In this article the new method for the accounting singular point influence to the postprocessing error estimation is proposed. Solution improvement in singular zones is achieved modifying physical coordinate matrix used in least square problem equations: instead of the standard quadratic polynomial a new polynomial with singular elements is taken. Numerical examples demonstrate the advantages o...

Singular Gordon potentials are defined to be distributions from the space W −1 2,unif (R) that are sufficiently fast approximated by periodic ones. We prove that Schrödinger operators with singular Gordon potentials have no point spectrum and show that a rich class of quasiperiodic distributions consists of singular Gordon potentials .

We give upper and lower bounds for the consistency strength of the failure of a combinatorial principle introduced by Jensen, Square on singular cardinals. A combinatorial principle of great importance in set theory is the Global principle of Jensen [6]: Global : There exists 〈Cα | α a singular ordinal 〉 such that for each α, Cα is a closed unbounded subset of α of ordertype less than α, the li...

In this paper, we discuss the recognition problem for Ak-type singularities on wave fronts. We give computable and simple criteria of these singularities, which will play a fundamental role in generalizing the authors’ previous work “the geometry of fronts” for surfaces. The crucial point to prove our criteria for Ak-singularities is to introduce a suitable parametrization of the singularities ...

We test the standard edge plasma code B2-solps5.0 on a model First-Wall Limiter (FWL) geometry. The presence of a tangency point between the solid wall and the magnetic separatrix introduces a singular point in the geometry. A quadrilateral computational mesh can fit the given configuration only if it is highly distorted, constituting a severe test for any numerical scheme. The original 5-point...

We propose and experimentally demonstrate the singular surface plasmon beam that presents a dark channel generated by a point dislocation and a long diffraction-free propagation distance up to 70λ(sp). The singular surface beam is the result of the interference of two surface plasmon polariton (SPP) plane waves, which are launched by two coupling gratings with lateral displacement. An aperture-...

In this paper, we discuss on the recognition problem of Ak-type singularities on wave fronts. We give computable and simple criteria of these singularities, which will play a fundamental role to generalize the authors’ previous work “the geometry of fronts” for surfaces. The crucial point to prove our criteria for Ak-singularities is to introduce a suitable parametrization of the singularities ...

In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions at the irregular singular point for the unfolded system. Our study covers a full neighborhood of the origin in the confluence parameter space. In particular, we show how the divergence of solutions at the irregular sin...

When a plane undergoes a deformation that can be represented by a planar linear vector eld, the projected vector eld on the image plane of an optical device is at most quadratic. This 2D motion eld has one singular point, with eigenvalues identical to those of the singular point describing the deformation. As a consequence, the nature of the singular point of the deformation is a projective inv...

This article is concerned with the defect indices of singular symmetric linear difference equations of order 2n with complex coefficients and one singular endpoint. We first show that the positive and negative defect indices d+ and dof a class of singular symmetric linear difference equations of order 2n with complex coefficients satisfy the inequalities n ≤ d+ = d≤ 2n and all values of this ra...