The aim of the book is to provide an analysis of the boundary element method for the numerical solution of Laplacian eigenvalue problems. The representation of Laplacian eigenvalue problems in the form of boundary integral equations leads to nonlinear eigenvalue problems for related boundary integral operators. The solution of boundary element discretizations of such eigenvalue problems require...

Optical eigenvalue communication is a promising technique for overcoming the Kerr nonlinear limit in optical systems. The associated with Schrödinger equation remains invariant during fiber-based dispersive transmission. However, practical applications involving use of such systems are limited by occurrence fiber loss and amplified noise that induce distortion. Thus, several time-domain neural-...

the right ventricle (rv) is a complex structure with abstruse function that reveals important differences when compared to the left ventricle (lv), so it cannot be described as a simple geometric form and achromatic physiology. as an inference from this fact, in the present review, we aim to describe rv structure including the embryology, anatomy, and physiology and present a functional, hemody...

The Pearcey kernel is a classical and universal arising from random matrix theory, which describes the local statistics of eigenvalues when limiting mean eigenvalue density exhibits cusp-like singularity. It appears in variety statistical physics models beyond as well. We consider Fredholm determinant trace class operator acting on $L^2\left(-s, s\right)$ with kernel. Based steepest descent ana...

This note starts from work done by Dai, Geary, and Kadanoff[1] on exact eigenfunctions for Toeplitz operators. It builds methods for finding convergent expansions for eigenvectors and eigenvalues of singular, largen Toeplitz matrices, using the infinite-n case[1] as a starting point. One expansion is derived from operator equations having a two-dimensional continuous spectrum of right eigenvalu...