In this paper, we investigatethe boundary value problem for differential pencils on the half-linewith a turning point. Using a fundamental system of solutions, wegive a asymptotic distribution of eigenvalues.

In this paper we consider the solutions of linear systems of saddle point problems‎. ‎By using the spectrum of a quadratic matrix polynomial‎, ‎we study the eigenvalues of the iterative matrix of the Hermitian and skew Hermitian splitting method‎.

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

Amongst the lattice gauge community it has recently become quite popular to study the distributions of eigenvalues of the Dirac operator in the presence of the background gauge fields generated in simulations. There are a variety of motivations for this. First, in a classic work, Banks and Casher1 related the density of small Dirac eigenvalues to spontaneous chiral symmetry breaking. Second, la...

Status of This Memo This document specifies an Internet standards track protocol for the Internet community, and requests discussion and suggestions for improvements. Please refer to the current edition of the "Internet Official Protocol Standards" (STD 1) for the standardization state and status of this protocol. Distribution of this memo is unlimited. Abstract This document specifies encoding...

In this paper we find explicit lower bounds for Dirichlet eigenvalues of a weighted quasilinear elliptic system of resonant type in terms of the eigenvalues of a single p-Laplace equation. Also we obtain asymptotic bounds by studying the spectral counting function which is defined as the number of eigenvalues smaller than a given value.

We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r = 40000. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130millionth eigenvalue.

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

Community structure of networks provides comprehensive insight into their organizational structure and functional behavior. LPA is one of the most commonly adopted community detection algorithms with nearly linear time complexity. But it suffers from poor stability and occurrence of monster community due to the introduced randomize. We note that different community-oriented node roles impact th...