92 On· the Asymptotic Distribution of the Eigenvalues of Discretizations of a Compact Operator

We obtain the asymptotic distribution of the nonprincipal eigenvalues associated with the singular problem x + λq(t)x = 0 on an infinite interval [a,+∞). Similar to the regular eigenvalue problem on compact intervals, we can prove a Weyl-type expansion of the eigenvalue counting function, and we derive the asymptotic behavior of the eigenvalues.

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 investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....

The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...

We present a simple method to calculate certain sums of the eigenvalues of the volume operator in loop quantum gravity. We derive the asymptotic distribution of the eigenvalues in the classical limit of very large spins which turns out to be of a very simple form. The results can be useful for example in the statistical approach to quantum gravity.

The eigenvalues of a graph is the root of its characteristic polynomial. A fullerene F is a 3- connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n is the number of vertices of F. In this paper we investigate the eigenvalues of a class of fullerene graphs.

We derive the joint limiting distribution for the largest eigenvalues of the adjacency matrix for stochastic blockmodel graphs when the number of vertices tends to infinity. We show that, in the limit, these eigenvalues are jointly multivariate normal with bounded covariances. Our result extends the classical result of Füredi and Komlós on the fluctuation of the largest eigenvalue for Erdős-Rén...

The distribution of eigenvalues and the upper bounds for spread interval matrices are significant in various fields mathematics applied sciences, including linear algebra, numerical analysis, control theory, combinatorial optimization. We present within determine their using Geršgorin’s theorem. Specifically, through an equality variance a discrete random variable, we derive symmetric matrices....