Related papers: Completion problems and scattering problems for Di…
In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…
We reduce the solution of the scattering problem defined on the half-line $[0,\infty)$ by a real or complex potential $v(x)$ and a general homogenous boundary condition at $x=0$ to that of the extension of $v(x)$ to the full line that…
We study canonical systems that are reflectionless on an open set. In this situation, the two half line $m$ functions are holomorphic continuations of each other and may thus be combined into a single holomorphic function. This idea was…
A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur…
The paper is concerned with the completeness property of the system of root vectors of a boundary value problem for the following $2 \times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \lambda y , \quad y= {\rm col}(y_1, y_2),…
In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is…
The scattering of a Dirac particle has been studied for a quaternionic potential step. In the potential region an additional diffusion solution is obtained. The quaternionic solution which generalizes the complex one presents an…
We study the Klein paradox for the semi-classical Dirac operator on $\R$ with potentials having constant limits, not necessarily the same at infinity. Using the complex WKB method, the time-independent scattering theory in terms of incoming…
We establish the unique solvability of a coupling problem for entire functions which arises in inverse spectral theory for singular second order ordinary differential equations/two-dimensional first order systems and is also of relevance…
The Douglas-Rachford reflection method is a general purpose algorithm useful for solving the feasibility problem of finding a point in the intersection of finitely many sets. In this chapter we demonstrate that applied to a specific…
To solve the Dirac equation with the finite difference method, one has to face up to the spurious-state problem due to the fermion doubling problem when using the conventional central difference formula to calculate the first-order…
A symmetry reduction of the Dirac equation is shown to yield the system of ordinary differential equations whose integrability by quadratures is closely connected to the stationary mKdV hierarchy.
We study the inverse problem of unique recovery of a complex-valued scalar function $V:\mathcal M \times \mathbb C\to \mathbb C$, defined over a smooth compact Riemannian manifold $(\mathcal M,g)$ with smooth boundary, given the Dirichlet…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
Singular equations with rank-deficient Jacobians arise frequently in algebraic computing applications. As shown in case studies in this paper, direct and intuitive modeling of algebraic problems often results in nonisolated singular…
The problem of matrix completion and decomposition in the cone of positive semidefinite (PSD) matrices is a well-understood problem, with many important applications in areas such as linear algebra, optimization, and control theory. This…
Interaction of waves with point and line defects are usually described by $\delta$-function potentials supported on points or lines. In two dimensions, the scattering problem for a finite collection of point defects or parallel line defects…
New inverse and half-inverse problems: {\it sliding problems} are introduced. In this way several physically important equations are recovered from the quantum defect. In particular, sliding problems are solved for radial Schr\"odinger…
We revisit completion modulo equational theories for left-linear term rewrite systems where unification modulo the theory is avoided and the normal rewrite relation can be used in order to decide validity questions. To that end, we give a…
A discrete version of the two-dimensional inverse scattering problem is considered. On this basis, algebraic transformations for the two-dimensional finite-difference Schredinger equation are elaborated.