相关论文: Generalized Master Function Approach to Quasi-Exac…

Given a prime power $q$ and positive integers $m,t,e$ with $e > mt/2$, we determine the number of all monic irreducible polynomials $f(x)$ of degree $m$ with coefficients in $\mathbb{F}_q$ such that $f(x^t)$ contains an irreducible factor…

We consider Hamiltonians, which are even polynomials of the forth order with the respect to Bose operators. We find subspaces, preserved by the action of Hamiltonian These subspaces, being finite-dimensional, include, nonetheless, states…

This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…

In this study, we address the challenge of obtaining a Green's function operator for linear partial differential equations (PDEs). The Green's function is well-sought after due to its ability to directly map inputs to solutions, bypassing…

General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases…

The supersymmetric intertwining relations with second order supercharges allow to investigate new two-dimensional model which is not amenable to standard separation of variables. The corresponding potential being the two-dimensional…

The main objective of this paper is to introduce an algorithm for solving fractional and classical differential equations based on a new generalized fractional power series. The algorithm relies on expanding the solution of an FDE or an ODE…

Let $p>3$ be a prime. We show that, for each integer $d$ with $p \leq d \leq 2(p-1)$, there exists a generalized almost perfect nonlinear (GAPN) binomial or trinomial over $\mathbb{F}_{p^2}$ of algebraic degree $d$. We start by deriving…

We define an enumerative function F(n,k,P,m) which is a generalization of binomial coefficients. Special cases of this function are also power function, factorials, rising factorials and falling factorials. The first section of the paper is…

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly…

We show how to solve explicitly an equation satisfied by a real function belonging to certain general quasianalytic classes. Examples of the classes under consideration are the collection of convergent generalised power series, a class of…

A master equation approach to molecular motors allows to describe a mechano-chemical cyclic system where chemical and translational degrees of freedom are treated on an equal footing. A generalized detailed balance condition in the out of…

We use the resolution of singularities algorithm of [G4] to provide new estimates for exponential sums as well as new bounds on how often a function f(x) such as a polynomial with integer coefficients is divisible by various powers of a…

Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…

In recent years, progress toward the classification of superintegrable systems with higher order integrals of motion has been made. In particular, a complete classification of all exotic potentials with a third or a fourth order integrals,…

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with…

We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can…

An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…

This paper introduces a new algorithm for solving a sub-class of quantified constraint satisfaction problems (QCSP) where existential quantifiers precede universally quantified inequalities on continuous domains. This class of QCSPs has…