The paper addresses the stability analysis of linear circuits and systems under interval parameter uncertainties. The problem is equivalent of estimating the eigenvalues of matrices, which elements are nonlinear functions of interval parameters. A method for obtaining the exact range of the eigenvalues is suggested. It can be applied if certain monotonicity conditions are fulfilled. A method fo...

This study describes amended parallel analysis (APA), a novel method for model selection in unsupervised learning problems such as information retrieval (IR). At issue is the selection of k, the number of dimensions retained under latent semantic indexing (LSI). APA is an elaboration of Horn’s parallel analysis, which advocates retaining eigenvalues larger than those that we would expect under ...

let $n$ be any positive integer and let $f_n$ be the friendship (or dutch windmill) graph with $2n+1$ vertices and $3n$ edges. here we study graphs with the same adjacency spectrum as the $f_n$. two graphs are called cospectral if the eigenvalues multiset of their adjacency matrices are the same. let $g$ be a graph cospectral with $f_n$. here we prove that if $g$ has no cycle of length $4$ or $...

The paper addresses the stability analysis of linear continuous systems under interval uncertainties. This problem initially described by the characteristic polynomial is transformed into a corresponding eigenvalue problem. The final analysis is equivalent to estimating the eigenvalues of matrices which elements are nonlinear functions of interval parameters. A method for obtaining the exact ra...

Given a family X(t) of continuous–time nearest–neighbor random walks on the one dimensional lattice Z, parameterized by n ∈ N+, we show that the spectral analysis of the Markov generator of X with Dirichlet conditions outside (0, n) reduces to the analysis of the eigenvalues and eigenfunctions of a suitable generalized second order differential operator −DmnDx with Dirichlet conditions outside ...

in this paper, the rayleigh's quotient and the inverse vector iteration method are presented. the latter approach helps to obtain the natural frequencies and mode shapes of a structure. inverse vector iteration method with shifting enables to determine the higher modes. some basic theorems of linear algebra are presented and extended to study the free vibration of structures. the variation...

In this paper, we review analytical methods for a rigorous study of the existence and stability of stationary, multiple spots for reaction-diffusion systems. We will consider two classes of reaction-diffusion systems: activator-inhibitor systems (such as the Gierer-Meinhardt system) and activator-substrate systems (such as the Gray-Scott system or the Schnakenberg model). The main ideas are pre...

In this paper, we obtain a comparison of Steklov eigenvalues and Laplacian on graphs discuss its rigidity. As applications the eigenvalues, Lichnerowicz-type estimates some combinatorial for graphs.

Mansfield College MMath in Mathematics Can you hear the shape of a cavity? In this paper we analyse the question " Can one hear the shape of a drum? " [1] presented by Mark Kac in 1966 [1]. We start in Chapter 1 by formalising the question in the form of a differential equation and introducing a simple finite difference scheme to analyse the question. We show how this relates to a matrix eigenv...

In this paper, we apply homotopy analysis method (HAM) for computing the eigenvalues of SturmLiouville problems. The parameter h, in this method, helps us to adjust and control the convergence region. The results show that this method has validity and high accuracy with less iteration number in compare to Variation Iteration Method (VIM) and Adomian decomposition method (ADM). Moreover it is il...