In this article we study the asymptotic behavior of small eigenvalues Riemann surfaces for large genus. We show that any positive integer $k$, as genus $g$ goes to infinity, smallest $k$-th eigenvalue in thick part moduli space is uniformly comparable $\frac{1}{g^2}$ $g$. proof upper bound, constant $\epsilon>0$, will construct a closed surface $\epsilon$-thick such it admits pants decompositio...

An efficient technique is presented for optimum design of structures with both natural frequency and complex frequency response constraints. The main ideals to reduce the number of dynamic analysis by introducing high quality approximation. Eigenvalues are approximated using the Rayleigh quotient. Eigenvectors are also approximated for the evaluation of eigenvalues and frequency responses. A tw...

the analysis of cross-correlations is extensively applied for understanding of interconnections in stock markets. variety of methods are used in order to search stock cross-correlations including the random matrix theory (rmt), the principal component analysis (pca) and the hierachical ‎structures.‎ in ‎this work‎, we analyze cross-crrelations between price fluctuations of 20 ‎company ‎stocks‎‎...

It is well known that spectral Turán type problem one of the most classical problems in graph theory. In this paper, we consider problem. Let G be a and let set graphs, say G-free if does not contain any element as subgraph. Denote by ?1 ?2 largest second eigenvalues adjacency matrix A(G) G, respectively. paper focus on characterization graphs without short odd cycles according to graphs. First...

Transposition graph Tn is defined as a Cayley over the symmetric group generated by all transpositions. It known that eigenvalues of are integers. However, an explicit description spectrum unknown. In this paper we prove for any integer k⩾0 there exists n(k) such n⩾n(k) and m∈{0,…,k}, m eigenvalue Tn. particular, it proved zero n≠2, 1 odd n⩾7 even n⩾14. We also present exact values third fourth...

In this study, we deal with an $m$ banded circulant matrix, generally called $m$-diagonal matrix. This special family of matrices arise in many applications such as prediction, time series analysis, spline approximation, difference solution partial differential equations, and so on. We firstly obtain the statements eigenvalues eigenvectors matrix based on Chebyshev polynomials first second kind...

Cvetković et al. [Appl. Math. Comput. 217 (2010), 2468–2480] presented an algorithm for dynamic load balancing in discrete load model based on the eigenvectors of the adjacency matrix of the processor network. In case of integral graphs, whose eigenvalues are integers and whose eigenvector basis may be chosen to consist of integers only, this algorithm executes in integer arithmetic, providing ...

We present the results of two-loop calculations of the anomalous dimension matrix for the Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills theory for polarized and unpolarized cases. This matrix can be transformed to a triangle form by the same similarity transformation as in the leading order. The eigenvalues of the anomalous dimension matrix are expressed in terms of an universal...

The paper is devoted to the eigenvalue problem for a second order strongly elliptic operator. The problem is considered on curved domains, which require interpolated boundary conditions in approximating finite element formulation. The necessary triangulations for solving the eigenvalue problem consists of isoparametric elements of degree n, where n is any integer greater than two. An approximat...

Let the Gaussian process Xm(t) be the m-fold integrated Brownian motion for positive integer m. The Laplace transform of the quadratic functional of Xm(t) is found by using an appropriate self-adjoint integral operator. The result is then used to show the power of a general connection between small ball probabilities for the Gaussian process. The connection is discovered by introducing an indep...