We study the eigenpairs of a model Schrödinger operator with a quadratic potential and Neumann boundary conditions on a half-plane. The potential is degenerate in the sense that it reaches its minimum all along a line which makes the angle θ with the boundary of the half-plane. We show that the first eigenfunctions satisfy localization properties related to the distance to the minimum line of t...

Magnetoencephalography (MEG) is a noninvasive technique for studying neuronal activity in the living human brain. Weak magnetic elds caused by the activity are measured from outside the head. Based on these measurements the source of the activity is located with the help of a mathematical model. A part of the localization is the repeated computation of the electric potential on the surface of t...

Localized eigenfunctions in the two-dimensional spectral problem containing a small parameter with higher derivatives are constructed on expected solution form. Localization this context means that exponentially decays both direc-tions starting from "weakest" point or line. The constructions based algo-rithm introduced by V.P. Maslov. A modification of algorithm for thin shell theory problems i...

The undirected power graph of a finite group $G$, $P(G)$, is a graph with the group elements of $G$ as vertices and two vertices are adjacent if and only if one of them is a power of the other. Let $A$ be an adjacency matrix of $P(G)$. An eigenvalue $lambda$ of $A$ is a main eigenvalue if the eigenspace $epsilon(lambda)$ has an eigenvector $X$ such that $X^{t}jjneq 0$, where $jj$ is the all-one...

the association of secreted frizzled related protein type 4 (sfrp4) as an antagonist of wnt mole-cules in apoptotic events has been reported previously. moreover, its increased expression has been reported in the ovary of women with polycystic ovary (pco). we have demonstrated in-creased sfrp4 in pco-induced rat ovary related to an increased number of apoptotic follicles showing nuclear ?cateni...

In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem ...

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example, which needs to be investigated first, the main bounds are extended to families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment Theorem and re...

Semi-solid materials undergo strain localization and shear band formation as a result of granular nature of semi-solid deformation. In the present study, to analyze the shear localization, a unified viscoplastic constitutive model was developed for the homogeneous flow. Then, a linearized analysis of the stability performed by examining the necessary condition for the perturbation growth. For t...

This paper introduces a method to extract ‘Shape-DNA’, a numerical fingerprint or signature, of any 2d or 3d manifold (surface or solid) by taking the eigenvalues (i.e. the spectrum) of its Laplace–Beltrami operator. Employing the Laplace–Beltrami spectra (not the spectra of the mesh Laplacian) as fingerprints of surfaces and solids is a novel approach. Since the spectrum is an isometry invaria...