Abstract Harmonic Analysis , Functional Analysis , Mathematical Physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9789462390249:ONLINE Show nearby items on shelf Title: Recent Progress in General Topology III [electronic resource] Author(s): K.P Hart J van Mill P Simon Date: 2014 Publisher: Paris : Atlantis Press : Imprint: Atlantis Press Size: 1 online resource Note: The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland,1992 and 2002). The boo k was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in2002. The following areas experienced signifi cant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems Contents: Topological Homogeneity Some Recent Progress Concerning Topology of Fractals A biased view of topology as a tool in functional analysis Large scale versus small scale Descriptive aspects of Rosenthal compacta Minimality conditions in topological groups Set Theoretic update on Topology Topics in Dimension Theory Representations of dynamical systems on Banach spaces Generalized metrizable spaces Permanence in Coarse Geometry Selections and Hyperspaces Continuum Theory Almost disjoint families and topology Some Topics in Geometric Topology II Topologic ISBN: 9789462390249 Series: eBooks Series: SpringerLink Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Functional analysis , Logic, Symbolic and mathematical , Topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9788132215998:ONLINE Show nearby items on shelf Title: Basic Modern Algebra with Applications [electronic resource] Author(s): Mahima Ranjan Adhikari Avishek Adhikari Date: 2014 Publisher: New Delhi : Springer India : Imprint: Springer Size: 1 online resource Note: The book is primarily intended as a textbook on modern algebra for undergraduate mathematics students. It is also useful for those who are interested in supplementary reading at a higher level. The text is designed in such a waythat it encourages ind ependent thinking and motivates students towards further study. The book covers all major topics in group, ring, vector space and module theory that are usually contained in a standard modern algebra text. Inaddition, it studies semigroup, group action, Hopf's group, topological groups and Lie groups with their actions, applications of ring theory to algebraic geometry, and defines Zariski topology, as well as applications of module theoryto structure theory of rings and homological algebra. Algebraic as pects of classical number theory and algebraic number theory are also discussed with an eye to developing modern cryptography. Topics on applications to algebraictopology, category theory, algebraic geometry, algebraic number theory, cryptography and theo retical computer science interlink the subject with different areas. Each chapter discusses individual topics, starting from the basics, withthe help of illustrative examples. This comprehensive text with a broad variety of concepts, applications, example s, exercises and historical notes represents a valuable and unique resource Contents: Prerequisites: Basics of Set Theory and Integers Groups: Introductory Concepts Actions of Groups, Topological Groups and semigroups Rings: Introductory Concepts Ideals of Rings: Introductory concepts Factorization in Integral Domains and in Polynomial Rings Rings with Chain Conditions Vector Spaces Modules Algebraic Aspects of Number Theory Algebraic Numbers Introduction to Mathematical Cryptography Appendix A: Some Aspects of Semirings Appendix B: Category Theory Appendix C: A Brief Historical Note ISBN: 9788132215998 Series: eBooks Series: SpringerLink Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Group theory , Number theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9783642553615:ONLINE Show nearby items on shelf Title: Algebra, Geometry and Mathematical Physics [electronic resource] : AGMP, Mulhouse, France, October 2011 Author(s): Abdenacer Makhlouf Eugen Paal Sergei D Silvestrov Alexander Stolin Date: 2014 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetriesand conservation laws and mathematical physics and applications, the book covers deformation theory and quantization Hom-algebras and n-ary algebraic structures Hopf algebra, integrable systems and related math structures jet theoryand Weil bundles Lie theory and applications non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures ofLie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry andapplications in physics and beyond. The book benefits a broad audience of researchers a nd advanced students Contents: Part I Algebra Part II Geometry Part III Dynamical Symmetries and Conservation Laws Part IV Mathematical Physics and Applications ISBN: 9783642553615 Series: eBooks Series: SpringerLink Series: Springer Proceedings in Mathematics & Statistics, 2194-1009 : v85 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry , Engineering mathematics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9783319078427:ONLINE Show nearby items on shelf Title: Probability on Compact Lie Groups [electronic resource] Author(s): David Applebaum Date: 2014 Publisher: Cham : Springer International Publishing : Imprint: Springer Size: 1 online resource Note: Probability theory on compact Lie groups deals with the interaction between chance and symmetry, a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applicationsin statistics and engineering (par ticularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topicspresented are: the study of measures via the non-commutative F ourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. Theemphasis on compact (rather than general) Lie groups helps readers to get acquaint ed with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance ofthese groups for applications. The book is primarily aimed at researchers working in probability, stochast ic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists,statisticians and engineers who are working on related applications. A background in first year graduate level measure theoreti c probability and functional analysis is essential a background in Lie groups and representation theory iscertainly helpful but the first two chapters also offer orientation in these subjects Contents: Introduction 1.Lie Groups 2.Representations, Peter Weyl Theory and Weights 3.Analysis on Compact Lie Groups 4.Probability Measures on Compact Lie Groups 5.Convolution Semigroups of Measures 6.Deconvolution Density Estimation Appendices Index Bibliography ISBN: 9783319078427 Series: eBooks Series: SpringerLink Series: Probability Theory and Stochastic Modelling, 2199-3130 : v70 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Harmonic analysis , Fourier analysis , Functional analysis , Distribution (Probability theory) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9783319059570:ONLINE Show nearby items on shelf Title: A Short Course in Computational Geometry and Topology [electronic resource] Author(s): Herbert Edelsbrunner Date: 2014 Publisher: Cham : Springer International Publishing : Imprint: Springer Size: 1 online resource Note: With the aim to bring the subject of Computational Geometry and Topology closer to the scientific audience, this book is written in thirteen ready-to-teach sections organized in four parts: TESSELLATIONS, COMPLEXES, HOMOLOGY,PERSISTENCE. To speak to the non-specialist, detailed formalisms are often avoided in favor of lively 2- and 3-dimensional illustrations. The book is warmly recommended to everybody who loves geometry and the fascinating world ofshapes Contents: Roots of Geometry and Topology Voronoi and Delaunay Diagrams Weighted Diagrams Three Dimensions Alpha Complexes Holes Area Formulas Topological Spaces Homology Groups Complex Construction Filtrations PL Functions Matrix Reduction Epilogue ISBN: 9783319059570 Series: eBooks Series: SpringerLink Series: SpringerBriefs in Applied Sciences and Technology, 2191-530X Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Computer science , Cell aggregation Mathematics , Biomedical engineering Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9783319052243:ONLINE Show nearby items on shelf Title: Descriptive Topology and Functional Analysis [electronic resource] : In Honour of Jerzy Kakols 60th Birthday Author(s): Juan Carlos Ferrando Manuel Lpez-Pellicer Date: 2014 Publisher: Cham : Springer International Publishing : Imprint: Springer Size: 1 online resource Note: Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topologicalAbelian groups, linear top ological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapterpresents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area Contents: 1Some aspects in the Mathematical work of Jerzy Kakol 2Weak barrelledness vs. P spaces 3On the topology of the sets of the real projections of the zeros ofexponential polynomials 4The density character of the space Cp(X) 5Compactness and distances to spaces of continuous functions andFrchet spaces 6Two classes of metrizable spaces lc invariant 7Characteristics of the Mackey topology for abelian topologicalgroups 8Bowens Entropy for Endomorphisms of Totally Bounded Abelian 9On preserved and unpreserved extreme pointsGroups 10Cantor set ISBN: 9783319052243 Series: eBooks Series: SpringerLink Series: Springer Proceedings in Mathematics & Statistics, 2194-1009 : v80 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Functional analysis , Operator theory , Topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9783319020457:ONLINE Show nearby items on shelf Title: Locally Convex Spaces [electronic resource] Author(s): M. Scott Osborne Date: 2014 Publisher: Cham : Springer International Publishing : Imprint: Springer Size: 1 online resource Note: For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convextopological vector spaces, is i ntended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convexspaces, which is why this is an important topic in function al analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varyingdifficulty. Key topics covered include point set topology, topological vector space s, the HahnBanach theorem, seminorms and Frchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach spacetheory typically taught in a beginning graduate real analysis course Contents: 1 Topological Groups 2 Topological Vector Spaces 3 Locally Convex Spaces 4 The Classics 5 Dual Spaces 6 Duals of Fr chet Spaces A Topological Oddities B Closed Graphs in Topological Groups C The Other KreinSmulian Theorem D Further Hints for Selected Exercises Bibliography Index ISBN: 9783319020457 Series: eBooks Series: SpringerLink Series: Graduate Texts in Mathematics, 0072-5285 : v269 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Functional analysis Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9783319020365:ONLINE Show nearby items on shelf Title: Contact and Symplectic Topology [electronic resource] Author(s): Frdric Bourgeois Vincent Colin Andrs Stipsicz Date: 2014 Publisher: Cham : Springer International Publishing : Imprint: Springer Size: 1 online resource Note: Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new researchfield worldwide. The inten se activity of many European research groups in this field is reflected by the ESF Research Networking Programme Contact And Symplectic Topology (CAST). The lectures of the Summer School in Nantes (June2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which havedeveloped in an amazing speed in the recent past. These topics include 3- dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embeddedcontact homology, and flexibility results for Stein manifolds Contents: Mathematical contributions from V.I. Arnold Topological methods in 3 dimensional contact geometry A short introduction to Fukaya categories Open books and Lefschetz pencils in contact geometry Introduction to contact topology in higher dimensions Bordered Heegaard Floer homology Stein structures: existence and flexibility Embedded contact homology, cobordism maps, and applications Knot contact homology and applications ISBN: 9783319020365 Series: eBooks Series: SpringerLink Series: Bolyai Society Mathematical Studies, 1217-4696 : v26 Series: Mathematics and Statistics (Springer-11649) Keywords: Geometry , Mathematical physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9781493909384:ONLINE Show nearby items on shelf Title: Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics [electronic resource] Author(s): Mahir Can Zhenheng Li Benjamin Steinberg Qiang Wang Date: 2014 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids. Topics presented include: v structure andrepresentation theory of reducti ve algebraic monoids v monoid schemes and applications of monoids v monoids related to Lie theory v equivariant embeddings of algebraic groups v constructions and properties of monoids fromalgebraic combinatorics v endomorphism monoids induced from vector bundles v HodgeNewton decompositions of reductive monoids A portion of these articles are designed to serve as a self-contained introduction to these topics,while the remaining contributions are research articles containing previously unpublished result s, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and LexRenner showing that the algebraic semigroups are strongly -regular. Graduate students as well as researchers working in the fields of algebraic (semi)group theory, algebraic combinatorics, and the theory of algebraic groupembeddings will benefit from this unique and broad compilation of some fundamental results in (semi)group theory, algebraic group embeddings, and alge braic combinatorics merged under the umbrella of algebraic monoids Contents: On Algebraic Semi groups and Monoids (M. Brion) Algebraic Semi groups are Strongly regular (M. Brion, L. E. Renner) Rees Theorem and Quotients in Linear Algebraic Semi groups (M. S. Putcha) Representations of Reductive Normal Algebraic Monoids (S. Doty) On Linear Hodge Newton Decomposition for Reductive Monoids (S. Varma) The Structure of Affine Algebraic Monoids in Terms of Kernel Data (W. Huang) Algebraic Monoids and Renner Monoids (Z. Li, Z. Li, Y. Cao) Conjugacy Decomposition of Canonical and Dual Canonical Monoids (R. K. Therkelsen) The Endomorphisms Monoid of a ISBN: 9781493909384 Series: eBooks Series: SpringerLink Series: Fields Institute Communications, 1069-5265 : v71 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Geometry, algebraic , Group theory , Topological Groups , Combinatorics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9781493907489:ONLINE Show nearby items on shelf Title: The Compressed Word Problem for Groups [electronic resource] Author(s): Markus Lohrey Date: 2014 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups.The authorpresents thenecessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontierofcurrent research which makes the book especially ap pealing for students looking for a currently active research topic at theintersection of group theory and computer science. The word problem introduced in 1910 by Max Dehnisone of the most important decision problems in group theory. For many groups, high ly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithmsfor word problems, has been developed, by representing long words over group generators in a compressed f orm using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressedword problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups Contents: 1. Preliminaries from Theoretical Computer Science 2. Preliminaries from Combinatorial Group Theory 3. Algorithms on Compressed Words 4. The Compressed Word Problem 5. The Compressed Word Problem in Graph Products 6. The Compressed Word Problem in HNN Extensions 7.Outlook References Index ISBN: 9781493907489 Series: eBooks Series: SpringerLink Series: SpringerBriefs in Mathematics, 2191-8198 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Group theory , Topological Groups , Global analysis (Mathematics) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2014-9781461491613:ONLINE Show nearby items on shelf Title: Nonlinear Maps and their Applications [electronic resource] : Selected Contributions from the NOMA 2011 International Workshop Author(s): Clara Grcio Daniele Fournier-Prunaret Tetsushi Ueta Yoshifumi Nishio Date: 2014 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: In the field of Dynamical Systems, nonlinear iterative processes play an important role. Nonlinear mappings can be found as immediate models for many systems from different scientific areas, such as engineering, economics,biology, or can also be obta ined via numerical methods permitting to solve non-linear differential equations. In both cases, the understanding of specific dynamical behaviors and phenomena is of the greatest interest for scientists.This volume contains papers that were presented at the International Workshop on Nonlinear Maps and their Applications (NOMA 2011) held in vora, Portugal, on September 15-16, 2011. This kind of collaborative effort is of paramountimportance in promoting communication among the various groups that work in dynamical systems and networks in their research theoretical studies as well as for applications. This volume is suitable for graduate students as well asresearchers in the field Contents: J. P. Almeida A. A. Pinto D. A. Rand, Renormalization of circlediffeomorphism sequences and Markov sequences F. Balibrea M. V. Caballero, Examples of Lyapunov exponents in two dimensional systems R. A. da Costa S. N. Dorogovtsev A.V. Goltsev J. F. F. Mendes, Characteristics of the explosive percolation transition E. S. Roberts A. Annibale A. C. C. Coolen, Controlled Markovian dynamics of graphs: unbiased generation of random graphs with prescribed topological properties G. Bettencourt, A case leading to rationalist of the drift L. S. Efremova, Remarks on the nonwanderi ISBN: 9781461491613 Series: eBooks Series: SpringerLink Series: Springer Proceedings in Mathematics & Statistics, 2194-1009 : v57 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Differentiable dynamical systems Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9789400753457:ONLINE Show nearby items on shelf Title: Differential Geometry and Mathematical Physics [electronic resource] : Part I. Manifolds, Lie Groups and Hamiltonian Systems Author(s): Gerd Rudolph Matthias Schmidt Date: 2013 Publisher: Dordrecht : Springer Netherlands : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Starting from an undergraduate level, this book systematically develops the basics of Calculus on manifolds, vector bundles, vector fields and differential forms, Lie groups and Lie group actions, Linear symplecticalgebra and symplectic geometry, Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. Thesecond and third items constitute the link between abstr act calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class andcaustics. The book guides the reader from elementary differential geometry to advan ced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematicaltextbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact Note: Springer eBooks Contents: 1 Differentiable manifolds 2 Vector bundles 3 Vector fields 4 Differential forms 5 Lie groups 6 Lie group actions 7 Linear symplectic algebra 8 Symplectic geometry 9 Hamiltonian systems 10 Symmetries 11 Integrability 12 Hamilton Jacobi theory References ISBN: 9789400753457 Series: e-books Series: SpringerLink (Online service) Series: Theoretical and Mathematical Physics, 1864-5879 Series: Physics and Astronomy (Springer-11651) Keywords: Topological Groups , Global analysis , Global differential geometry , Mathematical physics , Mechanics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9788847028418:ONLINE Show nearby items on shelf Title: Geometric Properties for Parabolic and Elliptic PDE's [electronic resource] Author(s): Rolando Magnanini Shigeru Sakaguchi Angelo Alvino Date: 2013 Publisher: Milano : Springer Milan : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The study of qualitative aspects of PDE's has always attracted much attention from the early beginnings. More recently, once basic issues about PDE's, such as existence, uniqueness and stability of solutions, have been understoodquite well, research on topological and/or geometric properties of their solutions has become more intense. The study of these issues is attracting the interest of an increasing number of researchers and is now a broad andwell-established research area, with contributions tha t often come from experts from disparate areas of mathematics, such as differential and convex geometry, functional analysis, calculus of variations, mathematical physics, to name afew. This volume collects a selection of original results and informative surveys by a group of international specialists in the field, analyzes new trends and techniques and aims at promoting scientific collaboration and stimulatingfuture developments and perspectives in this very active area of research Note: Springer eBooks Contents: Goro Akagi, Stability and instability of group invariant asymptotic profiles for fast diffusion equations Elvise Berchio, A family of Hardy Rellich type inequalities involving the L2 norm of the Hessian matrices Massimiliano Bianchini and Paolo Salani, Power concavity for solutions of nonlinear elliptic problems in convex domains Lorenzo Brasco and Rolando Magnanini, The heart of a convex set Giulio Ciraolo, A viscosity equation for minimizers of a class of very degenerate elliptic functionals Adele Ferone, Kato's inequality in the half space: an alternative proof and relative i ISBN: 9788847028418 Series: e-books Series: SpringerLink (Online service) Series: Springer INdAM Series, 2281-518X : v2 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Global analysis (Mathematics) , Functional analysis , Differential equations, partial , Discrete groups , Global differential geometry , Mathematical optimization Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9784431542704:ONLINE Show nearby items on shelf Title: Lie Theory and Its Applications in Physics [electronic resource] : IX International Workshop Author(s): Vladimir Dobrev Date: 2013 Publisher: Tokyo : Springer Japan : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Traditionally, Lie Theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrisation of the mathematical description of physical systems and objects. A geometric approach to asystem yields in general so me notion of symmetry which is very helpful in understanding its structure. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantumgroups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples ofthese new trends are presented in this volume, based on contributions fr om the Workshop Lie Theory and Its Applications in Physics held near Varna, Bulgaria, in June 2011. This book is suitable for an extensive audience ofmathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theo ry Note: Springer eBooks ISBN: 9784431542704 Series: e-books Series: SpringerLink (Online service) Series: Springer Proceedings in Mathematics & Statistics, 2194-1009 : v36 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Topological Groups , Geometry Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783642362163:ONLINE Show nearby items on shelf Title: Clifford Algebras and Lie Theory [electronic resource] Author(s): Eckhard Meinrenken Date: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results onsymmetric bilinear form s and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartans famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes apresentation of Petraccis proof of the PoincarBirk hoffWitt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lietheory include Duflos theorem for the case of quadratic Lie algebras, multiplets of rep resentations, and Dirac induction. The last part of the book is an account of Kostants structure theory of the Clifford algebra over asemisimple Lie algebra. It describes his Clifford algebra analogue of the HopfKoszulSamelson theorem, and explains his fa scinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principalsl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Cliffor d theory, relevant for students and researchers in mathematics andphysics Note: Springer eBooks Contents: Preface Conventions List of Symbols 1 Symmetric bilinear forms 2 Clifford algebras 3 The spin representation 4 Covariant and contravariant spinors 5 Enveloping algebras 6 Weil algebras 7 Quantum Weil algebras 8 Applications to reductive Lie algebras 9 D(g k) as a geometric Dirac operator 10 The HopfKoszulSamelson Theorem 11 The Clifford algebra of a reductive Lie algebra A Graded and filtered super spaces B Reductive Lie algebras C Background on Lie groups References Index ISBN: 9783642362163 Series: e-books Series: SpringerLink (Online service) Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 0071-1136 : v58 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry , Mathematical physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783642343643:ONLINE Show nearby items on shelf Title: A Guide to the Classification Theorem for Compact Surfaces [electronic resource] Author(s): Jean Gallier Dianna Xu Date: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those withoutdetailed background know ledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy andformal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be awork-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincar characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learningwhere it is required, without interrupting the carefully planned structure of the core expositi on. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuineconfidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and val uable techniques available in algebraic topology Note: Springer eBooks Contents: The Classification Theorem: Informal Presentation Surfaces Simplices, Complexes, and Triangulations The Fundamental Group, Orientability Homology Groups The Classification Theorem for Compact Surfaces Viewing the Real Projective Plane in R3 Proof of Proposition 5.1 Topological Preliminaries History of the Classification Theorem Every Surface Can be Triangulated Notes ISBN: 9783642343643 Series: e-books Series: SpringerLink (Online service) Series: Geometry and Computing, 1866-6795 : v9 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topology , Algebraic topology , Cell aggregation Mathematics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783642310904:ONLINE Show nearby items on shelf Title: Poisson Structures [electronic resource] Author(s): Camille Laurent-Gengoux Anne Pichereau Pol Vanhaecke Date: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of thesecontexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to theproblem in nearly all cases. Poisson Structu res is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures.The first part coverssolid foundations,the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications ofPoisson structures (integrable systems and deformation quantization). The clear structure of th e book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researcherswhoare interested in anintroduction to the many facets and applications of Poisson structures Note: Springer eBooks Contents: Part I Theoretical Background:1.Poisson Structures: Basic Definitions 2.Poisson Structures: Basic Constructions 3.Multi Derivations and Khler Forms 4.Poisson (Co)Homology 5.Reduction Part II Examples:6.Constant Poisson Structures, Regular and Symplectic Manifolds 7.Linear Poisson Structures and Lie Algebras 8.Higher Degree Poisson Structures 9.Poisson Structures in Dimensions Two and Three 10.R Brackets and r Brackets 11.PoissonLie Groups Part III Applications:12.Liouville Integrable Systems 13.Deformation Quantization A Multilinear Algebra B Real ISBN: 9783642310904 Series: e-books Series: SpringerLink (Online service) Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 0072-7830 : v347 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Topological Groups , Global analysis (Mathematics) , Global differential geometry Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783642309946:ONLINE Show nearby items on shelf Title: Linear Algebra and Geometry [electronic resource] Author(s): Igor R Shafarevich Alexey O Remizov Date: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book on linear algebra and geometry is based on a course given by renowned academician I.R. Shafarevich at Moscow State University. The book begins with the theory of linear algebraic equations and the basic elements ofmatrix theory and continue s with vector spaces, linear transformations, inner product spaces, and the theory of affine and projective spaces. The book also includes some subjects that are naturally related to linear algebra but areusually not covered in such courses: exterior alge bras, non-Euclidean geometry, topological properties of projective spaces, theory of quadrics (in affine and projective spaces), decomposition of finite abelian groups, and finitelygenerated periodic modules (similar to Jordan normal forms of linear opera tors). Mathematical reasoning, theorems, and concepts are illustrated with numerous examples from various fields of mathematics, including differential equationsand differential geometry, as well as from mechanics and physics Note: Springer eBooks Contents: Preface Preliminaries 1. Linear Equations 2. Matrices and Determinants 3. Vector Spaces 4. Linear Transformations of a Vector Space to Itself 5. Jordan Normal Form 6. Quadratic and Bilinear Forms 7. Euclidean Spaces 8. Affine Spaces 9. Projective Spaces 10. The Exterior Product and Exterior Algebras 11. Quadrics 12. Hyperbolic Geometry 13. Groups, Rings, and Modules 14. Elements of Representation Theory Historical Note References Index ISBN: 9783642309946 Series: e-books Series: SpringerLink (Online service) Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Matrix theory , Geometry Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783642307096:ONLINE Show nearby items on shelf Title: Variational, Topological, and Partial Order Methods with Their Applications [electronic resource] Author(s): Zhitao Zhang Date: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Nonlinear functional analysis is an important branch of contemporary mathematics. It's related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry,measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been usedextensively to solve existence of solutions for ellipt ic equations, wave equations, Schrdinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This bookis useful for researchers and graduate students in the field of nonlinear fu nctional analysis. Chapter 1 contains preliminaries. In Chapter 2, three kinds of operators are introduced: increasing operators, decreasing operators, andmixed monotone operators. In Chapter 3, the minimax methods are presented and in Chapter 4, the auth or uses bifurcation and critical point theory to study structures of the solutions of elliptic equations. Chapter 5 is concerned with aclass of MongeAmpre equations. In Chapter 6, the superlinear system of Hammerstein integral equations and applications i s studied. Chapter 7 is devoted to the DancerFucik spectrum. In Chapter 8, some results on sign-changingsolutions are introduced. In Chapter 9, a local minimizer problem of a functional in differential topology is studied. Chapter 10 focuses on a class of nonlocal Kirchhoff elliptic problems via different methods. In Chapter 11, thefocus is on free boundary problems, Schrdinger systems from BoseEinstein condensate and competing systems with many species Note: Springer eBooks Contents: 1 Preliminaries Sobolev spaces and embedding theorems Critical point Cone and partial order Brouwer Degree Compact map and Leray Schauder Degree Fredholm operators Fixed point index Banach's Contract Theorem, Implicit Functions Theorem Krein Rutman theorem Bifurcation theory Rearrangements of sets and functions Genus and Category Maximum principles and symmetry of solution Comparison theorems 2 Cone and Partial Order Methods Increasing operators Decreasing operators Mixed monotone operators Applications of mixed monotone operators Fur ISBN: 9783642307096 Series: e-books Series: SpringerLink (Online service) Series: Developments in Mathematics, 1389-2177 : v29 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Functional analysis Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783642306747:ONLINE Show nearby items on shelf Title: Rational Points and Arithmetic of Fundamental Groups [electronic resource] : Evidence for the Section Conjecture Author(s): Jakob Stix Date: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of itsfundamental group. Whi le the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only oneagainst rational points on curves. This monogr aph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and thelocal-to-global approach is studied in detail. The monograph concl udes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birationalanalogue in lieu of the fundamental group extension Note: Springer eBooks Contents: Part I Foundations of Sections 1 Continuous Non abelian H1 with Profinite Coefficients 2 The Fundamental Groupoid 3 Basic Geometric Operations in Terms of Sections 4 The Space of Sections as a Topological Space 5 Evaluation of Units 6 Cycle Classes in Anabelian Geometry 7 Injectivity in the Section Conjecture Part II Basic Arithmetic of Sections 7 Injectivity in the Section Conjecture 8 Reduction of Sections 9 The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers Part III On the Passage from Local to Global 10 Local Obstructions ISBN: 9783642306747 Series: e-books Series: SpringerLink (Online service) Series: Lecture Notes in Mathematics, 0075-8434 : v2054 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Geometry, algebraic , Number theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783319002576:ONLINE Show nearby items on shelf Title: The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups [electronic resource] Author(s): Daciberg Lima Goncalves John Guaschi Date: 2013 Publisher: Cham : Springer International Publishing : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks animportant step in th e computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysisof their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups.This manuscript will serve as a reference for the study of bra id groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra Note: Springer eBooks Contents: Introduction and statement of the main results Virtually cyclic groups: generalities, reduction and the mapping class group Realisation of the elements of V1(n) and V2(n) in Bn(S2) Appendix: The subgroups of the binary polyhedral groups References. ISBN: 9783319002576 Series: e-books Series: SpringerLink (Online service) Series: SpringerBriefs in Mathematics, 2191-8198 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Group theory , Algebraic topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783034805858:ONLINE Show nearby items on shelf Title: Pseudo-Differential Operators, Generalized Functions and Asymptotics [electronic resource] Author(s): Shahla Molahajloo Stevan Pilipovi Joachim Toft M. W Wong Date: 2013 Publisher: Basel : Springer Basel : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This volume consists of twenty peer-reviewed papers from the special sessions on pseudodifferential operators and on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples FriendshipUniversity of Russia in Moscow on August 2227, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifoldswith edges, heat kernels and Green functions of sub-Lapla cians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, L^p-boundedness of pseudo-differential operators on thetorus, and pseudo-differential operators related to time-frequency analysis. The s econd group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlineardifferential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differ ential equations. This second group of papers is related to the third collection of papers via the setting ofColombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volumecontains the synergi es of the three areas treatedand is a useful complement toitspredecessorspublished in the same series Note: Springer eBooks Contents: Preface Elliptic Theory for Operators Associated with Diffeomorphisms of Smooth Manifolds The Singular Functions of Branching Edge Asymptotics The Heat Kernel and Green Function of the Sub Laplacian on the Heisenberg Group Metaplectic Equivalence of the Hierarchical Twisted Laplacian The Heat Kernel and Green Function of a Sub Laplacian on the Hierarchical Heisenberg Group Lp Bounds for Pseudo Differential Operators on the Torus Multiplication Properties in Gelfand Shilov Pseudo Differential Calculus Operator Invariance Initial Value Problems in the Time Frequency Do ISBN: 9783034805858 Series: e-books Series: SpringerLink (Online service) Series: Operator Theory: Advances and Applications : v231 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Global analysis , Operator theory , Differential equations, partial Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9783034804813:ONLINE Show nearby items on shelf Title: Complex Kleinian Groups [electronic resource] Author(s): Angel Cano Juan Pablo Navarrete Jos Seade Date: 2013 Publisher: Basel : Springer Basel : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This monograph lays down the foundations of the theory of complex Kleinian groups, a newborn area of mathematics whose origin can be traced back to the work of Riemann, Poincar, Picard and many others. Kleinian groupsare, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions,there is a dichotomy: Should we look at conformal automorp hisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In thefirst case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition in the second, about an area of mathematics that is still in its infancy, and this is the focus ofstudy in this monograph. It brings together several important areas of mathematics, e.g. classical Kleini an group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds Note: Springer eBooks Contents: Preface Introduction Acknowledgments 1 A glance of the classical theory 2 Complex hyperbolic geometry 3 Complex Kleinian groups 4 Geometry and dynamics of automorphisms of P2C 5 Kleinian groups with a control group 6 The limit set in dimension two 7 On the dynamics of discrete subgroups of PU(n,1) 8 Projective orbifolds and dynamics in dimension two 9 Complex Schottky groups 10 Kleinian groups and twistor theory Bibliography Index. ISBN: 9783034804813 Series: e-books Series: SpringerLink (Online service) Series: Progress in Mathematics : v303 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Differentiable dynamical systems , Differential equations, partial Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461487814:ONLINE Show nearby items on shelf Title: Ricci Flow for Shape Analysis and Surface Registration [electronic resource] : Theories, Algorithms and Applications Author(s): Wei Zeng Xianfeng David Gu Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Ricci Flow for Shape Analysis and Surface Registration introduces the beautiful and profound Ricci flow theory in a discrete setting. By using basic tools in linear algebra and multivariate calculus, readers can deduce all themajor theorems in surfac e Ricci flow by themselves. The authors adapttheRicci flow theory to practical computational algorithms, apply Ricci flow for shape analysis and surface registration, and demonstrate the power of Ricciflow in many applications in medical imaging, computer graphics, computer vision and wireless sensor network. Due to minimal pre-requisites, this bookis accessible toengineersand medicalexperts, including educators,researchers, students and industry engineerswhohave an interest insolvingreal problems related to shape analysis and surface registration. Note: Springer eBooks Contents: 1. Introduction 2. Computational 3.Computational Geometry 4. Differential Geometry of Surface 5. Riemann Surface 6. Ricci Flow 7. Topological Algorithms 8. Harmonic Maps 9. Discrete Ricci Flow 10. Shape Analysis 11. Surface Diffeomorphism 12. Medical Imaging Applications 13. Computer Vision Applications 14. Computer Graphics Applications 15. Network Applications. ISBN: 9781461487814 Series: e-books Series: SpringerLink (Online service) Series: SpringerBriefs in Mathematics, 2191-8198 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Computer vision , Computer science Mathematics , Geometry , Discrete groups Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461480242:ONLINE Show nearby items on shelf Title: Lie Groups [electronic resource] Author(s): Daniel Bump Date: 2013 Edition: 2nd ed. 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range ofmaterial to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests.This second edition has substantial new material, including improved discussions ofunderlying principles, streamlining of some pro ofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the PeterWeyl theorem, Lie algebra, conjugacy of maximal tori, the Weylgroup, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flagvarieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics tha t are treated are symmetric function theory, the representation theory of the symmetric group, FrobeniusSchur duality andGL(n)GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatoric s of tableaux, Gelfand pairs, Hecke algebras, the philosophy of cusp forms and thecohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations Note: Springer eBooks Contents: Part I: Compact Topological Groups 1 Haar Measure 2 Schur Orthogonality 3 Compact Operators 4 The PeterWeyl Theorem Part II: Compact Lie Groups 5 Lie Subgroups of GL(n,C) 6 Vector Fields 7 Left Invariant Vector Fields 8 The Exponential Map 9 Tensors and Universal Properties 10 The Universal Enveloping Algebra 11 Extension of Scalars 12 Representations of sl(2,C) 13 The Universal Cover 14 The Local Frobenius Theorem 15 Tori 16 Geodesics and Maximal Tori 17 The Weyl Integration Formula 18 The Root System 19 Examples of Root Systems ISBN: 9781461480242 Series: e-books Series: SpringerLink (Online service) Series: Graduate Texts in Mathematics, 0072-5285 : v225 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461479727:ONLINE Show nearby items on shelf Title: Harmonic Analysis on Symmetric SpacesEuclidean Space, the Sphere, and the Poincar Upper Half-Plane [electronic resource] Author(s): Audrey Terras Date: 2013 Edition: 2nd ed. 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincar upper half plane. This book is intended for beginning graduate students inmathematics or researchers in phy sics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, andengineering. Many corrections, new topics, and updates have be en incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T.Sunada, Marie-France Vignras, Carolyn Gordon, and others on Mark Kac's question Can y ou hear the shape of a drum?, Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maasswaveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summationformula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon tr ansform, non-Euclidean geometry on the Poincar upper half plane H or unit disc andapplications to microwave engineering, fundamental domains in H for discrete groups , tessellations of H from such discrete group actions, automorphic forms, the Selberg tra ce formula and its applications in spectral theory as wellas number theory Note: Springer eBooks Contents: Chapter1 Flat Space. Fourier Analysis on R^m 1.1 Distributions or Generalized Functions 1.2 Fourier Integrals 1.3 Fourier Series and the Poisson Summation Formula 1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions 1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyls Criterion for Uniform Distribution Chapter2 A Compact Symmetric Space The Sphere 2.1 Fourier Analysis on the Sphere 2.2 O(3) and R^3. The Radon Transform Chapter 3 The Poincar Upper Half Plane 3.1 Hyperbolic Geometry 3.2 Harmonic Analysis on H 3.3 Fundamental Domains for ISBN: 9781461479727 Series: e-books Series: SpringerLink (Online service) Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Group theory , Topological Groups , Harmonic analysis , Fourier analysis , Functions of complex variables , Functions, special Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461473008:ONLINE Show nearby items on shelf Title: An Introduction to Quasisymmetric Schur Functions [electronic resource] Hopf Algebras, Quasisymmetric Functions, and Young Composition Tableaux Author(s): Kurt Luoto Stefan Mykytiuk Stephanie van Willigenburg Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: An Introduction to Quasisymmetric Schur Functions is aimed at researchers and graduate students in algebraic combinatorics. The goal of this monograph is twofold. The first goal is to provide a reference text for the basic theoryof Hopf algebras, in particular the Hopf algebras of symmetric, quasisymmetric and noncommutative symmetric functions and connections between them. The second goal is to give a survey of results with respect to an exciting new basis ofthe Hopf algebra of quasisymmetric functi ons, whose combinatorics is analogous to that of the renowned Schur functions Note: Springer eBooks Contents: 1. Introduction 2. Classical combinatorial concepts 3. Hopf algebras 4. Compsition tableaux and further combinatorial concepts 5. Quasisymmetric Schur functions References Index ISBN: 9781461473008 Series: e-books Series: SpringerLink (Online service) Series: SpringerBriefs in Mathematics, 2191-8198 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Algorithms , Combinatorics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461471936:ONLINE Show nearby items on shelf Title: Lie Groups: Structure, Actions, and Representations [electronic resource] : In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday Author(s): Alan Huckleberry Ivan Penkov Gregg Zuckerman Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Lie Groups: Structures, Actions, and Representations, In Honor of Joseph A. Wolf on the Occasion of his 75th Birthday consists of invited expository and research articles on new developments arising from Wolf's profoundcontributions to mathematics. D ue to Professor Wolfs broad interests, outstanding mathematicians and scholars in a wide spectrum of mathematical fields contributed to the volume. Algebraic, geometric, and analytic methods areemployed. More precisely, finite groups and classical finite dimensional, as well as infinite-dimensional Lie groups, and algebras play a role. Actions on classical symmetric spaces, and on abstract homogeneous and representationspaces are discussed. Contributions in the area of representation theory involve numero us viewpoints, including that of algebraic groups and various analytic aspects of harmonic analysis. Contributors D. Akhiezer T. Oshima A. Andrada I. Pacharoni M. L. Barberis F. Ricci L. Barchini S. Rosenberg I. Dotti N. Shimeno M. Eastwood J. Tirao V . Fischer S. Treneer T. Kobayashi C.T.C. Wall A. Kornyi D. Wallace B. Kostant K. Wiboonton P. Kostelec F. Xu K.-H. Neeb O. Yakimova G. Olafsson R. Zierau B. rsted Note: Springer eBooks Contents: Preface Real group orbits on flag manifolds Complex connections with trivial holonomy Indefinite harmonic theory and harmonic spinors Twistor theory and the harmonic hull Nilpotent Gelfand pairs and spherical transforms of Schwartz functions, II: Taylor expansions on singular sets Propagation of the multiplicity freeness property for holomorphic vector bundles Poisson transforms for line bundles from the Shilov boundary to bounded symmetric domains Cent(U(n)), cascade of orthogonal roots, and a construction of LipsmanWolf Weakly harmonic Maa forms and the princi ISBN: 9781461471936 Series: e-books Series: SpringerLink (Online service) Series: Progress in Mathematics : v306 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Topological Groups , Functional analysis Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461471165:ONLINE Show nearby items on shelf Title: Quantum Theory for Mathematicians [electronic resource] Author(s): Brian C Hall Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Springer eBooks ISBN: 9781461471165 Series: e-books Series: SpringerLink (Online service) Series: Graduate Texts in Mathematics, 0072-5285 : v267 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Functional analysis , Quantum theory , Mathematical physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461469568:ONLINE Show nearby items on shelf Title: Measure Theory [electronic resource] : Second Edition Author(s): Donald L Cohn Date: 2013 Edition: 2nd ed. 2013 Publisher: New York, NY : Springer New York : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Intended as a self-contained introduction to measure theory, this textbook also includesa comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haarmeasures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and theexistence of liftings. Measure Theory provides a soli d background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. Theprerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review ofessential background material. The author aims to present a straightforward treatment of thepart of measure theory necessary for analysis and probability' assuming only basic knowledge of analysis and topol ogy...Each chapter includes numerous well-chosen exercises, varying from very routine practice problems to importantextensions and developments of the theory for the difficult ones there are helpful hints. It is the reviewer's opinion that the author has succeeded in his aim. In spite of its lack of new results, the selection and presentation ofmaterials makes this a useful book for an introduction to measure and integration theory. Mathematical Reviews (Review of the First Edition) The book is a compreh ensive and clearly written textbook on measure andintegration...The book contains appendices on set theory, algebra, calculus and topology in Euclidean spaces, topological and metric spaces, and the Bochner integral. Each section of the book contains a nu mber of exercises.zbMATH (Review of the First Edition) Note: Springer eBooks Contents: 1. Measures Algebras and sigma algebras Measures Outer measures Lebesgue measure Completeness and regularity Dynkin classes 2. Functions and Integrals Measurable functions Properties that hold almost everywhere The integral Limit theorems The Riemann integral Measurable functions again, complex valued functions, and image measures 3. Convergence Modes of Convergence Normed spaces Definition of L^p and L^p Properties of L^p and L p Dual spaces 4. Signed and Complex Measures Signed and complex measures Absolute continuity Singu ISBN: 9781461469568 Series: e-books Series: SpringerLink (Online service) Series: Birkhuser Advanced Texts Basler Lehrbcher, 1019-6242 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Global analysis (Mathematics) , Distribution (Probability theory) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461464068:ONLINE Show nearby items on shelf Title: Asymptotic Geometric Analysis [electronic resource] : Proceedings of the Fall 2010 Fields Institute Thematic Program Author(s): Monika Ludwig Vitali D Milman Vladimir Pestov Nicole Tomczak-Jaegermann Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Asymptotic Geometric Analysis is concerned with the geometric and linear properties of finite dimensional objects, normed spaces, and convex bodies, especially with the asymptotics of their various quantitative parameters as thedimension tends to inf inity. The deep geometric, probabilistic, and combinatorial methods developed here are used outside the field in many areas of mathematics and mathematical sciences. The Fields Institute Thematic Program in theFall of 2010 continued an established traditi on of previous large-scale programs devoted to the same general research direction. The main directions of the program included: * Asymptotic theory of convexity and normed spaces *Concentration of measure and isoperimetric inequalities, optimal transport ation approach * Applications of the concept of concentration * Connections with transformation groups and Ramsey theory * Geometrization of probability * Randommatrices * Connection with asymptotic combinatorics and complexity theory These directions are represented in this volume and reflect the present state of this important area of research. It will be of benefit to researchers working ina wide range of mathematical sciencesin particular functional analysis, combinatorics, convex geometry, dynamical systems, operator algebras, and computer science Note: Springer eBooks Contents: Preface The Variance Conjecture on Some Polytopes (D. Alonso Gutirrez, J. Bastero) More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures (D. Bartosova) On the Lyapounov Exponents of Schrodinger Operators Associated with the Standard Map (J. Bourgain) Overgroups of the Automorphism Group of the Rado Graph (P. Cameron, C. Laflamme, M. Pouzet, S. Tarzi, R. Woodrow) On a Stability Property of the Generalized Spherical Radon Transform (D. Faifman) Banach Representations and Affine Compactification of Dynamical Systems (E. Glasner, M. Megrelishvili) F ISBN: 9781461464068 Series: e-books Series: SpringerLink (Online service) Series: Fields Institute Communications, 1069-5265 : v68 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topological Groups , Functional analysis , Operator theory , Discrete groups , Distribution (Probability theory) Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461458883:ONLINE Show nearby items on shelf Title: Drinfeld Moduli Schemes and Automorphic Forms [electronic resource] : The Theory of Elliptic Modules with Applications Author(s): Yuval Z Flicker Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the authors original work establishing the correspondence between ell-adic rank r Galois representations andautomorphic representations of GL( r) over a function field, in the local case, and,in the global case, under a restriction at a single place. It develops Drinfelds theory of elliptic modules, their moduli schemes and coveringschemes, the simple trace formula, the fixed point formula, as w ell as the congruence relations and a simpleconverse theorem, not yet published anywhere. This version, based on a recent course taught by the author at TheOhioState University, is updated with references to research that has extended and developed the or iginal work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as avaluable resource to facilitate anentrance to this fascinating area of mathematics Note: Springer eBooks Contents: Elliptic Moduli Hecke Correspondences Trace Formulae Higher Recipropcity Laws. ISBN: 9781461458883 Series: e-books Series: SpringerLink (Online service) Series: SpringerBriefs in Mathematics, 2191-8198 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Topological Groups , Number theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461453925:ONLINE Show nearby items on shelf Title: Interpolation and Sidon Sets for Compact Groups [electronic resource] Author(s): Colin C Graham Kathryn E Hare Date: 2013 Publisher: Boston, MA : Springer US : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Understanding special sets of integers was classically of interest to Hadamard, Zygmund and others, and continues to be of interest today. This book is a modern treatment of the subject of interpolation and Sidon sets. It is aunique book, aimed at bo th new and experienced researchers. In particular, this is the only book in Englishwhich featuresa complete treatment of the Pisier-Bourgain results on Sidon sets, many of which were originally in French, inhard to access publications. Applications of the P-B results, due to Pisier, Bourgain, Ramsey, and the authors are included.The book introduces the reader to a wealth of methods important in mathematics today: topological,probabilistic, algebraic, combinatoric and analytic. It prepares students to perf orm research in the area and provides both exercises and open problems. The book also provides direction to the literature for topics it does not fullycover. The book is self-contained, with appendices covering results that are required, but not necessari ly in the pre-requisite background of a student ready to choose an area for research in harmonic analysis Note: Springer eBooks Contents: Preface Introduction Hadamard Sets $\epsilon$ Kronecker sets Sidon sets: Introduction and decomposition properties Characterizations of $I_0$ sets Proportional characterizations of Sidon sets Decompositions of $I_0$ sets Sizes of thin sets Sets of zero discrete harmonic density Related results Open problems Appendices (Groups, Probability, Combinatoric results,...) Bibliography Author index Subject index Index of notation ISBN: 9781461453925 Series: e-books Series: SpringerLink (Online service) Series: CMS Books in Mathematics, Ouvrages de mathmatiques de la SMC, 1613-5237 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Harmonic analysis , Fourier analysis , Functional analysis Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781461450580:ONLINE Show nearby items on shelf Title: Uniform Spaces and Measures [electronic resource] Author(s): Jan Pachl Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Uniform Spaces and Measures addresses the need for an accessible and comprehensive exposition of the theory of uniform measures -- a need that became more critical when uniform measures recently reemerged in new results inabstract harmonic analysis. Until now, results about uniform measures have been scattered throughout many papers written by a number of authors, some unpublished, using a variety of definitions and notations. Uniform measures arefunctionals on the space of bounded uniformly continuo us functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in topological measure theory, probabilitytheory, and abstract harmonic analysis. They offer a natural framework for resu lts about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. Thisbook can serve as a reference for the theory of uniform measures. It includes a self-contained develop ment of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It also includes severalnew results, and presents diverse results from many sources organized in a logical whole. The content is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis, and containsa number of exercises with hints to solutions as well as several open problems with suggestions for further research Note: Springer eBooks Contents: Prerequisites 1. Uniformities and Topologies 2. Induced Uniform Structures 3. Uniform Structures on Semigroups 4. Some Notable Classes of Uniform Spaces 5. Measures on Complete Metric Spaces 6. Uniform Measures 7. Uniform Measures as Measures 8. Instances of Uniform Measures 9. Direct Product and Convolution 10. Free Uniform Measures 11. Approximation of Probability Distributions 12. Measurable Functionals Hints to Excercises References Notation Index Author Index Subject Index ISBN: 9781461450580 Series: e-books Series: SpringerLink (Online service) Series: Fields Institute Monographs, 1069-5273 : v30 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Fourier analysis , Functional analysis , Functions of complex variables Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9781441979100:ONLINE Show nearby items on shelf Title: A Course in Topological Combinatorics [electronic resource] Author(s): Mark Longueville Date: 2013 Publisher: New York, NY : Springer New York : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: A Course in Topological Combinatorics is the first undergraduate textbook on the field of topological combinatorics, a subject that has become an active and innovative research area in mathematics over the last thirty years withgrowing applications i n math, computer science, and other applied areas. Topological combinatorics is concerned with solutions to combinatorial problems by applying topological tools. In most cases these solutions are very elegant andthe connection between combinatorics and to pology often arises as an unexpected surprise. The textbook covers topics such as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discretegeometry. The text contains a large number of figures that suppo rt the understanding of concepts and proofs. In many cases several alternative proofs for the same result are given, and each chapter ends with a series of exercises. Theextensive appendix makes the book completely self-contained. The textbook is well sui ted for advanced undergraduate or beginning graduate mathematics students. Previous knowledge in topology or graph theory is helpful but notnecessary. The text may be used as a basis for a one- or two-semester course as well as a supplementary text for a topology or combinatorics class Note: Springer eBooks Contents: Preface List of Symbols and Typical Notation 1 Fair Division Problems 2 Graph Coloring Problems 3 Evasiveness of Graph Properties 4 Embedding and Mapping Problems A Basic Concepts from Graph Theory B Crash Course in Topology C Partially Ordered Sets, Order Complexes, and Their Topology D Groups and Group Actions E Some Results and Applications from Smith Theory References Index ISBN: 9781441979100 Series: e-books Series: SpringerLink (Online service) Series: Universitext, 0172-5939 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Combinatorics , Discrete groups Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9780817683856:ONLINE Show nearby items on shelf Title: New Foundations in Mathematics [electronic resource] : The Geometric Concept of Number Author(s): Garret Sobczyk Date: 2013 Publisher: Boston : Birkhuser Boston : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple androbust means of expressi ng a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematicsand physics. Much of the material presented h as been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modernabstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. The book begins with a discussion of modular numbers (clock arithmetic) and modularpolynomials. This leads to the idea of a spectral basis, the complex and hyperbolic numbers, and finally to geometric algebra, which lays the groundwork for the remainder of the text. Many topics are presented in a new light,including: * vector spaces and matrices * structure of linear operators and quadratic forms * Hermitian inner product spaces * geometry of moving planes * spacetime of special relativity * classical integration theorems *differential geometry of curves and smooth surfaces * projective geometry * Lie groups and Lie algebras. Exercises with selected solutions are provided, and cha pter summaries are included to reinforce concepts as they are covered.Links to relevant websites are often given, and supplementary material is available on the authors website. New Foundations in Mathematics will be of interest to undergraduate and grad uate students of mathematics and physics whoare looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a s Note: Springer eBooks Contents: 1 Modular Number Systems 2 Complex and Hyperbolic Numbers 3 Geometric Algebra 4 Vector Spaces and Matrices 5 Outer Product and Determinants 6 Systems of Linear Equations 7 Linear Transformations on R^n 8 Structure of a Linear Operator 9 Linear and Bilinear Forms 10 Hermitian Inner Product Spaces 11 Geometry of Moving Planes 12 Representations of the Symmetric Group 13 Calculus on m Surfaces 14 Differential Geometry of Curves 15 Differential Geometry of k Surfaces 16 Mappings Between Surfaces 17 Non Euclidean and Projective Geometries 18 Lie Gr ISBN: 9780817683856 Series: e-books Series: SpringerLink (Online service) Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Group theory , Matrix theory , Topological Groups , Mathematical physics , Engineering mathematics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2013-9780817683641:ONLINE Show nearby items on shelf Title: Configurations from a Graphical Viewpoint [electronic resource] Author(s): Toma Pisanski Brigitte Servatius Date: 2013 Publisher: Boston : Birkhuser Boston : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. Inthis self-contained tex tbook, algebraic graph theory is used to introduce groups topological graph theory is used to explore surfaces and geometric graph theory is implemented to analyze incidence geometries. After a preview ofconfigurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied.Geometric aspects, some historical remarks, references, and applicationsof classicalconfigurationsappear in the last chapter. With over two hundred illustrations, challenging exercises at t he end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint iswell suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicia ns and researchers Note: Springer eBooks Contents: Preface Introduction Graphs Groups, Actions, and Symmetry Maps Combinatorial Configurations Geometric Configurations Index Bibliography ISBN: 9780817683641 Series: e-books Series: SpringerLink (Online service) Series: Birkhuser Advanced Texts Basler Lehrbcher Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Geometry, algebraic , Combinatorics , Geometry , Topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9783642227172:ONLINE Show nearby items on shelf Title: The Schrdinger-Virasoro Algebra [electronic resource] Mathematical structure and dynamical Schrdinger symmetries Author(s): Jrmie Unterberger Claude Roger Date: 2012 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structurethe Schrdinger-Virasoro algebra. Just as Poincar invariance or conformal (Virasoro) invarianceplay a key role in understanding , respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study ofsome models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Liealgebra touches upon topics as various as statistical physics, vertex algebras, Po isson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and thespectral theory of Schrdinger operators. Note: Springer eBooks Contents: Introduction Geometric Definitions of SV Basic Algebraic and Geometric Features Coadjoint Representaion Induced Representations and Verma Modules Coinduced Representations Vertex Representations Cohomology, Extensions and Deformations Action of sv on Schrdinger and Dirac Operators Monodromy of Schrdinger Operators Poisson Structures and Schrdinger Operators Supersymmetric Extensions of sv Appendix to chapter 6 Appendix to chapter 11 Index ISBN: 9783642227172 Series: e-books Series: SpringerLink (Online service) Series: Theoretical and Mathematical Physics, 1864-5879 Series: Physics and Astronomy (Springer-11651) Keywords: Algebra , Topological Groups , Mathematical physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9783642227165:ONLINE Show nearby items on shelf Title: The Schringer-Virasoro Algebra [electronic resource] Author(s): Jie Unterberger Claude Roger Date: 2012 Publisher: Springer Berlin Heidelberg Size: 1 online resource Note: Monograph Note: Springer 2012 Physics and Astronomy eBook collection Note: Springer e-book platform ISBN: 9783642227165 Series: Texts and Monographs in Physics Series: e-books Keywords: Mathematical Methods in Physics , Topological Groups, Lie Groups , Mathematical Physics , Category Theory, Homological Algebra , Statistical Physics, Dynamical Systems and Complexity Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9783642225970:ONLINE Show nearby items on shelf Title: Topics in Noncommutative Algebra [electronic resource] : The Theorem of Campbell, Baker, Hausdorff and Dynkin Author(s): Andrea Bonfiglioli Roberta Fulci Date: 2012 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, NumericalAnalysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: 1) fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra ornot) to understand and apply the statements and numero us corollaries of the main result 2) provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view andnotation 3) provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincar, Pascal, Campbell, Baker, Hausdorff and Dynkin 4) give an outlook on theapplications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) 5 ) quickly enable the reader, through a description of the state-of-art and open problems, to understand the modernliterature concerning a theorem which, though having its roots in the beginning of the20th century, has not ceased to provide new problems an d applications. The book assumes some undergraduate-level knowledge of algebra and analysis,but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool fo r beginners in Algebra Note: Springer eBooks Contents: 1 Historical Overview Part I Algebraic Proofs of the CBHD Theorem 2 Background Algebra 3 The Main Proof of the CBHD Theorem 4 Some Short Proofs of the CBHD Theorem 5 Convergence and Associativity for the CBHD Theorem 6 CBHD, PBW and the Free Lie Algebras Part II Proofs of the Algebraic Prerequisites 7 Proofs of the Algebraic Prerequisites 8 Construction of Free Lie Algebras 9 Formal Power Series in One Indeterminate 10 Symmetric Algebra ISBN: 9783642225970 Series: e-books Series: SpringerLink (Online service) Series: Lecture Notes in Mathematics, 0075-8434 : v2034 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Topological Groups , Global differential geometry Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9783034801546:ONLINE Show nearby items on shelf Title: Frames and Locales [electronic resource] : Topology without points Author(s): Jorge Picado Ale Pultr Date: 2012 Publisher: Basel : Springer Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Until the mid-twentieth century, topological studies were focused on the theory of suitable structures on sets of points. The concept of open set exploited since the 1920s offered an expression of the geometric intuition of arealistic place (spot, gr ain) of non-trivial extent. Imitating the behaviour of open sets and their relationsled to a new approach to topology flourishing since the end of the 1950s. It has proved to be beneficial in manyrespects. Neglecting points, only little information was lo st, while deeper insights have been gained moreover, many results previously dependent onchoice principles became constructive. The result is often a smoother, rather than amore entangled, theory. No monograph of this nature has appeared since Johnstone's celebrated Stone Spaces in 1983. The present book is intended as a bridge from that time to the present. Most of the material appears here in book formfor the first time or is presented from new points of view. Two appendices provide an introduction to s ome requisite concepts from order and category theories Note: Springer eBooks Contents: Preface Introduction I. Spaces and lattices of open sets II. Frames and locales. Spectra III. Sublocales IV. Structure of localic morphisms. The categories Loc and Frm V. Separation axioms VI. More on sublocales VII. Compactness and local compactness VIII. (Symmetric) uniformity and nearness IX. Paracompactness X. More about completion XI. Metric frames XII. Entourages, non symmetric uniformity XIII. Connectedness XIV. The frame of reals and real functions XV. Localic groups Appendix I: Posets Appendix II: Categories Bibliography Index ISBN: 9783034801546 Series: e-books Series: SpringerLink (Online service) Series: Frontiers in Mathematics, 1660-8046 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9781447122944:ONLINE Show nearby items on shelf Title: Syzygies and Homotopy Theory [electronic resource] Author(s): F.E.A Johnson Date: 2012 Publisher: London : Springer London Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivialfundamental groups is much more problematic and far less well understood. Syzygies and Homotopy Theory explores the problem of nonsimply connected homotopy in the first nontrivial cases and presents, for the first time, a systematicrehabilitation of Hilbert's method of syzygies in the context of non-simply connected homotopy theory. The first part of the book is theoretical, formulated to allow a general finitely presented group as a fundamental group. Theinnovation here is to regard syzygies as stable modules rather than minimal modules. Inevitably this forces a reconsideration of the problems of noncancellation these are confronted in the second, practical, part of the book. Inparticular, the second part of the book considers how the theory works out in detail for the specific e xamples Fn F where Fn is a free group of rank n and F is finite. Another innovation is to parametrize the first syzygy in terms ofthe more familiar class of stably free modules. Furthermore, detailed description of these stably free modules is effected by a suitable modification of the method of Milnor squares. The theory developed within this book has potentialapplications in various branches of algebra, including homological algebra, ring theory and K-theory. Syzygies and Homotopy Theory will be of inte rest to researchers and also to graduate students with a background in algebra andalgebraic topology Note: Springer eBooks Contents: Preliminaries The restricted linear group The calculus of corners and squares Extensions of modules The derived module category Finiteness conditions The Swan mapping Classification of algebraic complexes Rings with stably free cancellation Group rings of cyclic groups Group rings of dihedral groups Group rings of quaternionic groups Parametrizing W1 (Z) : generic case Parametrizing W1 (Z) : singular case Generalized Swan modules Parametrizing W1 (Z) : G = C F Conclusion ISBN: 9781447122944 Series: e-books Series: SpringerLink (Online service) Series: Algebra and Applications, 1572-5553 : v17 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Group theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE
Call number: SPRINGER-2012-9780817683436:ONLINE Show nearby items on shelf Title: Singularities of Differentiable Maps, Volume 2 [electronic resource] : Monodromy and Asymptotics of Integrals Author(s): V.I Arnold S.M Gusein-Zade A.N Varchenko Date: 2012 Publisher: Boston : Birkhuser Boston : Imprint: Birkhuser Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Originally published inthe 1980s, Singularities of DifferentiableMaps: Monodromy and Asymptotics of Integrals was thesecond oftwovolumes that togetherformed a translation of the authors'influential Russian monographon singularity theory.This uncorrec ted softcover reprint of the work brings its still-relevant content back into the literature, making it availableand affordableto a global audience of researchers and practitioners. Whilethe first volume of this title, subtitled Classification of Critical Points, Caustics and Wave Fronts, contained the zoology of differentiable mapsthat is, was devoted to a description of what, where, and how singularities could beencounteredthis second volume concentrates on elements of theanatomy and physiology of singu larities of differentiable functions. The questions considered here are about the structure of singularities and how they function. Inthe first part the authors consider the topological structure of isolated critical points of holomorphic functions: vanis hing cycles distinguished bases intersection matricesmonodromy groupsthe variation operatorand theirinterconnections and method of calculation. The second part is devoted to the study of the asymptotic behavior of integrals of the method of stationary pha se, which is widely met within applications. The third and last part dealswith integrals evaluated over level manifolds in a neighborhood of the critical point of a holomorphic function. Thismonograph is suitablefor mathematicians, researchers, postgradua tes, and specialists in the areas ofmechanics, physics, technology, and other sciences dealing with the theory of singularities of differentiable maps Note: Springer eBooks Contents: Part I. The topological structure of isolated critical points of functions Introduction Elements of the theory of Picard Lefschetz The topology of the non singular level set and the variation operator of a singularity The bifurcation sets and the monodromy group of a singularity The intersection matrices of singularities of functions of two variables The intersection forms of boundary singularities and the topology of complete intersections Part II. Oscillatory integrals Discussion of results Elementary integrals and the resolution of singularities of the phase As ISBN: 9780817683436 Series: e-books Series: SpringerLink (Online service) Series: Modern Birkhuser Classics Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Geometry, algebraic , Topological Groups , Global analysis (Mathematics) , Global differential geometry , Cell aggregation Mathematics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE | 2019-04-25T00:10:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38380005955696106, "perplexity": 3787.97944286764}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578675477.84/warc/CC-MAIN-20190424234327-20190425020327-00181.warc.gz"} |
http://ask.sagemath.org/question/1534/how-do-i-quit-sage | # how do i quit sage?
0 I am trying to delete sage from my computer to prepare to give it away to a relative, but it says it is in use when I try to empty the garbage. How do I quit sage, and then uninstall it? I have mac osx 10.6.8 asked Jun 17 '12 This post is a wiki. Anyone with karma >150 is welcome to improve it. Anonymous
## 4 Answers:
2 I've had this problem with "ghost Python processes" before as well when trying to delete old copies of Sage. There is something weird with how Terminal finishes certain processes. Here's how I've dealt with it. Make sure you have all Sage and other Python-related processes closed. Might as well close everything you can. Open your Terminal.app program. This is located in Applications -> Utilities (if you go into Finder, you can also do Command+U). Make the Terminal window as tall as you can make it by dragging. Run the command top -o -command -O time. This will list all processes (a lot) in reverse alphabetical order by command name (the first thing) and then in order by how long they ran, if there is more than one with the same name. You'll be looking for the ones labeled python. If there are some that don't seem to be doing much and have fairly high PID values, they are probably from old Sage runs. I don't know why they don't die. Here's a sample from mine now. Quit top by pressing q. Kill the process with the command kill 47776, where you replace the number with your number. If that doesn't kill it (check with top again), then use kill -9 47776. I can't guarantee that this will be your process, but on a Mac the process ID should be something five digits, so this is quite likely it. It won't format right if I don't put it here - here is a piece of what top output looks like. Notice the ID number on the left. 05- scClient 0.0 03:54.38 3 1 65 79 332K 4340K 1268K 31M 86067 quicklookd 0.0 00:00.43 9 2 101 127 12M 14M 24M 557M 47776 python 0.0 01:59.77 1 0 19 79 1016K 244K 1632K 11M 169- prl_naptd 0.0 01:32.74 3 1 45 76 364K 8232K 2228K 30M 193- prl_disp_ser 0.1 15:21.21 12 1 5814 123 1996K 8296K 6232K 36M posted Jun 18 '12 kcrisman 7427 ● 17 ● 76 ● 166
2 I think the application Activity Monitor is the easiest way to track down rogue processes. It's in the utilities folder in the applications folder. Open that, and then take kcrisman's advice of killing python processes. Do that by selecting the process, and clicking the stop sign at the top left. You can normally just quit, but sometimes you need to force quit (which is like the kill -9 that kcrisman suggests.) posted Jun 18 '12 ooglyboogly 101 ● 1 ● 7 Hmm, that's probably even easier. I have admit I have never used it, because I don't know what it does as compared to top - but top is just something someone showed me once, I've only slowly gotten used to it.kcrisman (Jun 18 '12)
1 William's killemall shell script is another good option. answered Jun 18 '12 This post is a wiki. Anyone with karma >150 is welcome to improve it. benjaminfjones 2545 ● 4 ● 36 ● 67 http://bfj7.com/ A little too draconian for my taste, but nice.kcrisman (Jun 19 '12)
0 1) I suggest using Command-Option-Esc to see a list of what is currently running. Then, you can "Force Quit" Sage, if it is running. Dragging the sage folder to the trash should do it after that. 2) You might need to restart or just log out and log back in before emptying the trash. At times, I have had to do this with my Mac to make sure all processes are closed that might be related to what I was deleting. What you are encountering sounds more like a Mac issue than a Sage issue to me based on what you've written. (And it seems like an issue that I've seen before with other items.) answered Jun 17 '12 This post is a wiki. Anyone with karma >150 is welcome to improve it. calc314 2200 ● 7 ● 25 ● 62
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Copyright Sage, 2010. Some rights reserved under creative commons license. | 2013-12-05T04:19:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18042172491550446, "perplexity": 2255.9244874838146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163039773/warc/CC-MAIN-20131204131719-00093-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://mfix.netl.doe.gov/doc/tracker/19.1.0/userguide/process.html | # Process Images¶
After the media is opened, the individual frames are processed using a series of transforms. These transforms are applied and controlled on the Process tab. Unfortunately, which transforms to use depend heavily on the media. The basic goal is to maximize the contrast between the objects and the background. This process is very subjective, requiring trial and error.
Filters and transforms are applied sequentially in the order they are listed in. The results of individual steps can be seen by hovering over the filter or transform options.
## Histogram¶
The first widget on the processing tab shows the histograms of the pre-processed frame (light gray) and the final processed image (dark blue) of the currently displayed frame. The histogram shows the normalized counts of pixels at a certain value. A counts of pixel values of 0 (black) are on the left side and counts of pixel values of 255 (white) are on the right side.
## Decomposition Overlap¶
When using parallel processing, there needs to be an overlap between neighboring tiles just larger then the largest object being tracked. Having an overlap too small will cause tracks to be lost while having an overlap to large will cause extra processing of pixels.
Note
To see the tiles, go the the visualization tab and select the Show domain decomposition check-box.
## Rotating¶
Frames can be rotated in increments of 90° by checking the Rotate check-box and selecting the amount of rotation to apply.
## Cropping¶
Frames can be cropped by checking the Crop check-box and entering the amount of pixels to crop. The Left and Top entries are positive integers while the Right and Bottom entries are negative integers.
## Background Subtraction¶
If there are structures in the image that do not move, these can be removed by using background subtraction. Background subtraction can be enabled by selecting the Background Subtraction check-box. There are three methods available:
1. mean - builds and updates an array of frames which is used to calculate a moving mean for each pixel. This mean is then subtracted from every frame. This method is implemented using numpy.
2. MOG2 - “Improved adaptive Gaussian mixture model for background subtraction” as implemented in OpenCV
3. KNN - “K-nearest neighbors - based Background/Foreground Segmentation” as implemented in OpenCV
Note
The history of the background subtraction methods is constructed as the frames are processed, so the first frame will typically be blank since there is no history.
## Denoise¶
Noise can be removed from frames by selecting the Denoise check-box. There are three methods available:
1. Gaussian blur
2. Median blur
3. Bilateral filter
These three methods are implemented in OpenCV. See Smoothing Images for a tutorial with all three methods and more information.
## Brightness and Contrast¶
The brightness and contrast of the frames can be adjusted using a linear transformation of the pixel values by selecting the Brightness, Contrast check-box:
$g(i,j)=\alpha⋅f(i,j)+\beta$
Where $$\alpha > 0$$ and $$\beta$$ are said to control contrast and brightness respectively. $$f(i,j)$$ is the pixel value of the input and $$g(i,j)$$ is the pixel value of the output.
See Changing the contrast and brightness of an image for more information.
## Tone Curve¶
The brightness and contrast of the frames can be also be adjusted using a user controlled spline that is fit through 4 points, similar to tools found in Adobe’s Lightroom, by selecting the Adjust Tone curve check-box. This is similar to the linear transformation except that the input pixel values, $$f(i,j)$$, are transformed with a B-spline, $$h()$$, resulting in the pixel value of the output, $$g(i,j)$$:
$g(i,j)=h(f(i,j))$
Scipy’s splrep is used. This allows significant user control over increasing the contrast of the objects of interest.
## Equalize Histogram¶
The contrast of the frames can be also be adjusted by using histogram equalization by selecting the Equalize Histogram check-box. Histogram equalization tries to stretch the intensity of the pixels to use the full range of available values (0-255). In some cases where the lighting is not uniform, adaptive histogram equalization can be used by selecting the Adaptive check-box. This will use the Contrast Limited Adaptive Histogram Equalization (CLAHE) technique as implemented in OpenCV. See Histograms - 2: Histogram Equalization for more information.
## Threshold¶
A threshold can be applied to the frame by selecting the Threshold check-box. There are several types of thresholds that can be applied:
type condition
binary $$g(i,j)= 255 \text{ if } f(i,j)>thresh \text{ else } 0$$
binary inverted $$g(i,j)= 0 \text{ if } f(i,j)>thresh \text{ else } 255$$
truncated $$g(i,j)= thresh \text{ if } f(i,j)>thresh \text{ else } f(i,j)$$
to zero $$g(i,j)= f(i,j) \text{ if } f(i,j)>thresh \text{ else } 0$$
to zero inverted $$g(i,j)= 0 \text{ if } f(i,j)>thresh \text{ else } f(i,j)$$
Where $$f(i,j)$$ is the input pixel value, $$thresh$$ is the selected threshold value, and $$g(i,j)$$ is the resulting output pixel value.
## Particle Detection¶
The last step in the processing of the images is the identification of the objects. To apply a object detection filter, select the Particle Detection check-box. There are three object detection filters including Simple Blob, Label, and Hough Circles.
### Simple Blob¶
Simple blob is an efficient algorithm for finding blobs in an image. It works by finding centers of contours at several thresholds from Min Threshold to Max Threshold, groups the centers, and then filters the blobs based on area, circularity, inertia, and/or convexity. This method is the preferred method for identifying objects.
### Label¶
If either a binary or binary inverted threshold is used, then the groups of pixels can be labeled . The centers of the labels can then be determined and used. This technique does not work well when objects are touching.
### Hough Circles¶
The Hough Circle Transform tries to find circles in an image. This transform works well if the objects are nice, fairly uniform circles, however it is sensitive to the input parameters and can be expensive. It can find overlapping circles. | 2019-08-19T03:27:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3406795561313629, "perplexity": 1385.725164590327}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027314641.41/warc/CC-MAIN-20190819032136-20190819054136-00078.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/proc.2007.2007.855 | Article Contents
Article Contents
# Three state relays
• We consider a hysteresis operator that arises as a three state generalization of a bi-stable relay. Basic properties and a geometric interpretation of the three-state relay are considered. Analogously to Preisach operator, which can be introduced as an aggregation of all possible non-ideal relays, we consider a "Super-Preisach" operator, that is an aggregation of all possible three-state relays.
Mathematics Subject Classification: Primary: 34C55; Secondary: 47H99.
Citation:
Open Access Under a Creative Commons license | 2022-11-27T14:25:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.40673714876174927, "perplexity": 1655.3276151825303}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710409.16/warc/CC-MAIN-20221127141808-20221127171808-00084.warc.gz"} |
https://toontown.fandom.com/wiki/Megaphone | ## FANDOM
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Megaphone
Level 2 Toon-Up Gag
General information
Minimum Laff Heal: 15
Maximum Laff Heal: 18
Accuracy: Medium
Organic boost: 19 Laff Heal
Targets: All Toons
Minimum carry capacity: 5
Maximum carry capacity: 25
Experience points needed for next gag: 200
Lineage
Preceded by:
Feather
Succeeded by:
Lipstick
v • d • e
Megaphone is the level two Toon-Up gag. It succeeds the Feather but precedes the Lipstick.
## General
The Megaphone can be obtained after gaining twenty skill points in the Toon-Up track.
The Megaphone can heal all toons, excluding the user; the healing will be divided evenly among all toons. The minimum heal is fifteen for one toon, eight for two toons, and five for three toons. The maximum heal is eighteen for one toon, nine for two toons, and six for three toons. If the Megaphone is grown on a tree and is organic, the heal increases by one, totaling to a maximum of nineteen laff points healed.
In the event that the megaphone misses, it will still restore between "3" and "4" laff points depending on its skill points, and the laff is distributed amongst the other toons. This will result in a restoration of "3" to "4" laff points for one toon, "2" laff points for two toons, and "1" laff point for three toons.
At first, a toon can carry a minimum of five Megaphones. As the toon trains their Toon-Up track and obtains new gags, the toon will be able to carry more Megaphones. After obtaining the Juggling Balls, a maximum of twenty-five Megaphones can be carried at once.
## Skill points
Previous level Next level
20 200
Formula
In equation form: $\frac{X - Y}{(M - O)}$
• X represents the skill points for the next gag
• Y represents the starting point of this gag
• M represents the maximum laff heal
• O represents the original starting point
To determine the next increase in laff heal for a Megaphone, take the number of skill points required to obtain the next gag and divide it by the number of increase (the maximum laff heal - the original laff heal). You should therefore get an estimate.
The Megaphone equation:
$\frac{200-20}{18-14}=\frac{180}{4}=45$
For every 45 skill points, the Megaphone's healing attributes increase.
Laff heal Skill points
15 20
16 65
17 110
18 155
## Animation
1. The toon runs to the center of the cog battle.
2. A Megaphone is taken out from the toon's right pocket.
3. The toon says a joke through the Megaphone.
4. Other toons are healed by an amount of laff points depending on how funny the joke was (if it misses, it gives 2 points; if it hits when used on only one toon, it gives a maximum of 18 laff)
5. The toon runs back to the original position.
## Trading card
Gag
Does your megaphone sounds funny? Ours is downright hilarious! After a hard day of battling Cogs, did you ever wish you could cheer up your friends with a funny joke, but just can't think of one? Your troubles are over with MegO'Feeney's Mega-Funny Megaphones! Crammed full of dozens of the funniest jokes ever told in Toontown, your friends will be laffing themselves back to good health in no time!
## Jokes
What goes 'Ha Ha Ha Thud'?Someone laughing his head off. What goes TICK-TICK-TICK-WOOF?A watchdog! Why do male deer need braces?Because they have 'buck teeth'! Why is it hard for a ghost to tell a lie?Because you can see right through him. What did the ballerina do when she hurt her foot?She called the toe truck! What has one horn and gives milk?A milk truck! Why don't witches ride their brooms when they're angry?They don't want to fly off the handle! Why did the dolphin cross the ocean?To get to the other tide. What kind of mistakes do spooks make?Boo boos. Why did the chicken cross the playground?To get to the other slide! Where does a peacock go when he loses his tail?A retail store. Why didn't the skeleton cross the road?He didn't have the guts. Why wouldn't they let the butterfly into the dance?Because it was a moth ball. What's gray and squirts jam at you?A mouse eating a doughnut. What happened when 500 hares got loose on the main street?The police had to comb the area. What's the difference between a fish and a piano?You can tune a piano, but you can't tuna fish! What do people do in clock factories?They make faces all day. What do you call a blind dinosaur?An I-don't-think-he-saurus. If you drop a white hat into the Red Sea, what does it become?Wet. Why was Cinderella thrown off the basketball team?She ran away from the ball. Why was Cinderella such a bad player?She had a pumpkin for a coach. What two things can't you have for breakfast?Lunch and dinner. What do you give an elephant with big feet?Big shoes. Where do baby ghosts go during the day?Day-scare centers. What did Snow White say to the photographer?Some day my prints will come. What's Tarzan's favorite song?Jungle bells. What's green and loud?A froghorn. What's worse than raining cats and dogs?Hailing taxis. When is the vet busiest?When it's raining cats and dogs. What do you call a gorilla wearing ear-muffs?Anything you want, he can't hear you. Where would you weigh a whale?At a whale-weigh station. What travels around the world but stays in the corner?A stamp. What do you give a pig with a sore throat?Oinkment. What did the hat say to the scarf?You hang around while I go on a head. What's the best parting gift?A comb. What kind of cats like to go bowling?Alley cats. What did one eye say to the other?Between you and me, something smells. What's round, white and giggles?A tickled onion. What do you get when you cross Bambi with a ghost?Bamboo. Why do golfers take an extra pair of socks?In case they get a hole in one. What do you call a fly with no wings?A walk. Who did Frankenstein take to the prom?His ghoul friend. What lies on its back, one hundred feet in the air?A sleeping centipede. How do you keep a bull from charging?Take away his credit card. What do you call a chicken at the North Pole?Lost. What do you get if you cross a cat with a dog?An animal that chases itself. What did the digital watch say to the grandfather clock?Look dad, no hands. Where does Ariel the mermaid go to see movies?The dive-in. What do you call a mosquito with a tin suit?A bite in shining armor. What do giraffes have that no other animal has?Baby giraffes. Why did the man hit the clock?Because the clock struck first. Why did the apple go out with a fig?Because it couldn't find a date. What do you get when you cross a parrot with a monster?A creature that gets a cracker whenever it asks for one. Why didn't the monster make the football team?Because he threw like a ghoul! What do you get if you cross a Cocker Spaniel with a Poodle and a rooster?A cockapoodledoo! What goes dot-dot-dash-dash-squeak?Mouse code. Why aren't elephants allowed on beaches?They can't keep their trunks up. What is at the end of everything?The letter G. How do trains hear?Through the engineers. What does the winner of a marathon lose?His breath. Why did the pelican refuse to pay for his meal?His bill was too big. What has six eyes but cannot see?Three blind mice. What works only when it's fired?A rocket. Why wasn't there any food left after the monster party?Because everyone was a goblin! What bird can be heard at mealtimes?A swallow. What goes Oh, Oh, Oh?Santa walking backwards! What has green hair and runs through the forest?Moldy locks. Where do ghosts pick up their mail?At the ghost office. Why do dinosaurs have long necks?Because their feet smell. What do mermaids have on toast?Mermarlade. Why do elephants never forget?Because nobody ever tells them anything. What's in the middle of a jellyfish?A jellybutton. What do you call a very popular perfume?A best-smeller. Why can't you play jokes on snakes?Because you can never pull their legs. Why did the baker stop making donuts?He got sick of the hole business. Why do mummies make excellent spies?They're good at keeping things under wraps. How do you stop an elephant from going through the eye of a needle?Tie a knot in its tail. My friend thinks he's a rubber band.I told him to snap out of it. My sister thinks she's a pair of curtains.I told her to pull herself together! Did you hear about the dentist that married the manicurist?Within a month they were fighting tooth and nail. Why do hummingbirds hum?Because they don't know the words. Why did the baby turkey bolt down his food?Because he was a little gobbler. Where did the whale go when it was bankrupt?To the loan shark. How does a sick sheep feel?Baah-aahd. What's gray, weighs 10 pounds and squeaks?A mouse that needs to go on a diet. Why did the dog chase his tail?To make ends meet. Why do elephants wear running shoes?For jogging of course. Why are elephants big and gray?Because if they were small and yellow they'd be canaries. If athletes get tennis elbow what do astronauts get?Missile toe. Did you hear about the man who hated Santa?He suffered from Claustrophobia. Why did Donald sprinkle sugar on his pillow?Because he wanted to have sweet dreams. Why did Goofy take his comb to the dentist?Because it had lost all its teeth. Why did Goofy wear his shirt in the bath?Because the label said wash and wear. Why did the dirty chicken cross the road?For some fowl purpose. Why didn't the skeleton go to the party?He had no body to go with. Why did the burglar take a shower?To make a clean getaway. Why does a sheep have a woolly coat?Because he'd look silly in a plastic one. Why do potatoes argue all the time?They can't see eye to eye. Why did Pluto sleep with a banana peel?So he could slip out of bed in the morning. Why did the mouse wear brown sneakers?His white ones were in the wash. Why are false teeth like stars?They come out at night. Why are Saturday and Sunday so strong?Because the others are weekdays. Why did the archaeologist go bankrupt?Because his career was in ruins. What do you get if you cross the Atlantic on the Titanic?Very wet. What do you get if you cross a chicken with cement?A brick-layer. What do you get if you cross a dog with a phone?A golden receiver. What do you get if you cross an elephant with a shark?Swimming trunks with sharp teeth. What did the tablecloth say to the table?Don't move, I've got you covered. Did you hear about the time Goofy ate a candle?He wanted a light snack. What did the balloon say to the pin?Hi Buster. What did the big chimney say to the little chimney?You're too young to smoke. What did the carpet say to the floor?I got you covered. What did the necklace say to the hat?You go ahead, I'll hang around. What goes zzub-zzub?A bee flying backward. How do you communicate with a fish?Drop him a line. What do you call a dinosaur that's never late?A prontosaurus. What do you get if you cross a bear and a skunk?Winnie-the-phew. How do you clean a tuba?With a tuba toothpaste. What do frogs like to sit on?Toadstools. Why was the math book unhappy?It had too many problems. Why was the school clock punished?It tocked too much. What's a polygon?A dead parrot. What needs a bath and keeps crossing the street?A dirty double crosser. What do you get if you cross a camera with a crocodile?A snap shot. What do you get if you cross an elephant with a canary?A very messy cage. What do you get if you cross a jeweler with a plumber?A ring around the bathtub. What do you get if you cross an elephant with a crow?Lots of broken telephone poles. What do you get if you cross a plum with a tiger?A purple people eater. What's the best way to save water?Dilute it. What's a lazy shoe called?A loafer. What's green, noisy and dangerous?A thundering herd of cucumbers. What color is a shout?Yellow! What do you call a sick duck?A mallardy. What's worse then a giraffe with a sore throat?A centipede with athlete's foot. What goes ABC...slurp...DEF...slurp?Someone eating alphabet soup. What's green and jumps up and down?Lettuce at a dance. What's a cow after she gives birth?De-calf-inated. What do you get if you cross a cow and a camel?Lumpy milk shakes. What's white with black and red spots?A Dalmatian with measles. What's brown has four legs and a trunk?A mouse coming back from vacation. What does a skunk do when it's angry?It raises a stink. What's gray, weighs 200 pounds and says, Here Kitty, kitty?A 200 pound mouse. What's the best way to catch a squirrel?Climb a tree and act like a nut. What's the best way to catch a rabbit?Hide in a bush and make a noise like lettuce. What do you call a spider that just got married?A newly web. What do you call a duck that robs banks?A safe quacker. What's furry, meows and chases mice underwater?A catfish. What's a funny egg called?A practical yolker. What's green on the outside and yellow inside?A banana disguised as a cucumber. What did the elephant say to the lemon?Let's play squash. What weighs 4 tons, has a trunk and is bright red?An embarrassed elephant. What's gray, weighs 4 tons, and wears glass slippers?Cinderelephant. What's an elephant in a fridge called?A very tight squeeze. What did the elephant say to her naughty child?Tusk! Tusk! What did the peanut say to the elephant?Nothing -- Peanuts can't talk. What do elephants say when they bump into each other?Small world, isn't it? What did the cashier say to the register?I'm counting on you. What did the flea say to the other flea?Shall we walk or take the cat? What did the big hand say to the little hand?Got a minute. What does the sea say to the sand?Not much. It usually waves. What did the stocking say to the shoe?See you later, I gotta run. What did one tonsil say to the other tonsil?It must be spring, here comes a swallow. What did the soil say to the rain?Stop, or my name is mud. What did the puddle say to the rain?Drop in sometime. What did the bee say to the rose?Hi, bud. What did the appendix say to the kidney?The doctor's taking me out tonight. What did the window say to the venetian blinds?If it wasn't for you it'd be curtains for me. What did the doctor say to the sick orange?Are you peeling well? What do you get if you cross a chicken with a banjo?A self-plucking chicken. What do you get if you cross a hyena with a bouillon cube?An animal that makes a laughing stock of itself. What do you get if you cross a rabbit with a spider?A hare net. What do you get if you cross a germ with a comedian?Sick jokes. What do you get if you cross a hyena with a mynah bird?An animal that laughs at its own jokes. What do you get if you cross a railway engine with a stick of gum?A chew-chew train. What would you get if you crossed an elephant with a computer?A big know-it-all. What would you get if you crossed an elephant with a skunk?A big stinker. Why did Mickey Mouse take a trip to outer space?He wanted to find Pluto. What's wrong if you keep seeing talking animals?You're having Disney spells.
## Trivia
• This is the only gag where the toon speaks.
• On the trading card, the Megaphone icon looks similar to the Foghorn.
• Apparently, the Megaphone is just for aesthetic purposes, because when the toon is talking through it, the noise level does not rise.
• Other Disney characters are mentioned in the jokes.
• The Megaphone is also used in all Sound Gags and is used in conjunction with annoying, loud things (horns, whistles, etc.) with a Megaphone to deafen cogs.
• There is a spelling error in one of the Megaphone jokes: "What's worse then a giraffe with a sore throat?"
• There is also a spelling mistake in the trading card description: "Does your megaphone sounds funny?"
## In other languages
Language Name
French Mégaphone
Spanish ???
German Megafon
Brazilian Portuguese Megafone
Japanese ???
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https://www.federalreserve.gov/econres/notes/feds-notes/why-have-initial-unemployment-claims-stayed-so-high-for-so-long-20120702.html | July 02, 2021
### Why Have Initial Unemployment Claims Stayed So High for So Long?
Brendan M. Price
#### Introduction
As the labor market recovers from the COVID-19 pandemic, claims for unemployment insurance (UI) have been surprisingly slow to return to conventional levels. As recently as 2021Q1, initial claims for regular UI benefits averaged nearly 800,000 per week (see Figure 1)—more than twice as many as were observed at a comparable point during the recovery from the Great Recession.1 Although initial claims fell substantially this spring, the latest readings are still almost double those observed in the lead-up to the pandemic.2 Throughout the recovery, the UI numbers have been consistently hard to square with the degree of improvement evident in other labor market indicators, such as the unemployment rate, job postings, and layoffs.
##### Figure 1. Weekly initial claims for regular state UI and PUA benefits (in thousands)
Why have initial UI claims remained so high for so long? In this note, I argue that much of the answer lies with the expansions to UI eligibility and generosity implemented in response to the pandemic. I focus primarily on the role of Pandemic Unemployment Assistance (PUA), a federal program that extends income support to self-employed workers and others who are ineligible for traditional UI benefits. Although such individuals would normally have little reason to apply for regular UI, many states have required them to do so as a first step towards obtaining PUA. Using data on UI eligibility currently available through the first quarter of 2021, I estimate that initial claims for regular UI benefits would have been 20 percent lower from 2020Q3 through 2021Q1 if not for increased filing prompted by PUA.
Other changes in UI policy have also kept claims abnormally elevated deep into the recovery. Supplemental benefits of $300 per week (formerly$600) have given unemployed and underemployed workers unusually strong incentives to apply for UI. In addition, almost every state waived its usual job search requirements early in the pandemic. These waivers, most of which were still in effect earlier this year, have made UI benefits available to many individuals for whom caregiving responsibilities or fears of infection have complicated returning to work.
Accounting for last year's UI expansions can thus go a long way towards explaining why initial claims have taken so long to return to familiar levels. By the same token, declining claim volumes in spring 2021 may owe partly to a new round of policy changes, as most states have by now reinstated pre-pandemic search requirements and many are withdrawing from the federal UI programs prior to their nationwide expiration. Initial claims are likely to fall further as the pandemic UI programs phase out and as the labor market continues to heal.
#### The role of the PUA program
Eligibility for regular UI benefits is limited to workers who have accrued sufficient earnings in UI-covered jobs in a base period leading up to their claim.3 Three groups of workers commonly fall short of this requirement: self-employed workers and independent contractors, who do not pay into the UI system; recent labor market entrants, who have not yet established an earnings history; and wage workers whose earnings fall below the required threshold, either because they work part-time at low wages or because they were jobless for much of the base period.
These groups are strikingly overrepresented among claims filed during the pandemic. Figure 2 plots the share of new claims passing the earnings test, as reported in the Department of Labor's quarterly data on UI monetary determinations.4 Prior to the pandemic, this share ranged between 75 and 90 percent, with a modest decline after each recession.5 During the pandemic, however, the passage rate fell much more precipitously than in the past: just over 50 percent of new claims satisfied the earnings test in the latter half of 2020, with only a slight rebound in 2021Q1. These unusually low eligibility rates signify an unprecedented influx of applicants with limited earnings in UI-covered jobs.6
##### Figure 2. Percentage of new claims passing the earnings test for UI eligibility
This dramatic shift in the UI claimant pool owes largely to the federal PUA program, which was created in March 2020 to provide benefits to classes of workers not covered by traditional UI.7 Because federal guidelines restrict PUA to those who are ineligible for regular UI, many states instruct benefit-seekers that they must apply (and be denied) for regular UI before they can apply for PUA. As a result, many self-employed workers and other atypical claimants have been counted towards both regular UI and PUA in successive weeks, even though initial claims for these two programs are tallied separately in government statistics.
As evidence that PUA has fueled the surge in ineligible claimants, Figure 3 plots the share of new claimants passing the earnings test in three groups of states and territories: those that require claimants to apply for regular UI as a precondition for seeking PUA (27 programs); those that allow individuals to apply directly for PUA (16 programs); and those whose websites provide nuanced or ambiguous instructions (10 programs).8 Although passage rates have fallen nationwide, they have fallen much more steeply in states that instruct prospective PUA claimants to first apply for regular UI. These state-level patterns suggest that we would have seen a much more muted decline in eligibility rates nationwide if not for PUA.9
##### Figure 3. Percentage of new claims passing the earnings test, split by state application protocols
A simple back-of-the-envelope calculation can help us gauge what initial claim volumes might have looked like had the PUA program not been created. The first step is to note that initial claims fall into two separate categories, which differ in their relationship to PUA. New initial claims are filed by workers who have not received UI in the recent past. Reopened initial claims are filed by workers who were previously approved for benefits and who are now resuming benefit receipt after an intervening period of employment.10 I estimate counterfactual initial claims in the absence of PUA as
$$\text{reopened initial claims} + \left(\frac{\text{observed passage rate}}{\text{passage rate absent PUA}}\right) \times \text{new inital claims},$$
where I assume that 75 percent of new initial claims would have passed the earnings test in the absence of PUA, in line with the passage rate observed after the Great Recession.
The logic behind this formula is as follows. By definition, reopened claims originate from workers who have already passed the earnings test—in other words, standard claimants who would most likely be seeking benefits even in the absence of PUA. I therefore make no adjustment to the observed number of reopened claims. By contrast, new initial claims reflect a combination of standard and non-standard claimants. To weed out claims filed by non-standard claimants as a stepping-stone to PUA, I scale down the observed number of new claims based on the unusually low share of claimants passing the earnings test.11
Applying this formula quarter by quarter, I estimate that—if not for PUA—initial claims for regular UI benefits would have been about 7 percent lower in 2020Q2, when PUA was first being rolled out, and about 20 percent lower in each of 2020Q3, 2020Q4, and 2021Q1.
Even with this adjustment, initial claims would still have averaged over 600,000 per week in the first quarter of 2021. Such a tally would be comparable to the weekly counts reported in early 2009, even though monthly worker flows from employment into unemployment were about 50 percent higher in 2009 than they were in 2021Q1. Although PUA is a major reason why claims have been so slow to return to typical levels, it is clearly far from the only reason.
A second factor that has boosted initial claims is Federal Pandemic Unemployment Compensation (FPUC), which has provided supplemental benefits of $300 or$600 per week at various points during the pandemic.12 Take-up of UI benefits among eligible individuals is usually far from universal: qualifying workers may decline to file for UI because of a lack of information, stigma associated with benefit receipt, or an expectation that they will quickly be reemployed. FPUC has given unemployed and underemployed workers unusually strong incentives to claim UI, and there is good reason to believe that take-up rates have risen as a result.13 Although take-up rates are difficult to measure in available data, some indirect evidence comes from the unusually high share of 2020–21 UI claimants receiving partial UI benefits while working part-time. Partial UI recipients receive the $300/600 FPUC supplement in full, so FPUC has an especially large proportional impact on UI replacement rates for this group of workers.14 Alongside PUA, FPUC, and other federal programs created during the pandemic,15 many states broadened access to their UI programs at the start of the crisis by suspending waiting periods and by waiving their normal job search requirements. These state-level waivers may have drawn more applicants into the UI system, since individuals unable or unwilling to work—for example, because of childcare constraints associated with virtual schooling—might choose not to apply if they would be required to look for jobs. In addition, UI statistics were heavily impacted in the first months of the crisis by backlogged claims, fraudulent filings, and other irregularities (Cajner et al., 2020; Government Accountability Office, 2020). Although these issues are likely much less consequential than they were early on, they may still be having an appreciable impact on claim volumes in some states. These institutional factors should largely abate over the course of 2021. PUA, FPUC, and other federal programs are scheduled to expire in September, and many states have chosen to withdraw from them prior to their nationwide expiration.16 Most states have also reinstated their pre-pandemic job search requirements, and state and federal authorities have worked hard to resolve backlogs and to deter fraud. As the institutional landscape returns to pre-pandemic norms, policy measures unique to the pandemic should have a diminishing impact on reported claims. #### The state of the labor market A final consideration is that labor market conditions over the past year have likely been somewhat weaker than measured unemployment suggests. The official unemployment rate—which is calculated from household responses to the Current Population Survey (CPS)—excludes or undercounts at least four groups of individuals who may be filing UI claims. First, the Bureau of Labor Statistics has cautioned that some unemployed CPS respondents have been misclassified as employed but absent from work. Second, survey response rates have fallen during the pandemic, especially for groups that tend to have higher unemployment rates. The sampling weights used to estimate aggregate unemployment may not fully account for these missing respondents. Third, millions of workers have exited the labor force because of caregiving needs, fears of the virus, or a lack of suitable job opportunities. And lastly, the number of individuals working part-time for economic reasons is still well above pre-pandemic levels.17 In sum, while much of the recent disconnect between initial UI claims and other labor market indicators can be attributed to changes in UI policy in response to the pandemic, some of it may reflect forms of labor market weakness that other data sources do not adequately capture. As long as initial claims remain far above pre-pandemic levels, they will serve as a weekly reminder that the labor market recovery remains uneven and that much ground is still left to be regained. I close with a cautionary note about how to interpret these findings. Although last year's UI expansions amplified claim volumes given contemporaneous labor market conditions, they have also influenced those conditions in turn. The pandemic UI programs have provided critical income support to millions of American households, but their net effect on the labor market has been hotly debated: supporters of these programs argue that they have spurred the recovery by buttressing aggregate demand, whereas critics maintain that they have impeded the recovery by disincentivizing job search. My analysis is silent on the question of how the labor market would have fared had UI policy not responded to the pandemic. #### References • Cajner, Tomaz, Andrew Figura, Brendan M. Price, David Ratner, and Alison Weingarden. 2020. "Reconciling Unemployment Claims with Job Losses in the First Months of the COVID-19 Crisis." Finance and Economics Discussion Series Working Paper No. 2020-055. • Dube, Arindrajit. 2021. "Aggregate Employment Effects of Unemployment Benefits during Deep Downturns: Evidence from the Expiration of the Federal Pandemic Unemployment Compensation." National Bureau of Economic Research Working Paper No. 28470. • Finamor, Lucas, and Dana Scott. 2021. "Labor Market Trends and Unemployment Insurance Generosity during the Pandemic." Economics Letters, 199(2021): 109722. • Ganong, Peter, Pascal Noel, and Joseph Vavra. 2020. "US Unemployment Insurance Replacement Rates during the Pandemic." Journal of Public Economics, 191(2020), 104273. • Government Accountability Office. 2020. "Urgent Actions Needed to Better Ensure an Effective Federal Response." Report GAO-21-191. • Marinescu, Ioana, Daphne Skandalis, and Daniel Zhao. 2021. "The Impact of the Federal Pandemic Unemployment Compensation on Job Search and Vacancy Creation." National Bureau of Economic Research Working Paper No. 28567. #### Acknowledgements The views expressed here are strictly those of the author and do not necessarily represent the views of the Federal Reserve Board or its staff, nor those of the Department of Labor. I am grateful to Isabel Leigh for excellent research assistance and to Andrew Figura, Charles Fleischman, Ryan Michaels, Seth Murray, and Ivan Vidangos for helpful comments. 1. I compare 2021Q1 with 2014Q2. Using seasonally adjusted data from the Bureau of Labor Statistics, the unemployment rate averaged 6.2 percent in both quarters, and the share of workers transitioning from employment to unemployment was similar as well. Initial claims averaged about 315,000 per week in 2014Q2. Adjusting for subsequent growth in the labor force, this translates into about 330,000 claims per week in today's terms. Return to text 2. At the time of writing, the most recent Department of Labor press release reported that an average of 392,750 initial claims for regular UI benefits were filed weekly in the four weeks ending June 26, 2021. (This number is subject to revision in future releases.) By comparison, initial claims averaged about 220,000 per week in 2019. Return to text 3. Most states define the base period as the first four of the five most recent completed quarters. In addition to the earnings test, claimants must also satisfy a range of other eligibility criteria, such as having a valid reason for being unemployed, being able and available to work, and (absent a statewide waiver) engaging actively in job search. Return to text 4. At the time of analysis, state-level records were unavailable for Alabama throughout 2020 and for Alabama, Colorado, Montana, and New Jersey in 2021Q1. The passage rates plotted in Figures 2 and 3 were computed using data from all available states in each quarter. The patterns look virtually identical if I exclude these four states throughout the analysis period, so that the sample is defined consistently over time. Return to text 5. A plausible explanation for the post-recession decline in UI eligibility is that the longer and more frequent unemployment spells experienced during recessions gradually erode workers' base-period earnings. Some job losers may file claims without realizing they are ineligible, especially if they have been entitled to UI benefits in the past. Return to text 6. A similarly steep decline is evident in the ratio of the number of claims receiving first payments in each month to the number of new claims filed in that month—a proxy for the share of claims that are ultimately awarded benefits. However, because benefit payments are dated to the time of payment rather than the time of filing, this measure is potentially distorted by time lags in the adjudication of claims and the disbursal of benefits. The share of claims passing the earnings test is less susceptible to such distortions because monetary determinations are issued early in the process and because the numerator and denominator pertain to the same point in time. Return to text 7. The unusual sectoral and occupational profile of pandemic job losses may also have contributed to the record share of ineligible claimants. Since low-wage segments of the labor market have been hit hardest by the pandemic, recent job losses may be unusually concentrated among workers with insufficient base-period earnings to receive UI. Return to text 8. These 53 programs represent the 50 states, the District of Columbia, Puerto Rico, and the US Virgin Islands. I classify states based on a review of each state's UI website. In some cases, program websites explicitly indicate whether a two-stage application is required. For example, the Illinois UI website says: "You can file a claim for PUA only after you applied for regular unemployment insurance benefits and have been denied." By contrast, the Massachusetts website says that self-employed workers and others typically ineligible for UI benefits should apply directly to PUA. Other cases are less clear-cut; for example, some states recommend that PUA applicants first apply for regular UI but indicate that this is not a strict requirement. Return to text 9. Even in states where people can apply directly for PUA, some claimants who expect to ultimately receive PUA are likely to start by applying for regular UI. Advocate organizations encourage applicants to try regular UI first, even if they think they may be ineligible. Return to text 10. The date when a claim is first approved marks the beginning of a 12-month "benefit year." Reopened claims (known as "additional claims" in Department of Labor parlance) are initial claims filed within an existing benefit year, whereas new claims are those filed when no benefit year is in progress. The Department of Labor reports monthly breakdowns of initial claims into new versus additional claims in Employment and Training Administration form 5159. New claims accounted for 85 percent of initial claims in 2020Q2, but only about two-thirds of initial claims in subsequent quarters, as many workers have experienced recurrent spells of unemployment. Return to text 11. I derive the scaling factor as follows. We can express the observed number of new initial claims as the sum of three components: claimants who pass the earnings test (denoted P, for "pass"); claimants who fail the earnings test, but would have applied even in the absence of PUA (denoted SD, for "standard denied applicants"); and claimants who fail the earnings test and who would not have applied in the absence of PUA (denoted ND, for "non-standard denied applicants"). The observed passage rate is $\frac{P}{P+SD+ND}$, and the passage rate absent PUA is $\frac{P}{P+SD}$. The ratio of the observed passage rate to the counterfactual passage rate absent PUA is therefore $\frac{P+SD}{P+SD+ND}$, which equals the share of observed claimants who would have applied even in the absence of PUA. Return to text 12. From its creation in March 2020 through July 2020, FPUC provided supplemental benefits of$600 per week. From August to December 2020, FPUC was unavailable, though a short-lived program called Lost Wages Assistance provided $300 or$400 per week for part of this period. From January 2021 until its scheduled expiration in September 2021, FPUC provides \$300 per week. See Ganong, Noel, and Vavra (2020) for an analysis of UI replacement rates during the first phase of FPUC. Return to text
13. Note that the question of whether FPUC has boosted UI take-up rates is distinct from the question of whether FPUC has impeded the labor market recovery by disincentivizing claimants from returning to work. A spate of academic papers have found scant evidence that FPUC constrained employment last year (e.g., Dube [2021], Finamor and Scott [2021], and Marinescu, Skandaris, and Zhao [2021]), though its effects may differ in the tighter labor market of 2021. Regardless of how it may have affected employment, the program may have encouraged filing among unemployed and underemployed individuals who would otherwise not have applied for benefits. Return to text
14. Partial UI offers prorated benefits to workers who remain employed but experience significant declines in weekly earnings—for example, because they have lost one of two jobs, or because their weekly hours have been cut. (These partial benefits are distinct from the Short-Time Compensation or "work-sharing" program, which requires employer participation and is designed for workers experiencing more modest reductions in earnings.) The share of claimants receiving partial benefits surged above 16 percent in 2020Q4, compared with a pre-pandemic record high of about 11 percent. Furthermore, the average benefit amount among partial UI recipients (not counting the FPUC supplement) has fallen sharply during the pandemic. These patterns are consistent with increased take-up among underemployed claimants whose weekly benefits would normally be too meager to induce them to apply. Return to text
15. Other federal programs include Pandemic Emergency Unemployment Compensation (PEUC), which provides extra weeks of benefits to claimants who exhaust regular UI, and Mixed Earner Unemployment Compensation (MEUC), which covers claimants who have a combination of earned and self-employment income. The federal government has also provided full funding of Extended Benefits (EB), which are normally financed jointly with the states. PEUC and EB have accounted for large shares of UI beneficiaries in 2020–21, but neither is likely to be a major driver of initial claims, since they come into play at the end of a worker's UI spell rather than at the beginning. Return to text
16. As of mid-June, 26 states had announced plans to withdraw from FPUC in advance of its nationwide expiration (or had already done so). All but five of these states are withdrawing from PUA and PEUC, as well. See Coral Murphy Marcos (2021), "Here Are the States Eliminating Pandemic Unemployment Benefits, and When," The New York Times, June 15. Return to text
17. In addition to these factors, brief unemployment spells lasting less than four weeks can go unobserved if they fall in the space between the monthly CPS surveys. Such transient spells may be especially common in the pandemic labor market, as businesses alternately close and reopen in response to public-health conditions. Changes in the prevalence of short unemployment spells should not bias estimates of the stock of unemployed workers (the numerator in the unemployment rate), but they can distort measures of layoff activity and other labor market flows. Return to text
Price, Brendan M. (2021). "Why Have Initial Unemployment Claims Stayed So High for So Long?," FEDS Notes. Washington: Board of Governors of the Federal Reserve System July 02, 2021, https://doi.org/10.17016/2380-7172.2932.
Disclaimer: FEDS Notes are articles in which Board staff offer their own views and present analysis on a range of topics in economics and finance. These articles are shorter and less technically oriented than FEDS Working Papers and IFDP papers. | 2022-09-28T13:06:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19238919019699097, "perplexity": 4537.063013130371}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335254.72/warc/CC-MAIN-20220928113848-20220928143848-00331.warc.gz"} |
https://par.nsf.gov/biblio/10207151-unveiling-apparent-negative-capacitance-effects-resulting-from-pulse-measurements-ferroelectric-dielectric-bilayer-capacitors | Unveiling the Apparent “Negative Capacitance” Effects Resulting from Pulse Measurements of Ferroelectric-Dielectric Bilayer Capacitors
Apparent ‘Negative Capacitance’ (NC) effects have been observed in some ferroelectric-dielectric (FE-DE) bilayers by pulse measurements, and the associated results have been published that claim to be direct evidence to support the quasi-static ‘negative capacitance’ (QSNC) idea. However, the ‘NC’ effects only occur when sufficiently high voltage is applied, and even exist in stand-alone FE capacitors. These results contradict the QSNC theory, as it predicts that once stabilized (requires a DE layer), the FE remains in the ‘NC’ state regardless of the applied voltage. In this letter, by the use of Nucleation-Limited-Switching (NLS) model, we present our results obtained from simulation of pulse measurements on samples that are similar to the published ones. The simulation results indicate that reverse polarization switching occurs upon the falling edge of the pulses, which leads to the apparent hysteresis-free NC effect. This work provides an alternative interpretation of the experimental results without invoking the QSNC theory.
Authors:
; ; ;
Editors:
Award ID(s):
Publication Date:
NSF-PAR ID:
10207151
Journal Name:
IEEE electron device letters
Volume:
41
Issue:
10
Page Range or eLocation-ID:
1492-95
ISSN:
1558-0563
The device concept of ferroelectric-based negative capacitance (NC) transistors offers a promising route for achieving energy-efficient logic applications that can outperform the conventional semiconductor technology, while viable operation mechanisms remain a central topic of debate. In this work, we report steep slope switching in MoS2transistors back-gated by single-layer polycrystalline PbZr0.35Ti0.65O3. The devices exhibit current switching ratios up to 8 × 106within an ultra-low gate voltage window of$$V_{{{\mathrm{g}}}} = \pm \! 0.5$$${V}_{g}=±\phantom{\rule{0ex}{0ex}}0.5$V and subthreshold swing (SS) as low as 9.7 mV decade−1at room temperature, transcending the 60 mV decade−1Boltzmann limit without involving additional dielectric layers. Theoretical modeling reveals the dominant role of the metastable polar states within domain walls in enabling the NC mode, which is corroborated by the relation between SS and domain wall density. Our findings shed light on a hysteresis-free mechanism for NC operation, providing a simple yet effective material strategy for developing low-power 2D nanoelectronics. | 2022-12-01T14:47:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3157186508178711, "perplexity": 4112.7499803403425}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710813.48/warc/CC-MAIN-20221201121601-20221201151601-00487.warc.gz"} |
https://www.usgs.gov/media/images/map-shows-lava-flows-erupted-1983-november-2002 | # Map shows lava flows erupted 1983-November, 2002
## Detailed Description
Map shows lava flows erupted during the 1983-present activity of Puu Oo and Kupaianaha (see large map). Lava from the Mother's Day flow (red flow on west side of flow field) reached the sea at West Highcastle early on July 19, at Wilipea early on July 21, and at Highcastle on August 8. From near the southwest base of Puu Oo, the Mother's Day flow passes along the west side of the flow field and into the forest, where it started a large wildfire in May that continued into late July. By June 10, the Mother's Day flow had reached the base of Paliuli, the steep slope and cliff below Pulama pali and just above the coastal flat. At the base of Paliuli, the Mother's Day flow abruptly spread laterally in a series of small budding flows to cover an area nearly 2 km wide, gradually moving seaward until the West Highcastle and Wilipea lobes finally reached the ocean and started building benches. Activity at West Highcastle ended in early August, but entry began soon thereafter at Highcastle, eventually burying tiny kipuka of the Chain of Craters Road. The Wilipea entry died away slowly and had ended by mid-August. Highcastle and neighboring Highcastle Stairs entries ended on about August 23. For a time there were no active entries. Then Wilipea was reactivated on September 3 and remains active as of November 25. West Highcastle likewise renewed its activity on September 16-17, died away during the night of September 18-19, and returned soon thereafter to continue to time of mapping. East arm of Mother's Day flow branched from Highcastle lobe in late October and sent three fingers into ocean at Highcastle on November 15, West Laeapuki on November 19, and Laeapuki on November 20. Of these, only Laeapuki (the eastern of the two entries labeled "Laeapuki" on map) was still active on November 25, but it had stopped by November 29.
## Details
Image Dimensions: 800 x 520
Date Taken:
Location Taken: US | 2020-05-30T19:36:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1771792769432068, "perplexity": 10465.417413034045}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347410284.51/warc/CC-MAIN-20200530165307-20200530195307-00410.warc.gz"} |
https://atb.nrel.gov/electricity/2021/changes_in_2021 | You are viewing an older version of the ATB. The current content for ATB electricity is 2022.
# Changes in 2021
The Electricity ATB provides a transparent set of technology cost and performance data for electric sector analysis. The update of the 2020 ATB to the 2021 ATB includes general updates to all technologies as well as technology-specific updates—both of which are described below. Use the following charts to explore the changes from 2020 to 2021.
Parameter value projections by ATB projection year
Compare the 2020 ATB and the 2021 ATB. Click "more details" above the chart to select a parameter (LCOECAPEX, fixed operation and maintenance O&M [FOM], capacity factor, and fixed charge rate [FCR]) and other filters.
## General Updates to All Technologies
• The assumptions in each of the two financial assumptions cases are modified to reflect current assessments.
• Fixed O&M costs have been updated to ensure property taxes and insurance costs are included for all technologies.
• The Base Year is updated from 2018 to 2019 using new market data or analysis where applicable.
• The dollar year is updated from 2018 to 2019 with a 1.8% inflation rate (BLS, 2020).
• Historical data are updated to include data reported through year end 2019.
• Land-Based Wind: Projections are based on bottom-up technology analysis and cost modeling plus learning rates, with innovations that increase wind turbine size, improve controls, and enhance science-based modeling.
• Offshore Wind: Projections are based on experiential learning curves derived from market data and cost reductions associated with economies of size and scale.
• Photovoltaics: Projections are based on bottom-up techno-economic analysis of effects of improved module efficiency, inverters, installation efficiencies from assembly and design, all attributable to technological innovation. Resource categorization is split into 10 resource classes by irradiance instead of by representative location.
• Concentrating Solar Power: Component and system cost estimates for Base Year reference a 2017 industry survey, and a 2018 cost analysis of recent market developments.
• Geothermal: New data are consistent with GeoVision Study.
• Hydropower: Non-powered dam data are based on new, 2020 cost analysis.
• Battery Storage: Cost data are available broken down by grid scale, commercial, and residential technologies, and are updated with bottom up cost modeling for current costs.
• Pumped-Storage Hydropower: This technology is new to the 2021 ATB.
• Base Year: Capital expenditures (CAPEX) associated with wind plants installed in the interior of the country are used to characterize CAPEX for hypothetical wind plants with average annual wind speeds that correspond with the median conditions for recently installed wind facilities based on the 2019 Cost of Wind Energy Review (Stehly et al., 2020). The operations and maintenance (O&M) cost of 43/kW-yr is estimated (Stehly et al., 2020); no variation of FOM with wind speed class is assumed. Capacity factors align with performance in Wind Speed Classes 2–7, where most installations are located. • Projections: Specific technology innovations are associated with each scenario. In the Moderate Technology Innovation Scenario (Moderate Scenario), large, segmented blades are transported by truck, enabling larger rotors. Segmentation enables higher hubs and larger turbines, and advanced controls enable higher capacity factors and lower CAPEX. In the Advanced Technology Innovation Scenario (Advanced Scenario), even larger turbines and advanced rotor configurations increase turbine capacity, on-site manufacturing further increases hub heights, and high-fidelity modeling and advanced controls are fully implemented. ### Offshore Wind • Base Year: CAPEX and O&M costs are calculated with a combination of bottom-up techno-economic cost modeling (Beiter et al., 2016) and experiential learning effects with economies of size and scale from higher turbine and plant ratings (Beiter et al., 2020). Bottom-up estimates from the 2020 ATB are brought forward one year (2018 to 2019) using the learning methodology. Capacity factors are determined using a representative power curve for a generic NREL-modeled 6-MW offshore wind turbine (Beiter et al., 2016), and they include geospatial estimates of gross capacity factors for the entire resource (Musial et al., 2016). • Projections: Instead of projecting costs with literature estimates of cost reductions induced by specific technological innovations in each future year (Valpy et al., 2017)(Hundleby et al., 2017), the 2021 ATB uses experiential learning curves derived from empirical market data (Musial et al., 2019) along with economies of size and scale to project future costs (Beiter et al., 2020). As the learning curve predicts future costs as a function of future offshore wind deployment, future costs in each of the ATB technology innovation scenarios are driven by different levels of deployment based on literature estimates. ### Photovoltaics (PV): Utility-Scale, Commercial, and Residential • Base Year: CAPEX for 2019 and 2020 are based on new bottom-up modeling and market data from (Feldman et al., 2021), which focuses on larger systems to align with market trends. The O&M costs are based on modeled pricing for a 100-MWDC, one-axis tracking system (Feldman et al., 2021). • Projections: Projections that were based on literature surveys are now based on bottom-up CAPEX benchmarks. The Moderate Scenario is based on module efficiency gains consistent with PERC (passivated emitter and rear contact) n-type mono modules, improved inverter systems, and installation efficiencies that are due to automation, preassembly, and improved design. The Advanced Scenario assumes additional innovations, such as continuation of the historical rate of module efficiency improvement, simplification of inverter design and automation of inverter manufacturing, and greater installation efficiency from preassembly, automation, and materials innovations. Estimates for energy yield gain for utility-scale and commercial PV systems are also included. ### Concentrating Solar Power (CSP) • Base Year: Estimates are based on bottom-up cost modeling from (Turchi et al., 2019) for the updates to the System Advisor Model (SAM) cost components. Future year projections are informed by the literature, NREL expertise, and technology pathway assessments for reductions in capital expenditures. • Projections: The Moderate Scenario assumes a transition to a supercritical CO2 cycle in the powerblock, advanced coatings on the receiver, improved tanks, pumps, and component configurations for the thermal storage unit, and improved heliostat installation and learning that are due to deployment in the solar field. The Advanced Scenario assumes higher temperature supercritical CO2 , higher temperature receiver, advanced storage compatible with higher temperatures, and low-cost, modular solar fields with increased efficiency. ### Geothermal • Base Year: As before, estimates are based on bottom-up cost modeling using the Geothermal Electricity Technology Evaluation Model (GETEM) and inputs from the GeoVision Business-as-Usual (BAU) scenario (DOE, 2019).The Base Year is updated to 2019 dollar year based on the consumer price index and producer price indices.
• Projections: The projection of future geothermal plant CAPEX for the Advanced Scenario is based on the Technology Improvement scenario from the GeoVision Study ((DOE, 2019) and (Augustine et al., 2019)). The Moderate Scenario is based on the Intermediate 1 Drilling Curve detailed as part of the GeoVision report to 2030, and a minimum learning rate to 2050 which is implemented in AEO2015 (EIA, 2015) as a 10% CAPEX reduction by 2035. The Conservative Technology Innovation Scenario (Conservative Scenario) retains all cost and performance assumptions equivalent to the Base Year and assumes a minimum learning rate to 2050.
### Hydropower
• Base Year: The 2021 ATB data for non-powered dams (NPD) are based on a bottom-up modeling of reference sites using site-specific data (Oladosu, G. et al., 2021), whereas the 2020 data were based on econometric cost equations with assumed capacity factor estimates (DOE, 2016); thus, NPD categories for the 2020 ATB and the 2021 ATB are not directly comparable. NSD is updated to 2019\$ dollar year based on the consumer price index.
• Projections: New cost analysis is used to update NPD data in the 2021 ATB. The analysis involved identification of 20 reference sites for U.S. NPD hydropower and detailed bottom-up design and cost simulations under baseline and near-term innovation cases. The near-term innovation case is judged to be applicable in the next 5–10 years. (Oladosu, G. et al., 2021). New stream-reach development (NSD) data in the 2021 ATB retain previous years data, which are based on projections developed for the Hydropower Vision study (DOE, 2016) using technological learning assumptions and bottom-up analysis of process and/or technology improvements to provide a range of future cost outcomes (O'Connor et al., 2015). The NSD projections use a mix of U.S. Energy Information Administration (EIA) technological learning assumptions, input from a technical team of Oak Ridge National Laboratory researchers, and the experience of expert hydropower consultants.
### Utility-Scale PV-Plus-Battery
• This technology is new to the 2021 ATB.
• Base Year: CAPEX for 2019 is based on new bottom-up modeling and market data from (Feldman et al., 2021). The chosen configuration reflects recent and proposed utility-scale PV-plus-battery projects. Capacity factors and tax credits assume 75% of the energy used to charge the battery component is derived from the coupled PV.
• Projections: PV-plus-battery projections in the 2021 ATB are driven primarily by CAPEX cost improvements, but also by improvements in energy yield, operational cost, and cost of capital (for the Market+Policies Financial Assumptions Case).
### Battery Storage
• Base Year: CAPEX for 2019 is based on new bottom-up modeling and market data from (Feldman et al., 2021).
• Projections: Battery projections in the 2021 ATB are represented for utility-scale, commercial-scale and residential-scale battery systems. Cost improvements are driven by a literature survey as described by (Cole et al., 2021). This literature survey incorporates more-rapid reductions in battery pack and cell costs while soft costs and costs related to other factors decline more slowly.
### Pumped-Storage Hydropower (PSH)
• This technology is new to the 2021 ATB. Resource characterizations including capital costs are forthcoming and will accompany the national closed-loop PSH resource assessment.
### Natural Gas and Coal
• The 2021 ATB represents the first time the U.S. Department of Energy (DOE) Office of Fossil Energy and Carbon Management directly contributed to an ATB update. One notable change is the inclusion of assumptions for property taxes and insurance (PT&I) as a component of fixed operation and maintenance costs. PT&I are not included in prior ATB cost and performance estimates matched to EIA's Annual Energy Outlook (AEO).
### Nuclear and Biopower
• Cost and performance estimates are updated to match AEO2021 (EIA, 2021).
• Information about current published costs in the literature is updated.
## References
The following references are specific to this page; for all references in this ATB, see References.
Beiter, Philipp, Walt Musial, Patrick Duffy, Aubryn Cooperman, Matt Shields, Donna Heimiller, and Mike Optis. “The Cost of Floating Offshore Wind Energy in California between 2019 and 2032.” NREL Technical Report. Golden, CO, November 2020. https://www.nrel.gov/docs/fy21osti/77384.pdf.
Feldman, David, Vignesh Ramasamy, Ran Fu, Ashwin Ramdas, Jal Desai, and Robert Margolis. “U.S. Solar Photovoltaic System and Energy Storage Cost Benchmark: Q1 2020.” National Renewable Energy Lab. (NREL), Golden, CO (United States), January 27, 2021. https://doi.org/10.2172/1764908.
Cole, Wesley, Will A. Frazier, and Chad Augustine. “Cost Projections for Utility-Scale Battery Storage: 2021 Update.” Technical Report. Golden, CO: National Renewable Energy Laboratory, 2021. https://www.nrel.gov/docs/fy21osti/79236.pdf.
Oladosu, G., George, L., and Wells, J. “2020 Cost Analysis of Hydropower Options at Non-Powered Dams.” Oak Ridge, TN: Oak Ridge National Laboratory, 2021.
EIA. “Annual Energy Outlook 2021.” Energy Information Administration, January 2021. https://www.eia.gov/outlooks/aeo/.
Stehly, Tyler, Philipp Beiter, and Patrick Duffy. “2019 Cost of Wind Energy Review.” Technical. National Renewable Energy Laboratory, December 2020. https://www.nrel.gov/docs/fy21osti/78471.pdf.
Turchi, Craig, Matthew Boyd, Devon Kesseli, Parthiv Kurup, Mark Mehos, Ty Neises, Prashant Sharan, Michael Wagner, and Timothy Wendelin. “CSP Systems Analysis: Final Project Report.” Technical Report. Golden, CO: National Renewable Energy Laboratory, May 2019. https://doi.org/10.2172/1513197.
O’Connor, Patrick W., Scott T. DeNeale, Dol Raj Chalise, Emma Centurion, and Abigail Maloof. “Hydropower Baseline Cost Modeling, Version 2.” Oak Ridge, TN: Oak Ridge National Laboratory, 2015. https://doi.org/10.2172/1244193.
Musial, Walter, Philipp Beiter, Paul Spitsen, and Jake Nunemaker. “2018 Offshore Wind Technologies Market Report.” Technical Report. Golden, CO: National Renewable Energy Laboratory, December 2019. https://doi.org/10.2172/1226783.
DOE. “GeoVision: Harnessing the Heat Beneath Our Feet.” Washington, D.C.: U.S. Department of Energy, May 2019. https://www.energy.gov/sites/prod/files/2019/06/f63/GeoVision-full-report-opt.pdf.
BLS. “CPI for All Urban Consumers (CPI-U).” U.S. Bureau of Labor Statistics, 2020. https://beta.bls.gov/dataViewer/view/timeseries/CUSR0000SA0.
Beiter, Philipp, Walter Musial, Aaron Smith, Levi Kilcher, Rick Damiani, Michael Maness, Senu Sirnivas, et al. “A Spatial-Economic Cost-Reduction Pathway Analysis for U.S. Offshore Wind Energy Development from 2015-2030.” Technical Report. Golden, CO: National Renewable Energy Laboratory, 2016. https://doi.org/10.2172/1324526.
Augustine, Chad, Jonathan Ho, and Nate Blair. “GeoVision Analysis Supporting Task Force Report: Electric Sector Potential to Penetration.” Technical Report. Golden, CO: National Renewable Energy Laboratory, 2019. https://doi.org/10.2172/1524768.
Musial, Walt, Donna Heimiller, Philipp Beiter, George Scott, and Caroline Draxl. “2016 Offshore Wind Energy Resource Assessment for the United States.” Technical Report. Golden, CO: National Renewable Energy Laboratory, September 2016. https://doi.org/10.2172/1324533.
Hundleby, Giles, Kate Freeman, Andy Logan, and Ciaran Frost. “Floating Offshore: 55 Technology Innovations That Will Have Greater Impact on Reducing the Cost of Electricity from European Floating Offshore Wind Farms.” KiC InnoEnergy, and BVG Associates, 2017. http://www.innoenergy.com/new-floating-offshore-wind-report-55-technology-innovations-that-will-impact-the-lcoe-in-floating-offshore-wind-farms/.
Valpy, Bruce, Giles Hundleby, Kate Freeman, Alun Roberts, and Andy Logan. “Future Renewable Energy Costs: Offshore Wind: 57 Technology Innovations That Will Have Greater Impact on Reducing the Cost of Electricity From European Offshore Wind Farms.” KiC InnoEnergy, and BVG Associates, 2017. https://bvgassociates.com/wp-content/uploads/2017/11/InnoEnergy-Offshore-Wind-anticipated-innovations-impact-2017_A4.pdf.
DOE. “Hydropower Vision: A New Chapter for America’s Renewable Electricity Source.” Washington, D.C.: U.S. Department of Energy, 2016. https://www.energy.gov/sites/prod/files/2018/02/f49/Hydropower-Vision-021518.pdf.
EIA. “Annual Energy Outlook 2015 with Projections to 2040.” Annual Energy Outlook. Washington, D.C.: U.S. Energy Information Administration, 2015. https://www.eia.gov/outlooks/archive/aeo15/. | 2023-02-04T08:04:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5455523729324341, "perplexity": 10378.928163848865}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500095.4/warc/CC-MAIN-20230204075436-20230204105436-00460.warc.gz"} |
https://pos.sissa.it/282/153/ | Volume 282 - 38th International Conference on High Energy Physics (ICHEP2016) - Beyond the Standard Model
BSM physics at CLIC
R. Simoniello* On behalf of the CLICdp collaboration
*corresponding author
Full text: pdf
Pre-published on: 2017 February 06
Published on: 2017 April 19
Abstract
The Compact Linear Collider (CLIC) is an option for a future electron-positron collider operating at centre-of-mass energies from a few hundred GeV up to 3 TeV. The search for phenomena beyond the Standard Model through direct observation of new particles and precision measurements is one of the main motivations for the high-energy stages of CLIC. An overview of physics benchmark studies assuming different new physics scenarios is given in this contribution. These studies are based on full detector simulations.
New particles can be discovered in most of the considered scenarios almost up to the kinematic limit ($\sqrt{s} / 2$ for pair production).
The low background conditions at CLIC provide extended discovery potential compared to hadron colliders, for example in the case of non-coloured TeV-scale SUSY particles. In addition to direct particle searches, BSM models can be probed up to scales of tens of TeV through precision measurements. Examples, including recent results on the reaction $e^+e^-\to\gamma\gamma$, are given. Beam polarisation allows to constrain the underlying theory further in many cases. The discussion of LHC results relevant for the CLIC physics case is also included.
DOI: https://doi.org/10.22323/1.282.0153
Open Access
Copyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | 2018-05-20T10:13:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5558180212974548, "perplexity": 2215.9408647664154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794863277.18/warc/CC-MAIN-20180520092830-20180520112830-00122.warc.gz"} |
https://bestforall.tnedu.gov/resource/rising-grade-8-summer-learning-resources-math-week-4?book=5409&binder_id=5406 | ## Weekly Overview
Weekly Topics
The focus of this week’s instruction is to deepen students’ understanding of:
• Generating Equivalent Expressions (both lessons 1 and 2)
• Understanding Equations
• Using If-Then Moves in Solving Equations (both lessons 4 and 5)
Materials Needed
• Manila Envelopes (enough for each student in the class to have one)
• Expressions
• Equations
• Tape Diagram
• Pencil and Paper
Standard(s) Covered
7.EE.B.3
Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and decimals).
1. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate.
2. Assess the reasonableness of answers using mental computation and estimation strategies.
Representations
• Tape Diagram
• Numerical Sentences
• Variable: A variable is a symbol (such as a letter) that represents a number (i.e., it is a placeholder for a number). A variable is actually quite a simple idea: it is a placeholder—a blank—in an expression or an equation where a number can be inserted. A variable holds a place for a single number throughout all calculations done with the variable—it does not vary. It is the user of the variable who has the ultimate power to change or vary what number is inserted, as he/she desires. The power to vary rests in the will of the student, not in the variable itself.
• Numerical expression: A numerical expression is a number, or it is any combination of sums, differences, products, or divisions of numbers that evaluates to a number.
• Value of a numerical expression: The value of a numerical expression is the number found by evaluating the expression. For example, $${1 \over 3}$$ ∙ (2 + 4) - 7 is a numerical expression, and its value is -5.
• Expression: An expression is a numerical expression, or it is the result of replacing some (or all) of the numbers in a numerical expression with variables. There are two ways to build expressions: We can start out with a numerical expression, such as $${1 \over 3}$$ ∙ (2 + 4) - 7 and replace some of the numbers with letters to get $${1 \over 3}$$ ∙ (x + y) - z. We can build such expressions from scratch, as in x + x(y-z) , and note that if numbers were placed in the expression for the variables x, y, and z, the result would be a numerical expression. The key is to strongly link expressions back to computations with numbers through building and evaluating them. Building an expression often occurs in the context of a word problem by thinking about examples of numerical expressions first and then replacing some of the numbers with letters in a numerical expression. The act of evaluating an expression means to replace each of the variables with specific numbers to get a numerical expression, and then finding the value of that numerical expression.
• Equivalent expressions: Two expressions are equivalent if both expressions evaluate to the same number for every substitution of numbers into all the letters in both expressions.
• An expression in standard form: An expression that is in expanded form where all like terms have been collected is said to be in standard form. Expanded form is where the like terms are not collected (3x + 2y + 5x – y, is an example of expanded form. To write this in standard form would be 8x + y).
• Term (description): Each summand of an expression is called a term.
• Coefficient of a term: The coefficient of a term is the number multiplying a variable. For example, 3x + 2y – c + 2. 3x, 2y, -c, and 2 are all terms. 3 is the coefficient of x, 2 is the coefficient of y, -1 is the coefficient of c, and 2 is the constant term and will therefore have no coefficient.
• Equation: An equation is a statement of equality between two expressions. If A and B are two expressions in the variable x, then A=B is an equation in the variable x. Students sometimes have trouble keeping track of what is an expression and what is an equation. An expression never includes an equal sign (=) and can be thought of as part of a sentence. The expression 3+4 read aloud is, “Three plus four,” which is only a phrase in a possible sentence. Equations, on the other hand, always have an equal sign, which is a symbol for the verb is. The equation 3+4=7 read aloud is, “Three plus four is seven,” which expresses a complete thought (i.e., a sentence). Number sentences—equations with numbers only—are special among all equations.
• Number sentence: A number sentence is a statement of equality (or inequality) between two numerical expressions. A number sentence is by far the most concrete version of an equation. It also has the very important property that it is always true or always false, and it is this property that distinguishes it from a generic equation. Examples include 3+4=7 (true) and 3+3=7 (false). This important property guarantees the ability to check whether or not a number is a solution to an equation with a variable: just substitute a number into the variable. The resulting number sentence is either true or it is false. If the number sentence is true, the number is a solution to the equation. For that reason, number sentences are the first and most important type of equation that students need to understand.
• Solution: A solution to an equation with one variable is a number that, when substituted for all instances of the variable in both expressions, makes the equation a true number sentence.
## Materials List
The following materials list will be used for the entire four weeks: Materials List. | 2021-09-24T03:18:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5812419652938843, "perplexity": 746.368177945014}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057496.18/warc/CC-MAIN-20210924020020-20210924050020-00314.warc.gz"} |
https://clashofclans.fandom.com/wiki/Giant_Skeleton | ## FANDOM
1,020 Pages
Not AvailableThis troop is not available in the current version.
"Big boned from early age, the Giant Skeleton was always destined to blow up more than just walls. His massive bomb damages everything around him after he is destroyed."
Level 1-8
• Summary
• The Giant Skeleton was a temporary troop that was available during the 2017 Halloween, along with Pumpkin Barbarian. They were made available again during the "Jack Skellingboom" event, along with the Ice Wizard, which lasted from 12/28/17 until 1/3/18. They were made available once again on Halloween 2018, along with Skeleton Barrel.
• They have high hitpoints and do massive damage upon death.
• Giant Skeletons prioritize defensive structures above all other targets, and will bypass all other types of enemy buildings and troops while any defenses remain on the battlefield. This is true even if they are under attack by enemy Clan Castle troops, heroes or Skeleton Trap skeletons. Note that like all troops that prioritize defenses, Giant Skeletons do not consider the Clan Castle to be a defense regardless of whether or not it contains enemy troops, but do consider the defending Grand Warden and the level 12 or 13 Town Hall (if its Giga Tesla or Giga Inferno has been triggered) to be defensive buildings.
Once all defenses are destroyed, Giant Skeletons become like any other troop with no preferred target; they will attack the nearest building to them regardless of type, and will turn and attack enemy units if they become aware of any nearby.
• Trivia
• You could have a maximum of 14 Giant Skeletons at one time in a complete set of fully upgraded Army Camps. On the battlefield, you could clone an additional 3 Giant Skeletons with three level 2 or higher Clone Spells.
• Similar to all other temporary troops, the Giant Skeleton cannot be donated through a Clan.
• Like all other temporary troops and spells, the Giant Skeleton can't be upgraded in the Laboratory. Instead, they depend on the player's Town Hall level.
• To calculate the health and damage statistics, two factors are considered: the base statistic and Town Hall multiplier.
• The base statistic for each Town Hall level equals the DPH and HP of certain levels of Giants.
• Each base statistic is multiplied by a fixed multiplier for each Town Hall level; the multiplier follows a roughly linear scale. For Town Hall level x, the multiplier is $(\lfloor 30 + (x-1)*70/11 \rfloor)/100$. Once the multiplier is applied, the statistic is rounded down to give the final statistic.
• Note that other statistics, such as training cost and death damage, are not multiplied by the multiplier.
• The Giant Skeleton is the third temporary troop that comes from Clash Royale, after Ice Wizard and Battle Ram. It's one of the two temporary troops from Clash Royale that prioritize defenses in Clash of Clans but doesn't only attack buildings in Clash Royale, the other is the Ice Wizard. The Giant Skeleton was added to clash royale on 4/1/2016 the date of the game's soft launch.
• The Giant Skeleton does equal damage as a Giant of the same level and has 2.5 times the Giant's hitpoints.
• Unlike his Clash Royale Counterpart, he attacks only defenses instead of everything.
• In the picture, he wears a brown Russian hat. But in the game, he wears a red one, resembling an opponent's Giant Skeleton troop in Clash Royale. The same situation applies to the Ice Wizard and Skeleton Barrel.
• The spawning sound and the attacking sound of Giant Skeleton is the same as the Giant.
Preferred Target Attack Type Housing Space Movement Speed Attack Speed Barracks Level Required Range
Defenses Melee (Ground Only) 20 12 2s 3 1 tile
Training Time of Giant Skeletons
1 Barracks 2 Barracks 3 Barracks 4 Barracks
2m 1m 40s 30s
Level* Damage per Second Damage per Attack Death Damage Hitpoints Training Cost Town Hall Level Required
1 7 14 800 360 250 2
2 11 22 1,000 504 750 3
3 18 36 1,200 686 1250 4
4 20 40 1,200 770 1250 5
5 29 58 1,400 1,037 1750 6
6 32 64 1,400 1,156 1750 7
7 45 90 1,600 1,628 2250 8
8 68 136 1,800 2,480 3000 9
9 87 174 2,000 3,132 3500 10
10 106 212 2,200 3,813 4000 11
11 114 228 2,200 4,100 4000 12
*The "level" here does not match up with the in-game levels. This is for purposes of clarity between different Town Hall levels, which have different statistics.
Home Village Army
Elixir Troops BarbarianArcherGiantGoblinWall BreakerBalloonWizardHealerDragonP.E.K.K.ABaby DragonMinerElectro DragonYeti (Yetimite)
Dark Elixir Troops MinionHog RiderValkyrieGolem (Golemite) • Witch (Skeleton) • Lava Hound (Lava Pup) • BowlerIce GolemHeadhunter
Super Troops Super BarbarianSuper ArcherSuper GiantSneaky GoblinSuper Wall BreakerInferno DragonSuper Witch (Big Boy)
Heroes Barbarian KingArcher QueenGrand WardenRoyal Champion
Elixir Spells Lightning SpellHealing SpellRage SpellJump SpellFreeze SpellClone Spell
Dark Spells Poison SpellEarthquake SpellHaste SpellSkeleton SpellBat Spell
Siege Machines Wall WreckerBattle BlimpStone SlammerSiege Barracks
Temporary Contents
Temporary Troops Ice WizardBattle RamPumpkin BarbarianGiant SkeletonSkeleton BarrelEl PrimoParty WizardRoyal Ghost
Temporary Spells Santa's SurpriseBirthday Boom
Temporary Traps Pumpkin BombSanta StrikeFreeze TrapShrink Trap
Other Temporary Contents The Waterfall
Community content is available under CC-BY-SA unless otherwise noted. | 2020-09-27T11:37:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3008449971675873, "perplexity": 10508.340991638363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400274441.60/warc/CC-MAIN-20200927085848-20200927115848-00094.warc.gz"} |
https://nbviewer.ipython.org/github/TarrySingh/Machine-Learning-Tutorials/blob/master/scipy/hypothesis.ipynb | Hypothesis Testing¶
Credits: Forked from CompStats by Allen Downey. License: Creative Commons Attribution 4.0 International.
In [1]:
from __future__ import print_function, division
import numpy
import scipy.stats
import matplotlib.pyplot as pyplot
from IPython.html.widgets import interact, fixed
from IPython.html import widgets
import first
# seed the random number generator so we all get the same results
numpy.random.seed(19)
# some nicer colors from http://colorbrewer2.org/
COLOR1 = '#7fc97f'
COLOR2 = '#beaed4'
COLOR3 = '#fdc086'
COLOR4 = '#ffff99'
COLOR5 = '#386cb0'
%matplotlib inline
Part One¶
As an example, let's look at differences between groups. The example I use in Think Stats is first babies compared with others. The first module provides code to read the data into three pandas Dataframes.
In [2]:
live, firsts, others = first.MakeFrames()
The apparent effect we're interested in is the difference in the means. Other examples might include a correlation between variables or a coefficient in a linear regression. The number that quantifies the size of the effect, whatever it is, is the "test statistic".
In [3]:
def TestStatistic(data):
group1, group2 = data
test_stat = abs(group1.mean() - group2.mean())
return test_stat
For the first example, I extract the pregnancy length for first babies and others. The results are pandas Series objects.
In [4]:
group1 = firsts.prglngth
group2 = others.prglngth
The actual difference in the means is 0.078 weeks, which is only 13 hours.
In [5]:
actual = TestStatistic((group1, group2))
actual
Out[5]:
0.078037266777549519
The null hypothesis is that there is no difference between the groups. We can model that by forming a pooled sample that includes first babies and others.
In [6]:
n, m = len(group1), len(group2)
pool = numpy.hstack((group1, group2))
Then we can simulate the null hypothesis by shuffling the pool and dividing it into two groups, using the same sizes as the actual sample.
In [7]:
def RunModel():
numpy.random.shuffle(pool)
data = pool[:n], pool[n:]
return data
The result of running the model is two NumPy arrays with the shuffled pregnancy lengths:
In [8]:
RunModel()
Out[8]:
(array([36, 40, 39, ..., 43, 42, 40]), array([43, 39, 32, ..., 37, 35, 41]))
Then we compute the same test statistic using the simulated data:
In [9]:
TestStatistic(RunModel())
Out[9]:
0.081758440969863955
If we run the model 1000 times and compute the test statistic, we can see how much the test statistic varies under the null hypothesis.
In [10]:
test_stats = numpy.array([TestStatistic(RunModel()) for i in range(1000)])
test_stats.shape
Out[10]:
(1000,)
Here's the sampling distribution of the test statistic under the null hypothesis, with the actual difference in means indicated by a gray line.
In [11]:
def VertLine(x):
"""Draws a vertical line at x."""
pyplot.plot([x, x], [0, 300], linewidth=3, color='0.8')
VertLine(actual)
pyplot.hist(test_stats, color=COLOR5)
pyplot.xlabel('difference in means')
pyplot.ylabel('count')
None
The p-value is the probability that the test statistic under the null hypothesis exceeds the actual value.
In [12]:
pvalue = sum(test_stats >= actual) / len(test_stats)
pvalue
Out[12]:
0.14999999999999999
In this case the result is about 15%, which means that even if there is no difference between the groups, it is plausible that we could see a sample difference as big as 0.078 weeks.
We conclude that the apparent effect might be due to chance, so we are not confident that it would appear in the general population, or in another sample from the same population.
Part Two¶
We can take the pieces from the previous section and organize them in a class that represents the structure of a hypothesis test.
In [13]:
class HypothesisTest(object):
"""Represents a hypothesis test."""
def __init__(self, data):
"""Initializes.
data: data in whatever form is relevant
"""
self.data = data
self.MakeModel()
self.actual = self.TestStatistic(data)
self.test_stats = None
def PValue(self, iters=1000):
"""Computes the distribution of the test statistic and p-value.
iters: number of iterations
returns: float p-value
"""
self.test_stats = numpy.array([self.TestStatistic(self.RunModel())
for _ in range(iters)])
count = sum(self.test_stats >= self.actual)
return count / iters
def MaxTestStat(self):
"""Returns the largest test statistic seen during simulations.
"""
return max(self.test_stats)
def PlotHist(self, label=None):
"""Draws a Cdf with vertical lines at the observed test stat.
"""
def VertLine(x):
"""Draws a vertical line at x."""
pyplot.plot([x, x], [0, max(ys)], linewidth=3, color='0.8')
ys, xs, patches = pyplot.hist(ht.test_stats, color=COLOR4)
VertLine(self.actual)
pyplot.xlabel('test statistic')
pyplot.ylabel('count')
def TestStatistic(self, data):
"""Computes the test statistic.
data: data in whatever form is relevant
"""
raise UnimplementedMethodException()
def MakeModel(self):
"""Build a model of the null hypothesis.
"""
pass
def RunModel(self):
"""Run the model of the null hypothesis.
returns: simulated data
"""
raise UnimplementedMethodException()
HypothesisTest is an abstract parent class that encodes the template. Child classes fill in the missing methods. For example, here's the test from the previous section.
In [14]:
class DiffMeansPermute(HypothesisTest):
"""Tests a difference in means by permutation."""
def TestStatistic(self, data):
"""Computes the test statistic.
data: data in whatever form is relevant
"""
group1, group2 = data
test_stat = abs(group1.mean() - group2.mean())
return test_stat
def MakeModel(self):
"""Build a model of the null hypothesis.
"""
group1, group2 = self.data
self.n, self.m = len(group1), len(group2)
self.pool = numpy.hstack((group1, group2))
def RunModel(self):
"""Run the model of the null hypothesis.
returns: simulated data
"""
numpy.random.shuffle(self.pool)
data = self.pool[:self.n], self.pool[self.n:]
return data
Now we can run the test by instantiating a DiffMeansPermute object:
In [15]:
data = (firsts.prglngth, others.prglngth)
ht = DiffMeansPermute(data)
p_value = ht.PValue(iters=1000)
print('\nmeans permute pregnancy length')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())
means permute pregnancy length
p-value = 0.16
actual = 0.0780372667775
ts max = 0.173695697482
And we can plot the sampling distribution of the test statistic under the null hypothesis.
In [16]:
ht.PlotHist()
As an exercise, write a class named DiffStdPermute that extends DiffMeansPermute and overrides TestStatistic to compute the difference in standard deviations. Is the difference in standard deviations statistically significant?
In [17]:
class DiffStdPermute(DiffMeansPermute):
"""Tests a difference in means by permutation."""
def TestStatistic(self, data):
"""Computes the test statistic.
data: data in whatever form is relevant
"""
group1, group2 = data
test_stat = abs(group1.std() - group2.std())
return test_stat
data = (firsts.prglngth, others.prglngth)
ht = DiffStdPermute(data)
p_value = ht.PValue(iters=1000)
print('\nstd permute pregnancy length')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())
std permute pregnancy length
p-value = 0.155
actual = 0.176049064229
ts max = 0.44299505029
Now let's run DiffMeansPermute again to see if there is a difference in birth weight between first babies and others.
In [18]:
data = (firsts.totalwgt_lb.dropna(), others.totalwgt_lb.dropna())
ht = DiffMeansPermute(data)
p_value = ht.PValue(iters=1000)
print('\nmeans permute birthweight')
print('p-value =', p_value)
print('actual =', ht.actual)
print('ts max =', ht.MaxTestStat())
means permute birthweight
p-value = 0.0
actual = 0.124761184535
ts max = 0.0917504268392
In this case, after 1000 attempts, we never see a sample difference as big as the observed difference, so we conclude that the apparent effect is unlikely under the null hypothesis. Under normal circumstances, we can also make the inference that the apparent effect is unlikely to be caused by random sampling.
One final note: in this case I would report that the p-value is less than 1/1000 or 0.001. I would not report that p=0, because the apparent effect is not impossible under the null hypothesis; just unlikely. | 2021-09-19T17:22:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3931872248649597, "perplexity": 3945.5282959414317}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056892.13/warc/CC-MAIN-20210919160038-20210919190038-00365.warc.gz"} |
http://pdglive.lbl.gov/DataBlock.action?node=S060DML&home=BXXX045 | # ${\boldsymbol m}_{{{\boldsymbol \Xi}_{{b}}^{-}}}–{\boldsymbol m}_{{{\boldsymbol \Lambda}_{{b}}^{0}}}$ INSPIRE search
VALUE (MeV) DOCUMENT ID TECN COMMENT
$\bf{ 177.5 \pm0.5}$ OUR AVERAGE Error includes scale factor of 1.6.
$177.73$ $\pm0.33$ $\pm0.14$ 1
2017 BE
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$176.2$ $\pm0.9$ $\pm0.1$ 2
2013 AV
LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$177.08$ $\pm0.47$ $\pm0.16$ 3
2017 BE
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$178.36$ $\pm0.46$ $\pm0.16$ 4, 5
2014 BJ
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
1 Combination of the original statistically independent measurements of AAIJ 2014BE and AAIJ 2017BJ taking into account correlation between systematic uncertainties.
2 Reconstructed in ${{\mathit \Xi}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \Xi}^{-}}$ decays.
3 Reconstructed in ${{\mathit \Xi}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \Lambda}}{{\mathit K}^{-}}$ decays. Reference decays ${{\mathit \Lambda}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \Lambda}}$ were used.
4 Reconstructed in ${{\mathit \Xi}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit \Xi}_{{c}}^{0}}{{\mathit \pi}^{-}}$ , ${{\mathit \Xi}_{{c}}^{0}}$ $\rightarrow$ ${{\mathit p}}{{\mathit K}^{-}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$ decays. Reference ${{\mathit \Lambda}_{{b}}^{0}}$ $\rightarrow$ ${{\mathit \Lambda}_{{c}}^{+}}{{\mathit \pi}^{-}}$ .
5 Combined with AAIJ 2017BE.
References:
AAIJ 2017BE
PL B772 265 Observation of the ${{\mathit \Xi}_{{b}}^{-}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit \Lambda}}{{\mathit K}^{-}}$ Decay
AAIJ 2014BJ
PRL 113 242002 Precision Measurement of the Mass and Lifetime of the ${{\mathit \Xi}_{{b}}^{-}}$ Baryon
AAIJ 2013AV
PRL 110 182001 Measurement of the ${{\mathit \Lambda}_{{b}}^{0}}$, ${{\mathit \Xi}_{{b}}^{-}}$ and ${{\mathit \Omega}_{{b}}^{-}}$ Baryon Masses | 2020-04-05T19:20:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9426984190940857, "perplexity": 5097.440095850212}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371609067.62/warc/CC-MAIN-20200405181743-20200405212243-00461.warc.gz"} |
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