We investigate the eigengenvalues problem for self-adjoint operators with the singular perturbations. The general results presented here include weakly as well as strongly singular cases. We illustrate these results on two models which correspond to so-called additive strongly singular perturbations.

A general adaptive element subdivision technique is presented for the numerical evaluation of weakly singular integrals, which often appear in three-dimensional boundary element analysis equations. In this algorithm, the weakly singular boundary element is broken up into a few sub-elements through a sphere of decreasing radius. The sub-elements involving the singular point are evaluated numeric...

The singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to diverge, and hence, a measure of the predictability of the flow. In this paper, the singular vectors and singular values of stationary and evolving exa...

We study the approachability ideal I[κ+] in the context of large cardinals and properties of the regular cardinals below a singular κ. As a guiding example consider the approachability ideal I[אω+1] assuming that אω is a strong limit. In this case we obtain that club many points in אω+1 of cofinality אn for some n > 1 are approachable assuming the joint reflection of countable families of stati...

Straight-forward systematic derivations of the weakly singular boundary integral equations (BIEs) are presented, following the simple and directly-derived approach by Okada, Rajiyah, and Atluri (1989b) and Han and Atluri (2002). A set of weak-forms and their algebraic combinations have been used to avoid the hypersingularities, by directly applying the “intrinsic properties” of the fundamental ...