Related papers: New recursion relations of matrix elements of $r^\…
Relativistic magnetic reconnection is one of the most fundamental mechanisms considered responsible for the acceleration of relativistic particles in astrophysical jets and magnetospheres of compact objects. Understanding the properties of…
We obtain analytic solutions for the one-dimensional Dirac equation with the Morse potential as an infinite series of square integrable functions. These solutions are for all energies, the discrete as well as the continuous. The elements of…
It is shown that formulas for the radiative power loss and radiation reaction from a charge can be derived in a heuristic manner from the kinetic power (rate of change of the kinetic energy) of its electric inertial mass. The derivation…
We formulate a method to find the meromorphic solutions of higher-order recurrence relations in the form of the sum over poles with coefficients defined recursively. Several explicit examples of the application of this technique are given.…
We construct all (2+1)-dimensional PDEs depending only on 2nd-order derivatives of unknown which have the Euler-Lagrange form and determine the corresponding Lagrangians. We convert these equations and their Lagrangians to two-component…
The two-dimensional hydrogen-like atom in a constant magnetic field is considered. It is found that this is actually two separate problems. One for which the magnetic field causes an effective attraction between the nucleus and the electron…
Exceptional extensions of a class of Laurent biorthogonal polynomials (the so-called Hendriksen-van Rossum polynomials) have been presented by the authors recently. This is achieved through Darboux transformations of generalized eigenvalue…
In this paper, we derive new relative perturbation bounds for eigenvectors and eigenvalues for regular quadratic eigenvalue problems of the form $\lambda^2 M x + \lambda C x + K x = 0$, where $M$ and $K$ are nonsingular Hermitian matrices…
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the relativistic N-body problem in a separable two-body basis in which the particles interact pair-wise through scalar and vector interactions. The resultant N-body…
We derive the expression for the residual interaction to be used in the framework of the Second RPA with density-dependent forces. The adopted procedure is based on a variational approach. It is found that the residual interaction to be…
We study the additive eigenvalues on changing domains, along with the associated vanishing discount problems. We consider the convergence of the vanishing discount problem on changing domains for a general scaling type $\Omega_\lambda =…
We give a new combinatorial explanation for well-known relations between determinants and traces of matrix powers. Such relations can be used to obtain polynomial-time and poly-logarithmic space algorithms for the determinant. Our new…
A key point of Dirac Brueckner Hartree Fock calculations for nuclear matter is to decompose the self energy of the nucleons into Lorentz scalar and vector components. A new method is introduced for this decomposition. It is based on the…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is…
A new way to overcome the $\Lambda$ hyperon selective suppression, which is known as the $\Lambda$-anomaly, has been suggested. In particular, the additional radius of a $\Lambda$ hyperon is introduced into the model of hadron resonance gas…
Cosmic sources of gamma-ray radiation in the GeV range are often characterized by violent variability, in particular this concerns blazars, gamma-ray bursts, and the pulsar wind nebula Crab. Such gamma-ray emission requires a very efficient…
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay…
Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation a_{n+1} = Aa_n + Ba_{n-1}, by means of algebraic equations in two variables of…