We obtain the strong asymptotics of polynomials pn(λ), λ ∈ C, orthogonal with respect to measures in the complex plane of the form e 2s−tλs−tλs)dA(λ), where s is a positive integer, t is a complex parameter and dA stands for the area measure in the plane. Such problem has its origin from normal matrix models. We study the asymptotic behaviour of pn(λ) in the limit n,N → ∞ in such a way that n/N...

We investigate the asymptotic behaviour of spin-spin correlation functions for the integrable Heisenberg chain. To this end we use the Quantum Transfer Matrix (QTM) technique developed in 1 which results in a set of non-linear integral equations (NLIE). In the case of the largest eigenvalue the solution to these equations yields the free energy and by modifications of the paths of integration t...

In this study, modelling and control of a two-link robot manipulator whose first link is rigid and the second one is flexible is considered for both land and underwater conditions. Governing equations of the systems are derived from Hamilton’s Principle and differential eigenvalue problem. A computer program is developed to solve nonlinear ordinary differential equations defining the system dyn...

Let G be a graph with two non adjacent vertices and G′ the graph constructed from G by adding an edge between them. It is known that the trace of Q′ is 2 plus the trace of Q, where Q and Q′ are the signless Laplacian matrices of G and G′ respectively. So, the sum of the Q′-eigenvalues of G′ is the sum of the the Qeigenvalues of G plus two. It is said that Q-spectral integral variation occurs wh...

Recent works on the analysis of linear multiuser receivers for DS-CDMA applications have led to capacity-relevant expressions that are the solution of an integral equation involving Stieltjes transforms of the distribution of transmit powers. The key tools employed in these works are new results on the asymptotic eigenvalue distributions of random matrices. Unfortunately, it is only in the part...

We investigate the asymptotic behaviour of spin-spin correlation functions for the integrable Heisenberg chain. To this end we use the Quantum Transfer Matrix (QTM) technique developed in 1 which results in a set of non-linear integral equations (NLIE). In the case of the largest eigenvalue the solution to these equations yields the free energy and by modifications of the paths of integration t...

Abstract We prove the existence of Sobolev extension operators for certain uniform classes domains in a Riemannian manifold with an explicit bound on norm depending only geometry near their boundaries. use this quantitative estimate to obtain Neumann heat kernel upper bounds and gradient estimates positive solutions equation assuming integral Ricci curvature conditions geometric possibly non-co...

In this paper, we prove that, for compact warped product submanifolds Mn in an Euclidean space En+k, there are no stable p-currents, homology groups vanishing, and M3 is homotopic to the sphere S3 under various extrinsic restrictions, involving eigenvalue of function, integral Ricci curvature, Hessian tensor. The results paper can be considered extension Xin’s work framework a submanifold, when...

Dyson’s integration theorem is widely used in the computation of eigenvalue correlation functions in Random Matrix Theory. Here we focus on the variant of the theorem for determinants, relevant for the unitary ensembles with Dyson index β = 2. We derive a formula reducing the (n − k)-fold integral of an n × n determinant of a kernel of two sets of arbitrary functions to a determinant of size k×...

This paper is concerned with an integral equation that models discrete time dynamics of a population in patchy landscape. The patches the domain are reflected through discontinuity kernel operator at finite number points whole domain. We prove existence and uniqueness stationary state under certain assumptions on principal eigenvalue linearized growth term as well. also derive criteria which un...