Miracle-dz/UniFAR-FTUs huggingface dataset:
Gamma-Ray Line Signals from Supernovae within 100 Mpc

The average number of supernovae per year detectable by γ-rays emitted during the decay of 56Ni to 56Fe is estimated for galaxies within 100 Mpc as a function of limiting sensitivity using standard supernova yields and the Sternberg and Asiago supernova catalogs. An instrument having a broad-line (5000 km s-1) sensitivity of 2 × 10-6 γ s-1 cm-2 should detect a minimum of 1.0 ± 0.5 Type Ia supernovae per year, and observe all Type Ia events from the Virgo, Fornax, and possibly the Hydra galaxy clusters. Roughly 10%-30% of all Type Ia supernovae within 100 Mpc are detectable at this flux sensitivity. Instruments having broad-line flux sensitivities larger than 1.5 × 10-5 γ s-1 cm-2 will probably only detect rare Type Ia supernovae within 10 Mpc, such as SN 1972E or SN 1991T. Flux sensitivities of ≃2 × 10-6 γ s-1 cm-2 to intermediate-width γ-ray lines should enable the detection of a minimum of 0.2 ± 0.2 Type Ib and Type Ic supernovae per year, and easily allow events similar to SN 1983N and SN 1985F to be seen. Instruments of the near future will not detect the narrow-line γ rays from any Type II supernovae that originate beyond the Local Group of galaxies. These number and rate estimates provide guidelines for the design of future γ-ray missions.
Barotropic waves along an eastern continental shelf

Abstract An analysis is presented of the propagation of barotropic non-divergent oscillations along the western side of an ocean basin along which the persistent circulation in the basin is strongly intensified and laterally sheared. Because the Rossby number of a western boundary current is near unity, the properties of these waves are strongly affected by the steady circulation pattern. It is shown that for relatively long wavelengths, these waves can travel along the shelf in both directions; however, for a small range of short wavelengths they can only propagate northward and are unstable. Along the southeastern coast of North America, the unstable waves have wavelengths of order 150 km and periods of order 10 days. However, these waves can become stable oscillations in the deeper water northeast of Cape Hatteras. These oscillations are a possible explanation of the initiation of Gulf Stream meanders along the continental rise.
A13CO Survey of Molecular Clouds in Gemini and Auriga

A large-scale survey for molecular clouds in 13CO(J = 1-0) was performed toward the Gemini and Auriga regions (170° < l ≤ 196° and -10° ≤ b < 10°) with velocity coverages of -30 < VLSR < +30 km s-1 and -20 < VLSR < +40 km s-1 for 170° < l ≤ 188° and 188° < l ≤ 196°, respectively, by using the two 4 m millimeter-wave telescopes at Nagoya University. An area of 520 deg2 was covered at an 8' grid spacing with a 2. ′7 beam, and 29,250 positions were observed. Significant 13CO emission (≥1.2 K km s-1 = 3 σ) is detected at 1032 positions, and 139 distinct 13CO clouds are identified. Physical properties such as molecular column density, size, and mass are derived for each cloud. Comparison with known H II regions and other associated visible objects indicates that 98 of the 139 clouds are located at ~2 kpc, while the rest lie at ≲ 1 kpc. The candidates for protostars are selected from IRAS point sources and 141 sources are identified as protostellar candidates associated with the 13CO clouds. A statistical study of the 13CO clouds and of the candidates for protostars shows the following results: 1. The mass spectra of the 13CO clouds are well represented by a power law, Ncloud(≥Mcloud) = 1.4 × 104(Mcloud/M☉)-0.83 - 1.4 for the clouds at ~2 kpc and Ncloud(≥Mcloud) = 3.5 × 102(Mcloud/M☉)-0.64 - 2.4 for the rest. 2. The line width, ΔVcomp, and the size, R, of the 13CO clouds show a power-law relation with an index 0.24 ± 0.06, where the dispersion in the fitting is fairly large. 3. A virial analysis made for the 13CO clouds indicates that the relation between the virial mass, Mvir, and the mass measured in 13CO, Mcloud, is aproximated well by (Mvir/M☉) = 2.0 × 101(Mcloud/M☉)0.72, which suggests that smaller clouds tend to be more weakly bound gravitationally than larger clouds or are dispersing if the external pressure is negligible. This is probably the cuase of a small index value of the line width-size relation. 4. The luminosity function of the IRAS point sources associated with 13CO clouds are well represented by a power law with Nstar(≥Lstar) = 4.0 × 102L-1.9×10 for those at ~2 kpc and Nstar(≥Lstar) = 2.3 × 10L-3.2 for the rest. 5. The luminosity of the most luminous IRAS point source in a given molecular cloud increases systematically with the mass of the associated cloud. 6. The 13CO clouds associated with IRAS point sources, which are regarded as ongoing star-forming clouds, tend to be more massive and larger in size and to have higher column densities than those without any sign of star formation. These relations are found to be consistent with those derived in Cygnus by Dobashi, Bernard, & Fukui and in Cepheus-Cassiopeia by Yonekura et al. In order to study the star formation activities, we studied the ratio of virial mass and the mass measured in 13CO, Mvir/Mcloud, and its relation with star formation. It is clearly seen that the star-forming 13CO clouds have low Mvir/Mcloud, and all the clouds with high Mvir/Mcloud exhibit no sign of star formation. This suggests that star formation rarely occurs in clouds with overall kinetic energy higher than the gravitational energy.
Equivalent sets of coherent states of the 1D infinite square well and properties

We prove the equivalence (under some conditions) of two sets of coherent states built for the one-dimensional infinite square well: the so-called generalized and Gaussian Klauder coherent states. We then derive an approximate close expression approaching their probability density and wave function to explore their properties analytically. This process gives thereby explanation of the quasi-classical behavior of these states in terms of the main observables and the Heisenberg uncertainty product
Optimal Learning with a Neural Network

We introduce optimal learning with a neural network, which we define as minimising the expectation generalisation error. We find that the optimally-trained spherical perceptron may learn a linearly-separable rule as well as any possible network. We sketch an algorithm to generate optimal learning, and simulation results support our conclusions. Optimal learning of a well-known, significant unlearnable problem, the “mismatched weight” problem, gives better asymptotic learning than conventional techniques, and may be simulated enormously more easily. Unlike many other learning schemes, optimal learning extends to more general networks learning more complex rules.
A Theoretical Study of the Wet Removal of Atmospheric Pollutants. Part IV: The Uptake and Redistribution of Aerosol Particles through Nucleation and Impaction Scavenging by Growing Cloud Drops and Ice Particles

Abstract A theoretical model has been formulated which allows the study of the effects of an ice phase on the removal of atmospheric aerosol particles by nucleation and impaction scavenging in a convective cloud. This microphysical model—although in principle applicable to higher dimensional cloud dynamic models—was tested by using a simple parcel model with entrainment as the dynamic framework. The present model has been applied to and numerically evaluated for a convective cloud in which the cloud particles grow via vapor deposition, collision, and coalescence and riming. The computations were carried out for a rural-background aerosol of given particle size distribution. Two different chemical compositions of the aerosol particles and two different modes of ice initiation were considered. Our study shows for in-cloud scavenging (i) scavenging of aerosol particles by drop nucleation dominates impaction scavenging by drops as well as all other scavenging mechanisms; (ii) scavenging of aerosol particles b.
Inhomogeneous self-similar sets and box dimensions

We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than the upper box dimension, Hausdorff dimension and packing dimension.
MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms

Abstract We investigate a relationship between MacMahon's generalized sum-of-divisors functions and Chebyshev polynomials of the first kind. This determines a recurrence relation to compute these functions, as well as proving a conjecture of MacMahon about their general form by relating them to quasi-modular forms. These functions arise as solutions to a curve-counting problem on Abelian surfaces.
On Fourier Analytic Properties of Graphs

We study the Fourier dimensions of graphs of real-valued functions defined on the unit interval (0;1). Our results imply that the graph of fractional Brownian motion is almost surely not a Salem set, answering in part a question of Kahane from 1993, and that the graph of a Baire typical function inC(0;1) has Fourier dimension zero.
Slowly oscillating wavefronts of the KPP-Fisher delayed equation

This paper concerns the semi-wavefronts (i.e. bounded solutions $u=\phi(x \nu +ct) >0,$ $ |\nu|=1, $ satisfying $\phi(-\infty)=0$) to the delayed KPP-Fisher equation $$u_t(t,x) = \Delta u(t,x) + u(t,x)(1-u(t-\tau,x)), \ u \geq 0,\ x \in \R^m. \eqno(*)$$ First, we show that each semi-wavefront should be either monotone or slowly oscillating. Then a complete solution to the problem of existence of semi-wavefronts is provided. We prove next that the semi-wavefronts are in fact wavefronts (i.e. additionally $\phi(+\infty)=1$) if $c \geq 2$ and $\tau \leq 1$; our proof uses dynamical properties of some auxiliary one-dimensional map with the negative Schwarzian. The analysis of the fronts' asymptotic expansions at infinity is another key ingredient of our approach. It allows to indicate the maximal domain ${\mathcal D}_n$ of $(\tau,c)$ where the existence of non-monotone wavefronts can be expected. Here we show that the problem of wavefront's existence is closely related to the Wright's global stability conjecture.
Isomorphism of compactifications of moduli of vector bundles: nonreduced moduli

A morphism of the moduli functor of admissible semistable pairs to the Gieseker -- Maruyama moduli functor (of semistable coherent torsion-free sheaves) with the same Hilbert polynomial on the surface, is constructed. It is shown that these functors are isomorphic, and main components of moduli scheme for semistable admissible pairs are isomorphic to main components of the Gieseker -- Maruyama moduli scheme
Self-assembly of geometric space from random graphs

We present a Euclidean quantum gravity model in which random graphs dynamically self-assemble into discrete manifold structures. Concretely, we consider a statistical model driven by a discretisation of the Euclidean Einstein–Hilbert action; contrary to previous approaches based on simplicial complexes and Regge calculus our discretisation is based on the Ollivier curvature, a coarse analogue of the manifold Ricci curvature defined for generic graphs. The Ollivier curvature is generally difficult to evaluate due to its definition in terms of optimal transport theory, but we present a new exact expression for the Ollivier curvature in a wide class of relevant graphs purely in terms of the numbers of short cycles at an edge. This result should be of independent intrinsic interest to network theorists. Action minimising configurations prove to be cubic complexes up to defects; there are indications that such defects are dynamically suppressed in the macroscopic limit. Closer examination of a defect free model shows that certain classical configurations have a geometric interpretation and discretely approximate vacuum solutions to the Euclidean Einstein–Hilbert action. Working in a configuration space where the geometric configurations are stable vacua of the theory, we obtain direct numerical evidence for the existence of a continuous phase transition; this makes the model a UV completion of Euclidean Einstein gravity. Notably, this phase transition implies an area-law for the entropy of emerging geometric space. Certain vacua of the theory can be interpreted as baby universes; we find that these configurations appear as stable vacua in a mean field approximation of our model, but are excluded dynamically whenever the action is exact indicating the dynamical stability of geometric space. The model is intended as a setting for subsequent studies of emergent time mechanisms.
A Combinatorial Approach to the Number of Solutions of Systems of Homogeneous Polynomial Equations over Finite Fields

We give a complete conjectural formula for the number $e_r(d,m)$ of maximum possible ${\mathbb{F}}q$-rational points on a projective algebraic variety defined by $r$ linearly independent homogeneous polynomial equations of degree $d$ in $m+1$ variables with coefficients in the finite field ${\mathbb{F}}q$ with $q$ elements, when $d<q$. It is shown that this formula holds in the affirmative for several values of $r$. In the general case, we give explicit lower and upper bounds for $e_r(d,m)$ and show that they are sometimes attained. Our approach uses a relatively recent result, called the projective footprint bound, together with results from extremal combinatorics such as the Clements-Lindstr\"om Theorem and its variants. Applications to the problem of determining the generalized Hamming weights of projective Reed-Muller codes are also included.
MUA versus Arthroscopic Capsular Release of Idiopathic Frozen Shoulder

Background: Adhesive capsulitis is adisease characterized by the spontaneous onset of shoulder pain and global limitation of both active and passive shoulder motion. The main aim of this study was to evaluate and compare early results of MUA and ACR in management of primary frozen shoulder after failure of conservative treatment. Methods: This prospective study was carried out on Thirty patients with primary frozen shoulder, half of them were treated with MUA (group 1) and the other half treated with ACR (group 2) and followed for a minimum of 6 months. The study conducted at Orthopedic Surgery department, Faculty of Medicine, Benha University. Results: In the present study, no significant difference was found between MUA and ACR. We found negative moderate correlation between age and Constant Murley score. We found also that there was statistically significant negative strong correlation between HbA1C and Flexion and External rotation, and a statistically significant positive strong correlation was found between HbA1C, OSS and internal rotation. Both MUA and ACR treatments give high satisfaction rate but cases treated with ACR were more satisfied but with no significant difference with MUA treatment. Conclusion: Successful clinical and functional outcomes can be obtained with both MUA and ACR in the treatment of refractory FS without major serious complications.
Consumer Cities: The Role of Housing Variety*

Housing costs are key in understanding real income differences across space and time. Standard measures of housing costs do not account for availability differences, where some housing varieties are available in certain cities or time periods but not others. When households have idiosyncratic preferences over housing units, the set of available housing varieties in a city matters. This paper develops theoretically-founded housing price indices to measure housing costs that account for availability differences. To allow for flexible substitution patterns, I propose a method to jointly estimate the nests that varieties belong to and the elasticity of substitution across varieties within each nest. I find that households in larger cities benefit from having access to varieties not available in smaller cities. Utility-consistent housing prices reduce the elasticity of housing prices with respect to population by a half. Since housing is a third of household expenditure, this implies that we have systematically underestimated real income and overestimated residual amenities in larger cities. In contrast to previous estimates, I find that real income is increasing in city size after accounting for availability differences. *I am grateful to Don Davis, Bernard Salanié, and David Weinstein for their encouragement and support throughout this project. I thank Iain Bamford, Gautam Gowrisankaran, Yi Jie Gwee, Jessie Handbury, Réka Juhász, Amit Khandelwal, Cameron LaPoint, Simon Lee, Sang Hoon Kong, Serena Ng, Nathaniel Baum-Snow, Pietro Tebaldi, Stijn G. Van Nieuwerburgh, Eric Verhoogen, Pablo E. Warnes, and Yue Yu, for helpful comments and discussions. This work was completed in part with resources provided by the Columbia University’s Shared Research Computing Facility project. Data provided by Zillow through the Zillow Transaction and Assessment Dataset (ZTRAX). More information on accessing the data can be found at http://www.zillow. com/ztrax. The results and opinions are those of the author(s) and do not reflect the position of Zillow Group. †Department of Economics, Columbia University, 1022 International Affairs Building, 420 W 118th Street, New York, NY 10027. Email: howard.zhang@columbia.edu.
Loss of derivatives for hyperbolic boundary problems with constant coefficients

Symmetric hyperbolic systems and constantly hyperbolic systems with constant coefficients and a boundary condition which satisfies a weakened form of the Kreiss-Sakamoto condition are considered. A well-posedness result is established which generalizes a theorem by Chazarain and Piriou for scalar strictly hyperbolic equations and non-characteristic boundaries from 1972. The proof is based on an explicit solution of the boundary problem by means of the Fourier-Laplace transform. As long as the operator is symmetric, the boundary is allowed to be characteristic.
Variable Hardy spaces associated with operators satisfying Davies–Gaffney estimates on metric measure spaces of homogeneous type

Abstract Let L be a one-to-one operator of type ω in L(R), with ω ∈ [0, π/2), which has a bounded holomorphic functional calculus and satisfies the Davies-Gaffney estimates. Let p(·) : R → (0, 1] be a variable exponent function satisfying the globally log-Hölder continuous condition. In this article, the authors introduce the variable Hardy space H p(·) L (R ) associated with L. By means of variable tent spaces, the authors establish the molecular characterization of H p(·) L (R ). Then the authors show that the dual space of H p(·) L (R ) is the BMO-type space BMOp(·), L∗(R ), where L∗ denotes the adjoint operator of L. In particular, when L is the second order divergence form elliptic operator with complex bounded measurable coefficients, the authors obtain the non-tangential maximal function characterization of H p(·) L (R ) and show that the fractional integral L for α ∈ (0, 12 ] is bounded from H p(·) L (R ) to H q(·) L (R ) with 1 p(·) − 1 q(·) = 2α n and the Riesz transform ∇L−1/2 is bounded from H L (R) to the variable Hardy space H(R).
Simultaneous optimization of mechanical properties of steel by maximizing exponential desirability functions

A modelling approach to optimize a multiresponse system is presented. The approach aims to identify the setting of the input variables to maximize the degree of overall satisfaction with respect to all the responses. An exponential desirability functional form is suggested to simplify the desirability function assessment process. The approach proposed does not require any assumptions regarding the form or degree of the estimated response models and is robust to the potential dependences between response variables. It also takes into consideration the difference in the predictive ability as well as relative priority among the response variables. Properties of the approach are revealed via two real examples—one classical example taken from the literature and another that the authors have encountered in the steel industry.
Global measures of ionospheric electrodynamic activity inferred from combined incoherent scatter radar and ground magnetometer observations

An analysis of several global measures of high-latitude ionospheric electrodynamic activity is undertaken on the basis of results obtained from the Assimilative Mapping of Ionospheric Electrodynamics (AMIE) procedure applied to incoherent scatter radar and ground magnetometer observations for January 18–19, 1984. Different global measures of electric potentials, currents, resistances, and energy transfer from the magnetosphere show temporal variations that are generally well correlated. We present parameterizations of these quantities in terms of the AE index and the hemispheric power index of precipitating auroral particles. It is shown how error estimates of the mapped electric fields can be used to correct the estimation of Joule heating. Global measures of potential drop, field-aligned current, and Joule heating as obtained by the AMIE procedure are compared with similar measures presented in previous studies. Agreement is found to within the uncertainties inherent in each study. The mean potential drop through which field-aligned currents flow in closing through the ionosphere is approximately 28% of the total polar cap potential drop under all conditions during these 2 days. We note that order-of-magnitude differences can appear when comparing different global measures of total electric current flow and of effective resistances of the global circuit, so that care must be exercised in choosing characteristic values of these parameters for circuit-analogy studies of ionosphere-magnetosphere electrodynamic coupling.
Fourier transform containing a pair of complex gamma functions with a monomial: Mathematical and physical applications

One of the goals of the present paper is to propose an elementary method to find a general formula for the Fourier transform containing a pair of complex gamma functions with a monomial sm in terms of Gauss's hypergeometric functions 2F1. We further collect some mathematical results that follow by means of this transform. Physical applications requiring the expectation values of position and momentum operators for a quantum system endowed with position-dependent effective mass are presented.
On the convergence of the accelerated Riccati iteration method

ABSTRACT In this paper, we establish results fully addressing two open problems proposed recently by I. Ivanov, see Nonlinear Analysis 69 (2008) 4012–4024, with respect to the convergence of the accelerated Riccati iteration method for solving the continuous coupled algebraic Riccati equation, or CCARE for short. These results confirm several desirable features of that method, including the monotonicity and boundedness of the sequences it produces, its capability of determining whether the CCARE has a solution, the extremal solutions it computes under certain circumstances, and its faster convergence than the regular Riccati iteration method.