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In this paper we define a class of coverage processes with infinitely divisible finite dimensional distributions and a particular type of correlation structure that can be thought of as generalizations of the classical Ornstein--Uhlenbeck…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form f(Ricci) that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher…
We consider a natural way of extending the Lebesgue covering dimension to various classes of infinite dimensional separable metric spaces.
The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The…
Following "An infinite dimensional Schur-Horn theorem and majorization theory", Journal of Functional Analysis 259 (2010) 3115-3162, this paper further studies majorization for infinite sequences. It extends to the infinite case classical…
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
A general functional definition of the infinite dimensional quantum $R$-matrix satisfying the Yang-Baxter equation is given. A procedure for the extracting a finite dimensional $R$-matrix from the general definition is demonstrated in a…
Given finitely many consecutive terms of an infinite sequence, we discuss the construction of a polynomial difference equation that the sequence may satisfy. We also present a method to seek a candidate polynomial differential equation for…
In this paper we consider the multi-dimensional Quantum Hydrodynamics (QHD) system, by adopting an intrinsically hydrodynamic approach. The present work continues the analysis initiated in [6] where the one dimensional case was studied.…
The increasing rate of the Birkhoff sums in the infinite iterated function systems with polynomial decay of the derivative (for example the Gauss map) is studied. For different unbounded potential functions, the Hausdorff dimensions of the…
We describe the utility of integral representations for sums of basic hypergeometric functions. In particular we use these to derive an infinite sequence of transformations for symmetrizations over certain variables which the functions…
We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian…
We construct a class of infinite-dimensional Frobenius manifolds on the spaces of pairs of meromorphic functions with a pole at infinity and a movable pole. Such Frobenius manifolds are shown to be underlying the universal Whitham…
This work presents an algorithm for numerically computing Maass forms and their eigenvalues for Fuchsian groups of infinite covolume. By Patterson-Sullivan theory, this has the added benefit of computing Hausdorff dimensions of the limit…
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
It is shown that the question raised in Section 5.7 of [1] has an affirmative answer.
We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…
In this work we construct a infinite dimensional $\ell$-super Galilean conformal algebra, which is a generalization of the $\ell=1$ algebra found in the literature. We give a classification of central extensions, the vector field…
Expanding products of invariant functions of a group element as a series in the basis of characters of the irreducible representations of a group is widely used in many areas of physics and related fields. In this contribution a formula to…