bluuebunny/crossref_metadata_2025 huggingface dataset:
Targeted suppression of μ‐calpain and caspase 9 expression and its effect on caspase 3 and caspase 7 in satellite cells of Korean Hanwoo cattle
Authors: Yang You Bing , Pandurangan Muthuraman , Hwang InHo
Published: June 2012

The calpains play an important role in cell death and cell signalling. Caspases catalyse wholesale destruction of cellular proteins which is a major cause of cellular death. The current study looks at the function of μ‐calpain and caspase 9, using RNAi (RNA interference)‐mediated silencing, and to observe the mRNA expression level of caspase genes during satellite cell growth. The satellite cells were treated with siRNA (small interfering RNA) of μ‐calpain and caspase 9 separately. There was reduction of 16 and 24% in CAPN1 (calpain1)‐siRNA2 and CAPN1‐siRNA3 transfected cells respectively, whereas it was 60 and 56% in CAPN1‐siRNA1 and CAPN1‐siRNA4 transfected cells respectively. CAPN1‐siRNA4 and CAPN1‐siRNA1 treated cells showed more reduction in caspase 3 and 7 gene expression. CARD9 (caspase recruitment domain 9)‐siRNA1 and CARD9‐siRNA2‐treated cells showed reduction of 40 and 49% respectively. CARD9‐siRNA1 and CARD9‐siRNA2 showed an increase in caspase 3 gene expression, whereas CARD9‐siRNA2 showed reduction in caspase 7 gene expression. These results suggest a strong cross‐talk between μ‐calpain and the caspase enzyme systems. Suppression of target genes, such as μ‐calpain and caspase 9, might have genuine potential in the treatment of skeletal muscle atrophy.
Does the Relationship between Retained Mandibular Third Molar and Mandibular Angle Fracture Exist? An Assessment of Three Possible Causes
Authors: Duarte Bruno G. , Assis Diogo , Ribeiro-Júnior Paulo , Gonçales Eduardo Sanches
Published: June 2012

The objective of this study is to discuss problems associated with dental retention through three clinical cases of mandible fractures related to the presence of retained lower third molars, emphasizing the possibility of mandible fractures resulting from this or from the extraction procedure. The three evaluated patients had a fracture in the mandible angle. The third molars were present in all the cases, as was the relationship of the fracture with the teeth. After evaluating the three cases and reviewing literature, it is believed that the presence of the retained lower third molars and the surgical procedures for their extraction increase the risk of mandible angle fractures.
Imaging, Virtual Planning, Design, and Production of Patient-Specific Implants and Clinical Validation in Craniomaxillofacial Surgery
Authors: Dérand Per , Rännar Lars-Erik , Hirsch Jan-M
Published: June 2012

The purpose of this article was to describe the workflow from imaging, via virtual design, to manufacturing of patient-specific titanium reconstruction plates, cutting guide and mesh, and its utility in connection with surgical treatment of acquired bone defects in the mandible using additive manufacturing by electron beam melting (EBM). Based on computed tomography scans, polygon skulls were created. Following that virtual treatment plans entailing free microvascular transfer of fibula flaps using patient-specific reconstruction plates, mesh, and cutting guides were designed. The design was based on the specification of a Compact UniLOCK 2.4 Large (Synthes®, Switzerland). The obtained polygon plates were bent virtually round the reconstructed mandibles. Next, the resections of the mandibles were planned virtually. A cutting guide was outlined to facilitate resection, as well as plates and titanium mesh for insertion of bone or bone substitutes. Polygon plates and meshes were converted to stereolithography format and used in the software Magics for preparation of input files for the successive step, additive manufacturing. EBM was used to manufacture the customized implants in a biocompatible titanium grade, Ti6Al4V ELI. The implants and the cutting guide were cleaned and sterilized, then transferred to the operating theater, and applied during surgery. Commercially available software programs are sufficient in order to virtually plan for production of patient-specific implants. Furthermore, EBM-produced implants are fully usable under clinical conditions in reconstruction of acquired defects in the mandible. A good compliance between the treatment plan and the fit was demonstrated during operation. Within the constraints of this article, the authors describe a workflow for production of patient-specific implants, using EBM manufacturing. Titanium cutting guides, reconstruction plates for fixation of microvascular transfer of osteomyocutaneous bone grafts, and mesh to replace resected bone that can function as a carrier for bone or bone substitutes were designed and tested during reconstructive maxillofacial surgery. A clinically fit, well within the requirements for what is needed and obtained using traditional free hand bending of commercially available devices, or even higher precision, was demonstrated in ablative surgery in four patients.
Molecular dynamics modeling of solid phase epitaxial regrowth
Authors: Lai Haoyu , Cea Stephen M. , Kennel Harold , Dunham Scott T.
Published: June 2012

Solid phase epitaxial regrowth (SPER) is of great technological importance in semiconductor device fabrication. A better understanding and accurately modeling of its behavior are vital to the design of fabrication processes and the improvement of the device performance. In this paper, SPER was modeled by molecular dynamics (MD) with Tersoff potential. Extensive MD simulations were conducted to study the dependence of SPER rate on temperature, growth orientation, pressure, and uniaxial stress. The simulation data were fitted to empirical formula, and the results were compared with experimental data. It was concluded that MD with Tersoff potential can qualitatively describe the SPER process. For a more quantitatively accurate model, larger simulation systems and a better interatomic potential are needed.
Large magneto (thermo) dielectric effect in multiferroic orthorhombic LuMnO3
Authors: Wang L. J. , Chai Y. S. , Feng S. M. , Zhu J. L. , Manivannan N. , Jin C. Q. , Gong Z. Z. , Wang X. H. , Li L. T.
Published: June 2012

We have investigated the relation between ferroelectric and magnetic orders of orthorhombic (o-) LuMnO3 ceramics. The increase of dielectric constant ɛ exceeds 82% near incommensurate to commensurate E-type antiferromagnetic (AFM) spin ordering transition temperature TL, reflecting a large magneto (thermo) dielectric response. Meanwhile, distinct anomalies and thermal hysteresis behavior are observed near this temperature in both temperature dependence of ɛ and specific heat Cp, indicating a strong coupling between FE and magnetic orders in o-LuMnO3. Comparing to o-HoMnO3, TmMnO3, and YbMnO3 with similar E-type AFM ground state, o-LuMnO3 has the largest magneto (thermo) dielectric effect
Enhanced x-ray imaging for a thin film cochlear implant with metal artefacts using phase retrieval tomography
Authors: Arhatari B. D. , Harris A. R. , Paolini A. G. , Peele A. G.
Published: June 2012

Phase retrieval tomography has been successfully used to enhance imaging in systems that exhibit poor absorption contrast. However, when highly absorbing regions are present in a sample, so-called metal artefacts can appear in the tomographic reconstruction. We demonstrate that straightforward approaches for metal artefact reconstruction, developed in absorption contrast tomography, can be applied when using phase retrieval. Using a prototype thin film cochlear implant that has high and low absorption components made from iridium (or platinum) and plastic, respectively, we show that segmentation of the various components is possible and hence measurement of the electrode geometry and relative location to other regions of interest can be achieved.
Damping effect on resonance bounds relationship of nanostructured ferromagnets and composites
Authors: Zhou Peiheng , Liu Tao , Xie Jianliang , Deng Longjiang
Published: June 2012

In this paper, we introduce Gilbert damping parameter into the expression of resonance bounds relationship in nanomagnets to accomplish the depiction of damping effect, associated with an experimental study of ferromagnetic nanocrystalline flakes and their composites. Based on the intrinsic permeability retrieving and microwave spectrum fitting, a robust approach to the damping problem in the resonance study of high-frequency ferromagnets and composites is discussed.
Characterization of InGaN-based nanorod light emitting diodes with different indium compositions
Authors: Bai J. , Wang Q. , Wang T.
Published: June 2012

Blue and green InGaN/GaN-based nanorod array light emitting diodes (LEDs) with superior performance have been realized using self-assembled Ni nano-mask and dry etching techniques. Temperature-dependent photoluminescence measurement shows that the internal quantum efficiencies (IQEs) of the LED nanorods are significantly improved in comparison to the as-grown epiwafer, with enhancement factors of 2.8 and 1.5 for the green LED nanorods and blue LED nanorods, respectively. It is in good agreement with a theoretical calculation based on the reduction in the internal electrical field due to strain relaxation in strained InGaN/GaN QWs. As compared to the planar LEDs fabricated using the same wafer, the emission of both nanorod LEDs is greatly improved. More significant enhancement in the light output power is observed for the green nanorod LED, manifesting that the emission enhancement is mainly attributed to a significant enhancement in the IQE. Furthermore, the current-voltage characteristics of nanorod LEDs exhibit two distinct regions at moderate forward bias, in which diffusion-recombination process is involved to a large extent in later period in spite that tunnelling transport dominates over a wide range of bias. The reverse leakage current of nanorod LEDs is about one order of magnitude higher as compared to the planar ones.
Survey quality and cross‐national sports research: A case study of the 2007 ISSP survey
Authors: Van Tuyckom Charlotte , Bracke Piet
Published: June 2012

For the past 15 years there has been an increase in the number of cross‐national surveys on sports‐related issues. However, in cross‐national research, the quality of the conclusions always depends on the quality of each of the separate national studies. If any of these are flawed, it is possible that the observed variation in outcomes is nothing more than a methodological artefact. Unfortunately, the issue of survey quality has been seriously underdeveloped in sports research literature. Through a discussion of several components of survey quality by means of the 2007 International Social Survey Programme survey on leisure time and sports, this article addresses this lacuna. Our case study shows that the wide cross‐national variation in sampling methods, modes of data collection and response rates leaves room for various forms of survey error with the potential to generate misleading or biased findings. Although it is less clear what can be done about survey error, we give some possibilities. We suggest that ignoring these methodological problems will affect the validity of cross‐national research. Moreover, future research into the impact of various methodological factors related to survey quality is definitely needed.
Isoperimetric inequalities for convex hulls and related questions
Authors: Tilli Paolo
Published: June 2012

We consider the problem of maximizing the Lebesgue measure of the convex hull of a connected compact set of prescribed one-dimensional Hausdorff measure. In dimension two, we prove that the only solutions are semicircles. In higher dimensions, we prove some isoperimetric inequalities for convex hulls of connected sets; we focus on a classical open problem and discuss a possible new approach.
On the characterization of algebraically integrable plane foliations
Authors: Galindo C. , Monserrat F.
Published: June 2012

We give a characterization theorem for non-degenerate plane foliations of degree different from 1 having a rational first integral. Moreover, we prove that the degree

r
r

of a non-degenerate foliation as above provides the minimum number,

r
+
1

r+1

, of points in the projective plane through which pass infinitely many algebraic leaves of the foliation.
A Neumann problem with critical exponent in nonconvex domains and Lin-Ni’s conjecture
Authors: Wang Liping , Wei Juncheng , Yan Shusen
Published: June 2012

We consider the following nonlinear Neumann problem:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout Enlarged left-brace 1st Row 1st Column minus normal upper Delta u plus mu u equals u Superscript StartFraction upper N plus 2 Over upper N minus 2 EndFraction Baseline comma u greater-than 0 2nd Column a m p semicolon in normal upper Omega comma 2nd Row 1st Column StartFraction partial-differential u Over partial-differential n EndFraction equals 0 2nd Column a m p semicolon on partial-differential normal upper Omega comma EndLayout">

{

−
Δ
u
+
μ
u
=

u

N
+
2

N
−
2

,

u
>
0

a
m
p
;

in

 
Ω
,

∂
u

∂
n

=
0

a
m
p
;

on

 
∂
Ω
,

\left \{\begin {array}{lll} -\Delta u + \mu u = u^{\frac {N+2}{N-2}},\quad u>0 \quad & \mbox {in} \ \Omega , \\ \frac {\partial u}{\partial n}=0 & \mbox {on} \ \partial \Omega , \end {array}\right .

\]
where

Ω
⊂

R

N

\Omega \subset \mathbb {R}^N

is a smooth and bounded domain,

μ
>
0

\mu > 0

and

n
n

denotes the outward unit normal vector of

∂
Ω

\partial \Omega

. Lin and Ni (1986) conjectured that for

μ
\mu

small, all solutions are constants. We show that this conjecture is false for all dimensions in some (partially symmetric) nonconvex domains

Ω
\Omega

. Furthermore, we prove that for any fixed

μ
\mu

, there are infinitely many positive solutions, whose energy can be made arbitrarily large. This seems to be a new phenomenon for elliptic problems in bounded domains.
Multidimensional sofic shifts without separation and their factors
Authors: Boyle Mike , Pavlov Ronnie , Schraudner Michael
Published: June 2012

For

d
≥
2

d\geq 2

we exhibit mixing

Z

d

\mathbb {Z}^d

shifts of finite type and sofic shifts with large entropy but poorly separated subsystems (in the sofic examples, the only minimal subsystem is a single point). These examples consequently have very constrained factors; in particular, no non-trivial full shift is a factor. We also provide examples to distinguish certain mixing conditions and develop the natural class of “block gluing” shifts. In particular, we show that block gluing shifts factor onto all full shifts of strictly smaller entropy.
Hypersurfaces cutting out a projective variety
Authors: Noma Atsushi
Published: June 2012

Let

X
X

be a nondegenerate projective variety of degree

d
d

and codimension

e
e

in a projective space

P

N

\mathbb {P}^{N}

defined over an algebraically closed field. We study the following two problems: Is the length of the intersection of

X
X

and a line

L
L

in

P

N

\mathbb {P}^{N}

at most

d
−
e
+
1

d-e+1

if

L
⊈
X

L \not \subseteq X

? Is the scheme-theoretic intersection of all hypersurfaces of degree at most

d
−
e
+
1

d-e+1

containing

X
X

equal to

X
X

? To study the second problem, we look at the locus of points from which

X
X

is projected nonbirationally.
The emergence of the electrostatic field as a Feynman sum in random tilings with holes
Authors: Ciucu Mihai
Published: June 2012

We consider random lozenge tilings on the triangular lattice with holes

Q

1

,
…
,

Q

n

Q_{1},\dots ,Q_{n}

in some fixed position. For each unit triangle not in a hole, consider the average orientation of the lozenge covering it. We show that the scaling limit of this discrete field is the electrostatic field obtained when regarding each hole

Q

i

Q_{i}

as an electrical charge of magnitude equal to the difference between the number of unit triangles of the two different orientations inside

Q

i

Q_{i}

. This is then restated in terms of random surfaces, yielding the result that the average over surfaces with prescribed height at the union of the boundaries of the holes is, in the scaling limit, a sum of helicoids.
Time-frequency representations of Wigner type and pseudo-differential operators
Authors: Boggiatto P. , De Donno G. , Oliaro A.
Published: June 2012

We introduce a

τ
\tau

-dependent Wigner representation,

Wig
τ

\operatorname {Wig}_\tau

,

τ
∈
[
0
,
1
]

\tau \in [0,1]

, which permits us to define a general theory connecting time-frequency representations on one side and pseudo-differential operators on the other. The scheme includes various types of time-frequency representations, among the others the classical Wigner and Rihaczek representations and the most common classes of pseudo-differential operators. We show further that the integral over

τ
\tau

of

Wig
τ

\operatorname {Wig}_\tau

yields a new representation

Q
Q

possessing features in signal analysis which considerably improve those of the Wigner representation, especially for what concerns the so-called “ghost frequencies”. The relations of all these representations with respect to the generalized spectrogram and the Cohen class are then studied. Furthermore, a characterization of the

L
p

L^p

-boundedness of both

τ
\tau

-pseudo-differential operators and

τ
\tau

-Wigner representations are obtained.
Modular forms on non-linear double covers of algebraic groups
Authors: Loke Hung Yean , Savin Gordan
Published: June 2012

We construct automorphic representations of non-linear two-fold covers of simply connected Chevalley groups via residues of Eisenstein series. In the process, we establish some basic results in representation theory of local groups.
The coarse classification of countable abelian groups
Authors: Banakh T. , Higes J. , Zarichnyi I.
Published: June 2012

We prove that two countable locally finite-by-abelian groups

G
,
H

G,H

endowed with proper left-invariant metrics are coarsely equivalent if and only if their asymptotic dimensions coincide and the groups are either both finitely generated or both are infinitely generated. On the other hand, we show that each countable group

G
G

that coarsely embeds into a countable abelian group is locally nilpotent-by-finite. Moreover, the group

G
G

is locally abelian-by-finite if and only if

G
G

is undistorted in the sense that

G
G

can be written as the union

G
=

⋃

n
∈
ω

G
n

G=\bigcup _{n\in \omega }G_n

of countably many finitely generated subgroups such that each

G
n

G_n

is undistorted in

G

n
+
1

G_{n+1}

(which means that the identity inclusion

G
n

→

G

n
+
1

G_n\to G_{n+1}

is a quasi-isometric embedding with respect to word metrics on

G
n

G_n

and

G

n
+
1

G_{n+1}

).
Existence and uniqueness of the Riemann problem for a nonlinear system of conservation laws of mixed type
Authors: Hsiao L. , de Mottoni P.
Published: June 2012

We study the system of conservation laws given by
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace Subscript upsilon Sub Subscript t Subscript plus left-bracket upsilon left-parenthesis a plus u right-parenthesis right-bracket Sub Subscript x Subscript equals 0 left-parenthesis a greater-than 1 is a constant right-parenthesis comma Superscript u Super Subscript t Superscript plus left-bracket u left-parenthesis 1 minus upsilon right-parenthesis right-bracket Super Subscript x Superscript equals 0 comma">

{

υ
t

+

[
υ
(
a
+
u
)
]

x

=
0

(
a
>
1

is

a

constant

)
,

u
t

+

[
u
(
1
−
υ
)
]

x

=
0
,

\left \{ {_{{\upsilon _t} + {{[\upsilon (a + u)]}_x} = 0\quad (a > 1{\text {is}}{\text {a}}{\text {constant}}),}^{{u_t} + {{[u(1 - \upsilon )]}_x} = 0,}} \right .

\]
with any Riemann initial data

(

u
∓

,

υ
∓

)

({u_ \mp },{\upsilon _ \mp })

. The system is elliptic in the domain where

(
υ
−
u
+
a
−
1

)
2

+
4
(
a
−
1
)
u
>
0

{(\upsilon - u + a - 1)^2} + 4(a - 1)u > 0

and strictly hyperbolic when

(
υ
−
u
+
a
−
1

)
2

+
4
(
a
−
1
)
u
>
0

{(\upsilon - u + a - 1)^2} + 4(a - 1)u > 0

. We combine and generalize Lax criterion and Oleinik-Liu criterion to introduce the generalized entropy condition (G.E.C.) by which we can show that the Riemann problem always has a weak solution (any discontinuity satisfies the G.E.C.) for any initial data, however not necessarily unique. We introduce the minimum principle then in the definition of an admissible weak solution for the Riemann problem and the existence and uniqueness of the solution for any Riemann data.
Representing sets of ordinals as countable unions of sets in the core model
Authors: Magidor Menachem
Published: June 2012

We prove the following theorems. Theorem 1

(
¬

0
#

)

(\neg {0^\# })

. Every set of ordinals which is closed under primitive recursive set functions is a countable union of sets in

L
L

. Theorem 2. (No inner model with an Erdàs cardinal, i.e.

κ
→

(

ω
1

)

>
ω

\kappa \to {({\omega _1})^{ > \omega }}

.) For every ordinal

β
\beta

, there is in

K
K

an algebra on

β
\beta

with countably many operations such that every subset of

β
\beta

closed under the operations of the algebra is a countable union of sets in

K
K

.
Real analytic desingularization and subanalytic sets: an elementary approach
Authors: Sussmann H. J.
Published: June 2012

We give a proof of a theorem on desingularization of real-analytic functions which is a weaker version of H. Hironaka’s result, but has the advantage of being completely self-contained and elementary, and not involving any machinery from algebraic geometry. We show that the basic facts about subanalytic sets can be proved from this result.
Enlacements du mouvement brownien autour des courbes de l’espace
Authors: Le Gall Jean-François , Yor Marc
Published: June 2012

Limit theorems are proved for the winding numbers of a three-dimensional Brownian motion around certain curves in space. In particular, the joint asymptotic distribution of the winding numbers around two curves is obtained. This joint distribution generalizes the asymptotic law of the winding numbers of a planar Brownian motion around two points, which has recently been given by Pitman and Yor. The limiting distributions are closely related to the time spent by a linear Brownian motion above and below a multiple of its maximum process. Proofs rely on stochastic calculus for continuous semi-martingales.
Algebraically invariant extensions of 𝜎-finite measures on Euclidean space
Authors: Ciesielski Krzysztof
Published: June 2012

Let

G
G

be a group of algebraic transformations of

R

n

{{\mathbf {R}}^n}

, i,e., the group of functions generated by bijections of

R

n

{{\mathbf {R}}^n}

of the form

(

f
1

,
…
,

f
n

)

({f_1}, \ldots ,{f_n})

where each

f
i

{f_i}

is a rational function with coefficients in

R

{\mathbf {R}}

in

n
n

-variables. For a function

γ
:
G
→
(
0
,
∞
)

\gamma :G \to (0,\infty )

we say that a measure

μ
\mu

on

R

n

{{\mathbf {R}}^n}

is

γ
\gamma

-invariant when

μ
(
g
[
A
]
)
=
γ
(
g
)
⋅
μ
(
A
)

\mu (g[A]) = \gamma (g)\cdot \mu (A)

for every

g
∈
G

g \in G

and every

μ
\mu

-measurable set

A
A

. We will examine the question: "Does there exist a proper

γ
\gamma

-invariant extension of

μ
?

\mu ?

We prove that if

μ
\mu

is

σ
\sigma

-finite then such an extension exists whenever

G
G

contains an uncountable subset of rational functions

H
⊂

(

R

(

X
1

,
…
,

X
n

)

)
n

H \subset {({\mathbf {R}}({X_1}, \ldots ,{X_n}))^n}

such that

μ
(
{
x
:

h
1

(
x
)
=

h
2

(
x
)
}
)
=
0

\mu (\{ x:{h_1}(x) = {h_2}(x)\} ) = 0

for all

h
1

,

h
2

∈
H
,

h
1

≠

h
2

{h_1},{h_2} \in H,{h_1} \ne {h_2}

. In particular if

G
G

is any uncountable subgroup of affine transformations of

R

n

,
γ
(
g

)

{{\bf {R}}^n},\gamma (g{\text {)}}

is the absolute value of the Jacobian of

g
∈
G

g \in G

and

μ
\mu

is a

γ
\gamma

-invariant extension of the

n
n

-dimensional Lebesgue measure then

μ
\mu

has a proper

γ
\gamma

-invariant extension. The conclusion remains true for any

σ
\sigma

-finite measure if

G
G

is a transitive group of isometries of

R

n

{{\mathbf {R}}^n}

. An easy strengthening of this last corollary gives also an answer to a problem of Harazisvili.
Topological spaces whose Baire measure admits a regular Borel extension
Authors: Ohta Haruto , Tamano Ken-ichi
Published: June 2012

A completely regular, Hausdorff space

X
X

is called a Măík space if every Baire measure on

X
X

admits an extension to a regular Borel measure. We answer the questions about Măík spaces asked by Wheeler [29] and study their topological properties. In particular, we give examples of the following spaces: A locally compact, measure compact space which is not weakly Bairedominated; i.e., it has a sequence

F
n

↓
∅

{F_n} \downarrow \emptyset

of regular closed sets such that

∩

n
∈
ω

B
n

≠
∅

{ \cap _{n \in \omega }}{B_n} \ne \emptyset

whenever

B
n

{B_n}

’s are Baire sets with

F
n

⊂

B
n

{F_n} \subset {B_n}

; a countably paracompact, non-Măík space; a locally compact, non-Măík space

X
X

such that the absolute

E
(
X
)

E(X)

is a Măík space; and a locally compact, Măík space

X
X

for which

E
(
X
)

E(X)

is not. It is also proved that Michael’s product space is not weakly Baire-dominated.
Jumps of orderings
Authors: Ash C. J. , Jockusch C. G. , Knight J. F.
Published: June 2012

Here it is shown that for each recursive ordinal

α
⩾
2

\alpha \geqslant 2

and each Turing degree

d

>

0

(
α
)

{\mathbf {d}} > {{\mathbf {0}}^{(\alpha )}}

, there is a linear ordering

A

{\mathbf {A}}

such that

d

{\mathbf {d}}

is least among the

α
\alpha

th jumps of degrees of (open diagrams of) isomorphic copies of

A

{\mathbf {A}}

and for

β
>
α

\beta > \alpha

, the set of

β
\beta

th jumps of degrees of copies of

A

{\mathbf {A}}

has no least element.
Simple Lie algebras of characteristic 𝑝 with dependent roots
Authors: Benkart Georgia , Osborn J. Marshall
Published: June 2012

We investigate finite dimensional simple Lie algebras over an algebraically closed field

F

{\mathbf {F}}

of characteristic

p
⩾
7

p \geqslant 7

having a Cartan subalgebra

H
H

whose roots are dependent over

F

{\mathbf {F}}

. We show that

H
H

must be one-dimensional or for some root

α
\alpha

relative to

H
H

there is a

1
1

-section

L

(
α
)

{L^{(\alpha )}}

such that the core of

L

(
α
)

{L^{(\alpha )}}

is a simple Lie algebra of Cartan type

H

(
2
:

m
_

:
Φ

)

(
2
)

H{(2:\underline m :\Phi )^{(2)}}

or

W
(
1
:

n
_

)

W(1:\underline n )

for some

n
>
1

n > 1

. The results we obtain have applications to studying the local behavior of simple Lie algebras and to classifying simple Lie algebras which have a Cartan subalgebra of dimension less than

p
−
2

p - 2

.
Surfaces of 𝐸⁴ satisfying certain restrictions on their normal bundle
Authors: Hasanis Th. , Koutroufiotis D. , Pamfilos P.
Published: June 2012

We consider smooth surfaces in

E
4

{E^4}

whose normal bundles satisfy certain geometric conditions that entail the vanishing of the normal curvature, and prove that their Gauss curvatures cannot be bounded from above by a negative number. We also give some results towards a classification of flat surfaces with flat normal bundle in

E
4

{E^4}

.
Rational approximations to L-S category and a conjecture of Ganea
Authors: Jessup Barry
Published: June 2012

The rational version of Ganea’s conjecture for L-S category, namely that

cat
⁡
(
S
×

Σ
k

)
=
cat
⁡
(
S
)
+
1

\operatorname {cat} (S \times {\Sigma ^k}) = \operatorname {cat} (S) + 1

, if

S
S

is a rational space and

Σ
k

{\Sigma ^k}

denotes the

k
k

-sphere, is still open. Recently, a module type approximation to

cat
⁡
(
S
)

\operatorname {cat} (S)

, was introduced by Halperin and Lemaire. We have previously shown that

M
cat

M\operatorname {cat}

satisfies Ganea’s conjecture. Here we show that for

(
r
−
1
)

(r - 1)

connected

S
S

, if

M
cat
⁡
(
S
)

M\operatorname {cat} (S)

is at least

dim
⁡
S

/

2
r

\dim S/2r

, then

M
cat
⁡
(
S
)
=
cat
⁡
(
S
)

M\operatorname {cat} (S) = \operatorname {cat} (S)

. This yields Ganea’s conjecture for these spaces. We also extend other properties of

M
cat

M\operatorname {cat}

, previously unknown for cat, to these spaces.
Complete coinductive theories. I
Authors: Lachlan A. H.
Published: June 2012

Let

T
T

be a complete theory over a relational language which has an axiomatization by

∃
∀

\exists \forall

-sentences. The properties of models of

T
T

are studied. It is shown that quantifier-free formulas are stable. This limited stability is used to show that in

∃
∀

\exists \forall

-saturated models the elementary types of tuples are determined by their

∃
\exists

-types and algebraicity is determined by existential formulas. As an application, under the additional assumption that no quantifier-free formula has the FCP, the models

M

\mathcal {M}

of

T
T

are completely characterized in terms of certain

0
0

-definable equivalence relations on cartesian powers of

M
M

. This characterization yields a result similar to that of Schmerl for the case in which

T
T

is

ℵ
0

{\aleph _0}

-categorical.
Unique continuation for Δ+𝑣 and the C. Fefferman-Phong class
Authors: Chanillo Sagun , Sawyer Eric
Published: June 2012

We show that the strong unique continuation property holds for the inequality

|

Δ
u

|

≤

|
υ
|

|
u
|

\left | {\Delta u} \right | \leq \left | \upsilon \right |\left | u \right |

, where the potential

υ
(
x
)

\upsilon (x)

satisfies the C. Fefferman-Phong condition in a certain range of

p
p

values. We also deal with the situation of

u
(
x
)

u(x)

vanishing at infinity. These are all consequences of appropriate Carleman inequalities.
Invariant Radon transforms on a symmetric space
Authors: Orloff Jeremy
Published: June 2012

Injectivity and support theorems are proved for a class of Radon transforms,

R
μ

{R_\mu }

, for

μ
\mu

a smooth family of measures defined on a certain space of affine planes in

X

0

{\mathbb {X}_0}

, where

X

0

{\mathbb {X}_0}

is the tangent space, of a Riemannian symmetric space of rank one. The transforms are defined by integrating against

μ
\mu

over these planes. We show that if

R
μ

f

{R_\mu }f

is supported inside a ball of radius

R
R

then so is

f
f

. This is true for

f
∈

L
c
2

(

X

0

)

f \in L_c^2({\mathbb {X}_0})

or

f
∈

E

′

(

X

0

)

f \in \mathcal {E}’({\mathbb {X}_0})

. Furthermore,

R
μ

{R_\mu }

is invertible on either of these domains. The main technique is to use facts about spherical harmonics to reduce the problem to a one-dimensional integral equation.
Local rigidity of symmetric spaces
Authors: Schroeder V. , Ziller W.
Published: June 2012

We show that on a symmetric space of noncompact or compact type the metric is locally rigid in the sense that if one changes the metric locally but preserves the curvature bounds, then the new metric is isometric to the old one. We also prove an analytic continuation property for symmetric spaces of rank

≥
3

\ge 3

.
Lie algebra representations of dimension <𝑝²
Authors: Strade Helmut
Published: June 2012

Various methods of representation theory of modular Lie algebras are improved. As an application the structure of the Lie algebras having a faithful irreducible module of dimension

>

p
2

> {p^2}

is determined. Applications to the classification theory of modular simple Lie algebras are given.
Immersions of positively curved manifolds into manifolds with curvature bounded above
Authors: Menninga Nadine L.
Published: June 2012

Let

M
M

be a compact, connected, orientable Riemannian manifold of dimension

n
−
1
⩾
2

n - 1 \geqslant 2

, and let

x
x

be an isometric immersion of

M
M

into an

n
n

-dimensional Riemannian manifold

N
N

. Let

K
K

denote sectional curvature and

i
i

denote the injectivity radius. Assume, for some constant positive constant

c
c

, that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper K left-parenthesis upper N right-parenthesis less-than-or-slanted-equals 1 slash left-parenthesis 4 c squared right-parenthesis comma 1 slash c squared less-than-or-slanted-equals upper K left-parenthesis upper M right-parenthesis">

K
(
N
)
⩽
1

/

(
4

c
2

)
,

1

/

c
2

⩽
K
(
M
)

K(N) \leqslant 1/(4{c^2}),\quad 1/{c^2} \leqslant K(M)

, and

π
c
⩽
i
(
N
)

\pi c \leqslant i(N)

. Then the radius of the smallest

N
N

-ball containing

x
(
M
)

x(M)

is less than

1
2

π
c

\tfrac {1} {2}\pi c

and

x
x

is in fact an imbedding of

M
M

into

N
N

, whose image bounds a convex body.
Two differential-difference equations arising in number theory
Authors: Wheeler Ferrell S.
Published: June 2012

We survey many old and new results on solutions of the following pair of adjoint differential-difference equations: (1)
\[

u

p
′

(
u
)
=
−
a
p
(
u
)
−
b
p
(
u
−
1
)
,

up’(u) = - ap(u) - bp(u - 1),

\]
(2) (
\[

(
u
q
(
u
)

)
′

=
a
q
(
u
)
+
b
q
(
u
+
1
)
.

(uq(u))’ = aq(u) + bq(u + 1).

\]
We bring together scattered results usually proved only for specific

(
a
,
b
)

(a,b)

pairs, while emphasizing the connections between the two equations. We also point out some of the ways these two equations are used in number theory. We giv s several new integral relationships between (1) and (2) and use them to prove a new application of (2) in number theory, namy el
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript StartLayout 1st Row 1 greater-than n less-than-or-slanted-equals x 2nd Row upper P 2 left-parenthesis n right-parenthesis less-than-or-slanted-equals upper P 1 left-parenthesis n right-parenthesis Superscript 1 slash u Baseline EndLayout Endscripts left-parenthesis log upper P 1 left-parenthesis n right-parenthesis right-parenthesis Superscript alpha Baseline tilde u Superscript alpha Baseline f left-parenthesis u right-parenthesis x left-parenthesis log x right-parenthesis Superscript alpha Baseline left-parenthesis x right-arrow normal infinity comma u greater-than-or-slanted-equals 1 comma alpha element-of bold upper R right-parenthesis">

∑

1
>
n
⩽
x

P
2

(
n
)
⩽

P
1

(
n
)

1

/

u

(
log
⁡

P
1

(
n
)
)

α

∼

u
α

f
(
u
)
x

(
log
⁡
x
)

α

(
x
→
∞
,

u
⩾
1
,

α
∈

R

)

\sum \limits _{\begin {array}{*{20}{c}} {1 > n \leqslant x} \\ {{P_2}(n) \leqslant {P_1}{{(n)}^{1/u}}} \\ \end {array} } {{{(\log {P_1}(n))}^\alpha } \sim {u^\alpha }f(u)x{{(\log x)}^\alpha }} \qquad (x \to \infty ,\;u \geqslant 1,\;\alpha \in {\mathbf {R}})

\]
where

P
1

(
n
)

{P_1}(n)

and

P
2

(
n
)

{P_2}(n)

are the first and second largest prime divisors of

n
n

and

f
(
u
)

f(u)

satisfies (2) with

(
a
,
b
)
=
(
1
−
α
,
−
1
)

(a,b) = (1 - \alpha , - 1)

.
Bounds for projection constants and 1-summing norms
Authors: König Hermann , Tomczak-Jaegermann Nicole
Published: June 2012

It is shown that projection constants

λ
(

X
n

)

\lambda ({X_n})

of

n
n

-dimensional normed spaces

X
n

{X_n}

satisfy

λ
(

X
n

)
⩽

n

−
c

/

n

\lambda ({X_n}) \leqslant \sqrt n - c/\sqrt n

where

c
>
0

c > 0

is a numerical constant. Similarly, the

1
1

-summing norms of (the identity of)

X
n

{X_n}

can be estimated by

π
1

(

X
n

)
⩾

n

+
c

/

n

{\pi _1}({X_n}) \geqslant \sqrt n + c/\sqrt n

. These estimates are the best possible: for prime

n
n

, translation-invariant

n
n

-dimensional spaces

X
n

{X_n}

such that

λ
(

X
n

)
⩾

n

−
2

/

n

\lambda ({X_n}) \geqslant \sqrt n - 2/\sqrt n

and

π
1

(

X
n

)
⩽

n

+
2

/

n

{\pi _1}({X_n}) \leqslant \sqrt n + 2/\sqrt n

can be constructed. For these spaces Gordon-Lewis constants and distances to Hilbert spaces are large as well:
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g l left-parenthesis upper X Subscript n Baseline right-parenthesis greater-than-or-slanted-equals one third StartRoot n EndRoot comma d left-parenthesis upper X Subscript n Baseline comma l 2 Superscript n Baseline right-parenthesis equals StartRoot n EndRoot">

gl
⁡
(

X
n

)
⩾

1
3

n

,
d
(

X
n

,

l
2
n

)
=

n

\operatorname {gl} ({X_n}) \geqslant \tfrac {1} {3}\sqrt n ,d({X_n},l_2^n) = \sqrt n

.
A fixed point theorem for weakly chainable plane continua
Authors: Minc Piotr
Published: June 2012

In this paper the fixed point theorem is proven for every plane acyclic continuum

X
X

with the property that every indecomposable continuum in the boundary of

X
X

is contained in a weakly chainable subcontinuum of

X
X

.
The enumerative geometry of plane cubics. I. Smooth cubics
Authors: Aluffi Paolo
Published: June 2012

We construct a variety of complete plane cubics by a sequence of five blow-ups over

P

9

{\mathbb {P}^9}

. This enables us to translate the problem of computing characteristic numbers for a family of plane cubics into one of computing five Segre classes, and to recover classic enumerative results of Zeuthen and Maillard.
𝑁-body Schrödinger operators with finitely many bound states
Authors: Evans W. D. , Lewis Roger T.
Published: June 2012

In this paper we consider a class of second-order elliptic operators which includes atomic-type

N
N

-body operators for

N
>
2

N > 2

. Our concern is the problem of predicting the existence of only a finite number of bound states corresponding to eigenvalues below the essential spectrum. We obtain a criterion which is natural for the problem and easy to apply as is demonstrated with various examples. While the criterion applies to general second-order elliptic operators, sharp results are obtained when the Hamiltonian of an atom with an infinitely heavy nucleus of charge

Z
Z

and

N
N

electrons of charge

1
1

and mass

1
2

\tfrac {1} {2}

is considered.
Identities on quadratic Gauss sums
Authors: Gérardin Paul , Li Wen-Ch’ing Winnie
Published: June 2012

Given a local field

F
F

, each multiplicative character

θ
\theta

of the split algebra

F
×
F

F \times F

or of a separable quadratic extension of

F
F

has an associated generalized Gauss sum

γ
θ
F

\gamma _\theta ^F

. It is a complex valued function on the character group of

F
×

×
F

{F^ \times } \times F

, meromorphic in the first variable. We define a pairing between such Gauss sums and study its properties when

F
F

is a nonarchimedean local field. This has important applications to the representation theory of

G
L
(
2
,
F
)

GL(2,F)

and correspondences

[

GL

3
]

[{\text {GL}}3]

.
Generalized local Fatou theorems and area integrals
Authors: Mair B. A. , Philipp Stan , Singman David
Published: June 2012

Let

X
X

be a space of homogeneous type and

W
W

a subset of

X
×
(
0
,
∞
)

X \times (0,\infty )

. Then, under minimal conditions on

W
W

, we obtain a relationship between two modes of convergence at the boundary

X
X

for functions defined on

W
W

. This result gives new local Fatou theorems of the Carleson-type for solutions of Laplace, parabolic and Laplace-Beltrami equations as immediate consequences of the classical results. Lusin area integral characterizations for the existence of limits within these more general approach regions are also obtained.
Parametrization of domains in 𝐂̂: the logarithmic domains
Authors: Michaliček Johannes , Wehrhahn Rodolfo
Published: June 2012

We prove a generalization of Riemann’s mapping theorem: Every

n
n

-fold connected domain in

C

^

\widehat {\mathbf {C}}

, whose boundary does not contain isolated points, is conformal equivalent to a logarithmic domain. The logarithmic domains are characterized by a Green’s function consisting of a finite sum of logarithms.
On linear topological properties of 𝐻¹ on spaces of homogeneous type
Authors: Müller Paul F. X.
Published: June 2012

Let

(
X
,
d
,
μ
)

(X,d,\mu )

be a space of homogeneous type. Let

B
=
{
x
∈
X
:
μ
{
x
}
=
0
}

B = \{ x \in X:\mu \{ x\} = 0\}

, then

μ
(
B
)
>
0

\mu (B) > 0

implies that

H
1

(
X
,
d
,
μ
)

{H^1}(X,d,\mu )

contains a complemented copy of

H
1

(
δ
)

{H^1}(\delta )

. This applies to Hardy spaces

H
1

(
∂
Ω
,
d
,
ω
)

{H^1}(\partial \Omega ,d,\omega )

associated to weak solutions of uniformly elliptic operators in divergence form. Under smoothness assumptions of the coefficients of the elliptic operators, we obtain that

H
1

(
∂
Ω
,
d
,
ω
)

{H^1}(\partial \Omega ,d,\omega )

is isomorphic to

H
1

(
δ
)

{H^1}(\delta )

.
Mean summability methods for Laguerre series
Authors: Stempak Krzysztof
Published: June 2012

We apply a construction of generalized convolution in
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript 1 Baseline left-parenthesis double-struck upper R Subscript plus Baseline times double-struck upper R comma x Superscript 2 alpha minus 1 Baseline d x d t right-parenthesis comma alpha greater-than-or-slanted-equals 1 comma">

L
1

(

R

+

×

R

,

x

2
α
−
1

d
x
d
t
)
,

α
⩾
1
,

{L^1}({\mathbb {R}_ + } \times \mathbb {R},{x^{2\alpha - 1}}dxdt),\qquad \alpha \geqslant 1,

\]
cf. [8], to investigate the mean convergence of expansions in Laguerre series. Following ideas of [4, 5] we construct a functional calculus for the operator
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L equals minus left-parenthesis StartFraction partial-differential squared Over partial-differential x squared EndFraction plus StartFraction 2 alpha minus 1 Over x EndFraction StartFraction partial-differential Over partial-differential x EndFraction plus x squared StartFraction partial-differential squared Over partial-differential t squared EndFraction right-parenthesis comma x greater-than 0 comma t element-of double-struck upper R comma alpha greater-than-or-slanted-equals 1 period">

L
=
−

(

∂
2

∂

x
2

+

2
α
−
1

x

∂

∂
x

+

x
2

∂
2

∂

t
2

)

,

x
>
0
,

t
∈

R

,

α
⩾
1.

L = - \left ( {\frac {{{\partial ^2}}} {{\partial {x^2}}} + \frac {{2\alpha - 1}} {x}\frac {\partial } {{\partial x}} + {x^2}\frac {{{\partial ^2}}} {{\partial {t^2}}}} \right ),\qquad x > 0,\quad t \in \mathbb {R},\quad \alpha \geqslant 1.

\]
Then, arguing as in [3], we prove results concerning the mean convergence of some summability methods for Laguerre series. In particular, the classical Abel-Poisson and Bochner-Riesz summability methods are included.
Replacing homotopy actions by topological actions. II
Authors: Smith Larry
Published: June 2012

A homotopy action of a group

G
G

on a space

X
X

is a homomorphism from

G
G

to the group

HAUT

(
X
)

{\operatorname {HAUT}}(X)

of homotopy classes of homotopy equivalences of

X
X

. George Cooke developed an obstruction theory to determine if a homotopy action is equivalent up to homotopy to a topological action. The question studied in this paper is: Given a diagram of spaces with homotopy actions of

G
G

and maps between them that are equivariant up to homotopy, when can the diagram be replaced by a homotopy equivalent diagram of

G
G

-spaces and

G
G

-equivariant maps? We find that the obstruction theory of Cooke has a natural extension to this context.
Hölder domains and Poincaré domains
Authors: Smith Wayne , Stegenga David A.
Published: June 2012

A domain

D
⊂

R
d

D \subset {R^d}

of finite volume is said to be a

p
p

-Poincaré domain if there is a constant

M
p

(
D
)

{M_p}(D)

so that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript upper D Endscripts StartAbsoluteValue u minus u Subscript upper D Baseline EndAbsoluteValue Superscript p Baseline d x less-than-or-equal-to upper M Subscript p Superscript p Baseline left-parenthesis upper D right-parenthesis integral Underscript upper D Endscripts StartAbsoluteValue nabla u EndAbsoluteValue Superscript p Baseline d x">

∫
D

|

u
−

u
D

|

p

d
x
≤

M
p
p

(
D
)

∫
D

|

∇
u

|

p

d
x

{\int \limits _D {|u - {u_D}|} ^p}dx \leq M_p^p(D){\int \limits _D {|\nabla u|} ^p}dx

\]
for all functions

u
∈

C
1

(
D
)

u \in {C^1}(D)

. Here

u
D

{u_D}

denotes the mean value of

u
u

over

D
D

. Techniques involving the quasi-hyperbolic metric on

D
D

are used to establish that various geometric conditions on

D
D

are sufficient for

D
D

to be a

p
p

-Poincaré domain. Domains considered include starshaped domains, generalizations of John domains and Hàlder domains.

D
D

is a Hàlder domain provided that the quasi-hyperbolic distance from a fixed point

x
0

∈
D

{x_0} \in D

to

x
x

is bounded by a constant multiple of the logarithm of the euclidean distance of

x
x

to the boundary of

D
D

. The terminology is derived from the fact that in the plane, a simply connected Hàlder domain has a Hàlder continuous Riemann mapping function from the unit disk onto

D
D

. We prove that if

D
D

is a Hàlder domain and

p
≥
d

p \ge d

, then

D
D

is a

p
p

-Poincaré domain. This answers a question of Axler and Shields regarding the image of the unit disk under a Hàlder continuous conformal mapping. We also consider geometric conditions which imply that the imbedding of the Sobolev space

W

1
,
p

(
D
)
→

L
p

(
D
)

{W^{1,p}}(D) \to {L^p}(D)

is compact, and prove that this is the case for a Hàlder domain

D
D

.
Nonmonomial characters and Artin’s conjecture
Authors: Foote Richard
Published: June 2012

If

E

/

F

E/F

is a Galois extension of number fields with solvable Galois group

G
G

, the main result of this paper proves that if the Dedekind zeta-function of

E
E

has a zero of order less than

M

G

{\mathcal {M}_G}

at the complex point

s
0

≠
1

{s_0} \ne 1

, then all Artin

L
L

-series for

G
G

are holomorphic at

s
0

{s_0}

— here

M

G

{\mathcal {M}_G}

is the smallest degree of a nonmonomial character of any subgroup of

G
G

. The proof relies only on certain properties of

L
L

-functions which are axiomatized to give a purely character-theoretic statement of this result.
Construction by isotopy. II
Authors: Silver Daniel S.
Published: June 2012

Construction by isotopy is a technique introduced by Iain R. Aitchison for obtaining doubly slice fibered knots in any dimension. We show that if

k
k

is any doubly slice fibered

(
n
−
2
)

(n - 2)

-knot,

n
⩾
5

n \geqslant 5

, such that

π
1

(

S
n

−
k
)
≅
Z

{\pi _1}({S^n} - k) \cong Z

, then

k
k

is constructible by isotopy. We also prove that the

m
m

-twist-spin of any doubly slice knot is constructible by isotopy. Consequently, there exists a double slice knot constructible by isotopy that is not the double of any disk knot. We also give an example of a doubly slice fibered

6
6

-knot that is not constructible by isotopy.
Maximal functions on classical Lorentz spaces and Hardy’s inequality with weights for nonincreasing functions
Authors: Ariño Miguel A. , Muckenhoupt Benjamin
Published: June 2012

A characterization is given of a class of classical Lorentz spaces on which the Hardy Littlewood maximal operator is bounded. This is done by determining the weights for which Hardy’s inequality holds for nonincreasing functions. An alternate characterization, valid for nondecreasing weights, is also derived.
Symmetric derivates, scattered, and semi-scattered sets
Authors: Freiling Chris
Published: June 2012

We call a set right scattered (left scattered) if every nonempty subset contains a point isolated on the right (left). We establish the following monotonicity theorem for the symmetric derivative. If a real function

f
f

has a nonnegative lower symmetric derivate on an open interval

I
I

, then there is a nondecreasing function

g
g

such that

f
(
x
)
>
g
(
x
)

f(x) > g(x)

on a right scattered set and

f
(
x
)
>
g
(
x
)

f(x) > g(x)

on a left scattered set. Furthermore, if

R
R

is any right scattered set and

L
L

is any left scattered set disjoint with

R
R

, then there is a function which is positive on

R
R

, negative on

L
L

, zero otherwise, and which has a zero lower symmetric derivate everywhere. We obtain some consequence including an analogue of the Mean Value Theorem and a new proof of an old theorem of Charzynski.