相关论文: Computable Integrability. Chapter 5: Factorization…

We present two algorithms for computing what we call the absolute factorization of a difference operator. We also give an algorithm to solve third order difference equations in terms of second order equations, together with applications to…

A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…

Recently, a remarkable correspondence has been unveiled between a certain class of ordinary linear differential equations (ODE) and integrable models. In the first part of the report, we survey the results concerning the 2nd order…

We revisit integrable discretizations for the nonlinear Schr\"odinger equation due to Ablowitz and Ladik. We demonstrate how their main drawback, the non-locality, can be overcome. Namely, we factorize the non-local difference scheme into…

The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…

INTRODUCTION This papers deals with partial differential equations of second order, linear, with constant and not constant coefficients, in two variables, which admit real characteristics. I face the study of PDEs with the mentality of the…

The main objective of this work is to investigate the integrability and linearizability problems around a singular point at the origin of the family of differential systems Particularly we are interested in the three-dimensional cubic…

Binary matrix factorisation is an essential tool for identifying discrete patterns in binary data. In this paper we consider the rank-k binary matrix factorisation problem (k-BMF) under Boolean arithmetic: we are given an n x m binary…

We give a constructive proof of the factorization theorem for the classical Hardy space in terms of fractional integral operator. Moreover, the result is extended to the multilinear case and weighted case. As an application, we obtain the…

LU-factorization of matrices is one of the fundamental algorithms of linear algebra. The widespread use of supercomputers with distributed memory requires a review of traditional algorithms, which were based on the common memory of a…

We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear…

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…

Here we present a very efficient method to search for Liouvillian first integrals of second order rational ordinary differential equations (rational 2ODEs). This new algorithm can be seen as an improvement to the S-function method we have…

The operator level proof of factorization theorem exhibited in [1] is extended to the semi-inclusive deep inelastic scattering process(SIDIS). Factorization theorem can be proved at operator level if there are not detected soft hadrons.

There was proposed the method of a factorization of PDE. The method is based on reduction of complicated systems to more easy ones (for example, due to dimension decrease). This concept is proposed in general case for the arbitrary PDE…

In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…

We describe explicit algorithms for factoring q-difference operators and solving q-difference equations. These are well known results, presented in a "concrete" form. ----- Nous decrivons des algorithmes explicites pour la factorisation…

A factorization formula for wave functions, which is basic in the inverse spectral transform approach to initial-boundary value problems, is proved in greater generality than before. Applications follow. Related compatibility questions for…

We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two…

For fragments L of first-order logic (FO) with counting quantifiers, we consider the definability problem, which asks whether a given L-formula can be equivalently expressed by a formula in some fragment of L without counting, and the more…