Related papers: Factorization method and general second order line…

Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…

We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…

Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a…

In this second paper on the method of deriving linearizing transformations for nonlinear ODEs, we extend the method to a set of two coupled second order nonlinear ODEs. We show that besides the conventional point, Sundman and generalized…

We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…

The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator which is shown to be bounded and symmetric on…

We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.

We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat's method in…

In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.

The elements of the class of non-homogeneous differential operators which are based on the same vector field, when viewed as acting on appropriate Hilbert spaces, are shown to be isomorphic to each other. It shown that the replacement of a…

Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on…

The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…

New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…

For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…

We consider different variants of factorization of a 2x2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to…

This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…

Type A N-fold supercharge admits a one-parameter family of factorizations into product of N first-order linear differential operators due to an underlying GL(2,C) symmetry. As a consequence, a type A N-fold supersymmetric system can have…

The detailed construction of the general solution of a second order non-homogenous linear operatordifference equation is presented. The wide applicability of such an equation as well as the usefulness of its resolutive formula is shown by…

The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…

In this paper we implement the Darboux transformation, as well as an analogue of Crum's theorem, for a discrete version of Schr\"odinger equation. The technique is based on the use of first order operators intertwining two difference…