Related papers: Amalgamated R-diagonal Pairs
This paper studies the asymptotic behaviors of the pairwise angles among n randomly and uniformly distributed unit vectors in R^p as the number of points n -> infinity, while the dimension p is either fixed or growing with n. For both…
Orthogonal polynomials are of fundamental importance in many fields of mathematics and science, therefore the study of a particular family is always relevant. In this manuscript, we present a survey of some general results of the Hermite…
In this work, we obtained separation results via codimension-1 maps to generalized manifolds. More specifically, we proved results that allow us to estimate the number of connected components of the complement of the image of such maps.
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
We study dg-manifolds which are R[2]-bundles over R[1]-bundles over manifolds, we calculate its symmetries, its derived symmetries and we introduce the concept of T-dual dg-manifolds. Within this framework we construct the T-duality map as…
We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.
We generalize the array orthogonality property for perfect autocorrelation sequences to $n$-dimensional arrays. The generalized array orthogonality property is used to derive a number of $n$-dimensional perfect array constructions.
In this paper, we introduce the notion of conditionally bi-free independence in an amalgamated setting. We define operator-valued conditionally bi-multiplicative pairs of functions and construct operator-valued conditionally bi-free moment…
We introduce the notion of a bivariate random discrete copula on an equidistant mesh and explore its stochastic properties. A random discrete copula is a discrete random field, hence, its value at a given point on the mesh is a random…
A disordered structure embedding an active gain material and able to lase is called random laser (RL). The RL spectrum may appear either like a set of sharp resonances or like a smooth line superimposed to the fluorescence. A recent letter…
We study a prototypical model of two coupled two-level systems, where the competition between coherent and dissipative coupling gives rise to a rich phenomenology. In particular, we analyze the case of asymmetric coupling, as well as the…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
We present a pairing of automorphic distributions that applies in situations where a Lie group acts with an open orbit on a product of generalized flag varieties. The pairing gives meaning to an integral of products of automorphic…
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…
In this note we study inhomogeneous random bipartite graphs in random environment. These graphs can be thought of as an extension of the classical Erd\"os-R\'enyi random graphs in a random environment. We show that the expected number of…
Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the ratio $X/Y$ is derived. Some basic distributional properties are also derived, including…
Let a polygon be composed of equal rectangles. We find all quadratic irrationals r for which the polygon can be tiled by similar rectangles with given side ratio r.
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
We study the mutual information estimation for mixed-pair random variables. One random variable is discrete and the other one is continuous. We develop a kernel method to estimate the mutual information between the two random variables. The…
Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…