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.

‎let $g$ be a graph without an isolated vertex‎, ‎the normalized laplacian matrix $tilde{mathcal{l}}(g)$‎‎is defined as $tilde{mathcal{l}}(g)=mathcal{d}^{-frac{1}{2}}mathcal{l}(g) mathcal{d}^{-frac{1}{2}}$‎, where ‎$‎mathcal{‎d}‎$ ‎is a‎ diagonal matrix whose entries are degree of ‎vertices ‎‎of ‎$‎g‎$‎‎. ‎the eigenvalues of‎‎$tilde{mathcal{l}}(g)$ are ‎called ‎ ‎ as ‎the ‎normalized laplacian ...

This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.

The low-frequency eigenmodes of a fractal drum are studied through experimental observation of the acoustical resonances of a fractal-shaped liquid crystal film. The resonance frequencies agree with the numerical predictions for the Laplacian eigenvalues in the fractal domain with Dirichlet boundary conditions. The amplitude distribution of the modes is detected by scanning the excitation posit...

A wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by Dyson’s circular ensemble. We argue that the impact of localization in such systems is to provide certain restrictions on the eigenvalues. We consider a solvable model which takes into account such restrictions qualitatively and find that within the model...

Abstract Focusing on the diffusion-localization transition, we theoretically analyzed a nonlinear gravity-type transport model defined networks called regular ring lattices, which have an intermediate structure between complete graph and simple ring. Exact eigenvalues were derived around steady states, values of transition points evaluated for control parameter characterizing nonlinearity. We a...

Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...

The aim of the presentation is to introduce some new localization techniques for generalized eigenvalues of a matrix pair obtained via famous Geršgorin theorem and its different generalizations. Special attention will be given to the techniques of computation and visual presentation of the obtained localization areas using MATLAB. Since the work that will follow involves much about nonnegative ...

  The distribution and localization of acid and neutral mucins in various cells lining the olfactory epithelium of Cyprinus carpio have been studied histochemically by employing the PAS-AB technique. Variations in the localization of protein in different cells lining the olfactory epithelium have been correlated with the functional significance of the region concerned. Intense localization of t...

We have calculated wave functions and matrix elements of the dipole operator in the two-and three-dimensional Anderson model of localization and have studied their statistical properties in the limit of weak disorder. In particular, we have considered two cases. First, we have studied the uctuations as an external Aharonov-Bohm ux is varied. Second, we have considered the innuence of incipient ...