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5
5.0

Jun 30, 2018
06/18

by
Praveen S. Venkataramana

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Statistics over the Gaussian unitary ensemble and the Wishart ensemble of random matrices often have nice closed-form expressions. These are related to multivariate extensions of the Hermite, Laguerre, and Jacobi polynomials, which often occur in the study of these ensembles. In the paper, we develop a formal $q$-analog of the Gaussian unitary ensemble, using $q$-Hermite polynomials and coefficient extraction instead of integration. This way we derive $q$-analogs for many well-known eigenvalue...

Topics: Mathematics, Combinatorics, Mathematical Physics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1407.7960

5
5.0

Jun 30, 2018
06/18

by
Meysam Alishahi; Hossein Hajiabolhassan

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For a graph $G$, the tree graph ${\cal T}_{G,t}$ has all tree subgraphs of $G$ with $t$ vertices as vertex set and two tree subgraphs are neighbors if they are edge-disjoint. Also, the $r^{th}$ cut number of $G$ is the minimum number of edges between parts of a partition of vertex set of $G$ into two parts such that each part has size at least $r$. We show that if $t=(1-o(1))n$ and $n$ is large enough, then for any dense graph $G$ with $n$ vertices, the chromatic number of the tree graph ${\cal...

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1407.8035

4
4.0

Jun 30, 2018
06/18

by
Zh. G. Nikoghosyan

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Let $G$ be a graph on $n$ vertices, $p$ the order of a longest path and $\kappa$ the connectivity of $G$. In 1989, Bauer, Broersma Li and Veldman proved that if $G$ is a 2-connected graph with $d(x)+d(y)+d(z)\ge n+\kappa$ for all triples $x,y,z$ of independent vertices, then $G$ is hamiltonian. In this paper we improve this result by reducing the lower bound $n+\kappa$ to $p+\kappa$.

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1407.8129

4
4.0

Jun 30, 2018
06/18

by
Markus Seidel

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In this paper we study the semi-Fredholm property of band-dominated operators $A$ and prove that it already implies the Fredholmness of $A$ in all cases where this is not disqualified by obvious reasons. Moreover, this observation is applied to show that the Fredholmness of a band-dominated operator already follows from the surjectivity of all its limit operators.

Topics: Functional Analysis, Mathematics

Source: http://arxiv.org/abs/1407.8104

3
3.0

Jun 30, 2018
06/18

by
Teruhisa Tsuda

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We study the linear Pfaffian systems satisfied by a certain class of hypergeometric functions, which includes Gau\ss's ${}_2 F_{1}$, Thomae's ${}_L F_{L-1}$ and Appell-Lauricella's $F_D$. In particular, we present a fundamental system of solutions with a characteristic local behavior by means of Euler-type integral representations. We also discuss how they are related to the theory of isomonodromic deformations or Painlev\'e equations.

Topics: Mathematics, Classical Analysis and ODEs

Source: http://arxiv.org/abs/1407.8052

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61

Jun 30, 2018
06/18

by
A. O. Smirnov; E. G. Semenova; V. Zinger; N. Zinger

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A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is investigated. An existence of a real smooth finite-gap solution of NLS equation with complex initial phase is proven. Degenerations of the constructed solution to one-phase traveling wave solution and solutions in the form of the plane waves are carried.

Topics: Mathematics, Nonlinear Sciences, Exactly Solvable and Integrable Systems, Mathematical Physics,...

Source: http://arxiv.org/abs/1407.7974

8
8.0

Jun 30, 2018
06/18

by
Timothy C. Burness; Elisa Covato

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Let $G$ be a finite group, let $\pi(G)$ be the set of prime divisors of $|G|$ and let $\Gamma(G)$ be the prime graph of $G$. This graph has vertex set $\pi(G)$, and two vertices $r$ and $s$ are adjacent if and only if $G$ contains an element of order $rs$. Many properties of these graphs have been studied in recent years, with a particular focus on the prime graphs of finite simple groups. In this note, we determine the pairs $(G,H)$, where $G$ is simple and $H$ is a proper subgroup of $G$ such...

Topics: Mathematics, Combinatorics, Group Theory

Source: http://arxiv.org/abs/1407.8128

5
5.0

Jun 30, 2018
06/18

by
Oxana A. Manita; Maxim S. Romanov; Stanislav V. Shaposhnikov

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We study uniqueness of flows of probability measures solving the Cauchy problem for nonlinear Fokker-Planck-Kolmogorov equation with unbounded coefficients. Sufficient conditions for uniqueness are indicated and examples of non-uniqueness are constructed.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.8047

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