We bound the second eigenvalue of random d $$ -regular graphs, for a wide range degrees , using novel approach based on Fourier analysis. Let G n {G}_{n,d} be uniform graph vertices, and λ ( ) \lambda \left({G}_{n,d}\right) its largest by absolute value. For some constant c > 0 c>0 any degree with log 10 ≪ ≤ {\log}^{10}n\ll d\le cn we show that = 2 + o 1 − / \left({G}_{n,d}\right)=\left(2+o(1)\...

given four complex matrices a, b, c and d where a 2 cnn and d 2 cmm andlet the matrix(a bc d)be a normal matrix and assume that  is a given complex number that is not eigenvalue of matrix a. we present a method to calculate the distance norm (with respect to 2-norm) from d to the set of matrices x 2 cmm such that,  be a multiple eigenvalue of matrix(a bc x). we also nd the nearest matrix ...

In this paper we prove that all pure Artin braid groups $$P_n$$ ( $$n\ge 3$$ ) have the $$R_\infty $$ property. order to obtain result, analyse naturally induced morphism $${\text {Aut}}\left( {P_n}\right) \longrightarrow {\text {\Gamma _2 (P_n)/\Gamma _3(P_n)}\right) which turns out factor through a representation $$\rho :S_{{n+1}} . We can then use theory of symmetric show any automorphism $$...

We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized problems same size as matrices initial The is applicable for right definite problems, possibly after performing an affine transformation. This includes class Helmholtz equations when separation variables applied. provide convergence proof ...

We consider general linear non-degenerate weak-coupled cooperative elliptic systems and study certain monotonicity properties of the generalized principal eigenvalue in Rd with respect to potential. It is shown that on right equivalent recurrence property twisted operator which is, turn, minimal growth at infinity eigenfunctions. The strict be exponential stability operators. An equivalence bet...

This is a technical note where we solve the additive eigenvalue problem associated to a dynamics of a 2D-traffic system. The traffic modeling is not explained here. It is available in [2]. It consists of a microscopic road traffic model of two circular roads crossing on one junction managed with the priority-to-the-right rule. It is based on Petri nets and minplus algebra. One of our objectives...

In this paper we give a new method to convert results dealing with graph theoretic (or Markov chain) Laplacians into results concerning Laplacians in analysis, such as on Riemannian manifolds. We illustrate this method by using the results of [CGY97] to prove λ1 ≤ 1 dist(X,Y ) ( cosh−1 √ μXc μY c μX μY )2 . for λ1 the first positive Neumann eigenvalue on a connected compact Riemannian manifold,...

Two inverse eigenvalue problems are discussed. First, given the eigenvalues and a weight vector an extended Hessenberg matrix is computed. This matrix represents the recurrences linked to a (rational) Arnoldi inverse problem. It is well-known that the matrix capturing the recurrence coefficients is of Hessenberg form in the standard Arnoldi case. Considering, however, rational functions and adm...

Given an eigenvalue of a symplectic matrix, we analyze its change under small structure-preserving perturbations, i.e., perturbations which maintain the symplectic nature of the matrix. Modelling such perturbations multiplicatively allows us to make use of the first order multiplicative perturbation theory developed in [2] via Newton diagram techniques. This leads to both leading exponents and ...