相关论文: Completion problems and scattering problems for Di…
Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
In this paper we give a novel solution to a classical completion problem for square matrices. This problem was studied by many authors through time, and it is completely solved in [2, 3]. In this paper we relate this classical problem to a…
In this research, we present a Python-based solution designed to simulate a one-dimensional quantum system that incorporates multiple Dirac $\delta -$% potentials. The primary aim of this research is to investigate the scattering problem…
The paper is concerned with the completeness property of root functions of the Dirac operator with summable complexvalued potential and non-regular boundary conditions. We also obtain explicit form for the fundamental solution system of the…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
We prove nonuniqueness results for complete metrics with constant positive fractional curvature conformal to the round metric on $S^n \setminus S^k$, using bifurcation techniques. These are singular (positive) solutions to a non-local…
We introduce a Dirac equation which reproduces the usual radial sextic oscillator potential in the non-relativistic limit. We determine its energy spectrum in the presence of the magnetic field. It is shown that the equation is solved in…
A new discretization of the radial equations that appear in the solution of separable second order partial differential equations with some rotational symmetry (as the Schrodinger equation in a central potential) is presented. It cures a…
A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
The inverse scattering problem for Sturm-Liouville operators on the line with a matrix transfer condition at the origin is considered. We show that the transfer matrix can be reconstructed from the eigenvalues and reflection coefficient. In…
We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a system and answer a question on the characterization of the…
Hamiltonians are 2-by-2 positive semidefinite real symmetric matrix-valued functions satisfying certain conditions. In this paper, we solve the inverse problem for which recovers a Hamiltonian from the solution of a first-order system…
In this paper, we study the inverse scattering problem for energy-dependent Schr\"{o}dinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions,…
In this paper we investigate the existence and uniqueness of bounded, periodic and almost periodic solutions for second order differential equations involving reflection of the argument.The relationship between frequency modules of forced…
The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of solution is given, by recasting the…
In this paper, we present and analyze methods for solving a system of linear equations over idempotent semifields. The first method is based on the pseudo-inverse of the system matrix. We then present a specific version of Cramer's rule…
We consider the differential system $y'-x^{-1}Ay-q(x)y=\rho By $ with $n\times n$ matrices $A,B, q(x)$, where $A,B$ are constant, $B$ is diagonal, $A$ and $q(x)$ are off-diagonal, $q(\cdot)\in W^1_1[0,\infty)$. Some distinguished…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…