Sublinear Differential Polynomials

Fractional differential equations with Legendre polynomials

Computing Elementary Symmetric Polynomials with a Sublinear Number of Multiplications

Elementary symmetric polynomials S n are used as a benchmark for the boundeddepth arithmetic circuit model of computation. In this work we prove that S n modulo composite numbersm = p1p2 can be computed with much fewer multiplications than over any field, if the coefficients of monomials xi1xi2 · · ·xik are allowed to be 1 either mod p1 or mod p2 but not necessarily both. More exactly, we prove...

fractional differential equations with legendre polynomials

Brenstien polynomials and its application to fractional differential equation

The paper is devoted to the study of Brenstien Polynomials and development of some new operational matrices of fractional order integrations and derivatives. The operational matrices are used to convert fractional order differential equations to systems of algebraic equations. A simple scheme yielding accurate approximate solutions of the couple systems for fractional differential equations is ...

Differential polynomials and symbolic representation

In the Symmetry Approach the existence of infinite hierarchies of higher symmetries and/or local conservation laws is taken as a definition of integrability. The main aims of the approach are to obtain easily verifiable necessary conditions of integrability, to identify integrable cases and even to give complete description and classification of integrable system of a particular type. It proved...