Related papers: Matching variables to equations in infinite linear…
In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…
We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…
In the variety of all linear algebras over the infinite field the difference between geometric and automorphic equivalence of algebras can be big.
We find a formula for the number of solutions of linear congruence systems, by using elementary methods.
In this work I discuss briefly the calculation of the algebraic entropy for systems of quad equations. In particular, I observe that since systems of multilinear equations can have algebraic solution, in some cases one might need to…
We consider a stochastic variant of the packing-type integer linear programming problem, which contains random variables in the objective vector. We are allowed to reveal each entry of the objective vector by conducting a query, and the…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
The paper studies homogenization problem for a non-autonomous parabolic equation with a large random rapidly oscillating potential in the case of one dimensional spatial variable. We show that if the potential is a statistically homogeneous…
Algebraic effects are computational effects that can be described with a set of basic operations and equations between them. As many interesting effect handlers do not respect these equations, most approaches assume a trivial theory,…
Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…
It has been shown earlier that the solubility of the Legendre and the associated Legendre equations can be understood as a consequence of an underlying supersymmetry and shape invariance. We have extended this result to the hypergeometric…
We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differential equations has a full set of algebraic solutions or not. This criterion generalises the so-called interlacing criterion in the case of…
We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
A double algebra is a linear space $V$ equipped with linear map $V\otimes V\to V\otimes V$. Additional conditions on this map lead to the notions of Lie and associative double algebras. We prove that simple finite-dimensional Lie double…
Evidently, the linear superposition principle can not be exactly established as a general principle in the presence of nonlinearity, and, at the first glance, there is no expectation for it to hold even approximately. In this letter, it is…