For the method and problems under consideration we estimate the error in the maximum norm as well as at individual nodal points. In order to obtain full superconvergence at all nodal points we have to introduce local mesh refinements, even though the exact solution is smooth for the given class of problems.

Topological semimetals can support one-dimensional Fermi lines or zero-dimensional Weyl points in momentum space, where the valence and conduction bands touch. While the degeneracy points in Weyl semimetals are robust against any perturbation that preserves translational symmetry, nodal lines require protection by additional crystalline symmetries such as mirror reflection. Here we report, base...

In this paper, the inverse problem of recovering the potential function, on a general finite interval, of a singular Sturm–Liouville problem with a new spectral parameter, called the nodal point, is studied. In addition, we give an asymptotic formula for nodal points and the density of the nodal set. c © 2006 Elsevier Ltd. All rights reserved.

In the paper a linear-quadratic optimization problem (LCTOR) with unseparated two-point boundary conditions is considered. To solve this problem is proposed a new sweep algorithm which increases doubles the dimension of the original system. In contrast to the well-known methods, here it refuses to solve linear matrix and nonlinear Riccati equations, since the solution of such multi-point optimi...

The paralysis-by-analysis phenomenon, i.e., attending to the execution of one's movement impairs performance, has gathered a lot of attention over recent years (see Wulf, 2007, for a review). Explanations of this phenomenon, e.g., the hypotheses of constrained action (Wulf et al., 2001) or of step-by-step execution (Masters, 1992; Beilock et al., 2002), however, do not refer to the level of und...

In this note, we make an observation that Laplacian eigenfunctions fail equidistribution at the Planck scale. Furthermore, same scale also fails around points where have large values.