Related papers: ODE/IM correspondence for affine Lie algebras: A n…
Finite dimensional modular Lie superalgebras over algebraically closed fields with indecomposable Cartan matrices are classified under some technical, most probably inessential, hypotheses. If the Cartan matrix is invertible, the…
We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…
In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…
A constructive procedure is proposed for formulation of linear differential equations invariant under global symmetry transformations forming a semi-simple Lie algebra f. Under certain conditions f-invariant systems of differential…
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 present a new method for solving symbolically zero--dimensional polynomial equation systems in the affine and toric case. The main feature of our method is the use of problem adapted data structures: arithmetic networks and…
By affine arithmetic is meant the set of affine consequences of Peano arithmetic. This is a continuous theory which is studied in the framework of affine logic, a sublogic of continuous logic. Affine arithmetic is undecidable. Also, its…
Algorithms for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. The algorithms are based on global fixed point iterations which apply to families of functions satisfying…
An algorithm for the numerical solution of a nonlinear integro-differential equation arising in the single-species annihilation reaction $A + A \rightarrow\varnothing$ modeling is discussed. Finite difference method together with the linear…
The exact factorisable quantum S-matrices are known for simply laced as well as non-simply laced affine Toda field theories. Non-simply laced theories are obtained from the affine Toda theories based on simply laced algebras by folding the…
This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all $(n+1)$-dimensional real solvable…
We present an explicit character formula for the irreducible highest weight representations of the non-twisted affine Kac-Moody Lie algebra at the critical level which are integrable over the corresponding finite-dimensional simple Lie…
A new (algebraic) approximation scheme to find {\sl global} solutions of two point boundary value problems of ordinary differential equations (ODE's) is presented. The method is applicable for both linear and nonlinear (coupled) ODE's whose…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
A new general Lie-algebraic approach is proposed to solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras $su_{pd}(2)$ as their dynamic symmetry algebras. The method makes use of an…
We study sympathetic Lie algebras, namely perfect and complete Lie algebras. They arise among other things in the study of adjoint Lie algebra cohomology. This is motivated by a conjecture of Pirashvili, which says that a non-trivial…
We describe a framework for solving a broad class of infinite-dimensional linear equations, consisting of almost banded operators, which can be used to resepresent linear ordinary differential equations with general boundary conditions. The…
In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…
Here we present a new approach to compute symmetries of rational second order ordinary differential equations (rational 2ODEs). This method can compute Lie symmetries (point symmetries, dynamical symmetries and non-local symmetries)…
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…