The development of the notion of group contraction first introduced by E. Inönü and E.P. Wigner in 1953 is briefly reviewed. The fundamental role of the idea of degenerate transformations is stressed. The significance of contractions of algebraic structures for exactly solvable problems of mathematical physics is noticed.

This paper presents an original practical criterion of global stability analysis of nonlinear polynomial systems. This criterion derived from the application of the Lyapunov direct method with a quadratic function generalizes the famous Lyapunov stability condition for linear systems. Useful mathematical transformations have allowed the formulation of the obtained conditions as an LMI (Linear M...

A bicomplex is a simple mathematical structure, in particular associated with completely integrable models. The conditions defining a bicomplex are a special form of a parameter-dependent zero curvature condition. We generalize the concept of a Darboux matrix to bicomplexes and use it to derive Bäcklund transformations for several models. The method also works for Moyal-deformed equations with ...

It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In this note we extend the approach to asymptotic symmetries for the analysis of PDEs, to the case of difference equations.

In this paper, the notion Affine Discrete Dynamical Systems (ADDS) in terms of Integral Value Transformations (IVTs), is introduced and their mathematical properties, particularly their equilibrium and stability as a dynamical system, are studied. It is shown that some ADDS are Collatz-like, which generate fractals. It is also shown that ADDS can model Optimal Distributed and Parallel Environme...

In this paper we give a mathematical framework for the treatment of the bidomain equations used to model propagation in cardiac tissue. We show how previous work ts into this framework and discuss the implications of various linear transformations of the equations on the numerical methods of solution.

We present a mathematical analysis of transformations used in fast calculation of inverse square root for single-precision floating-point numbers. Optimal values of the so called magic constants are derived in a systematic way, minimizing either absolute or relative errors at subsequent stages of the discussed algorithm.

A certificate is a mathematical object that can be used to establish that a piece of mobile code satisfies some security policy. Since in general certificates cannot be generated automatically, there is an interest in developing methods to reuse certificates. This article formalises in the setting of abstract interpretation a method to transform certificates of program correctness along program...

Students of our department solve algebraic exercises in mathematical logic in a computerized environment. They construct transformations step by step and the program checks the syntax, equivalence of expressions and completion of the task. With our current project, we add a program component for checking relevance of the steps.

In neuro-biological modeling, no good software technologies currently exist that are memorye/cient and give access to all the mathematical details of a large model. Here we present enabling technologies that deal with transformations of parameters of a large model. The discussed techniques allow to store models in a memory-e2ective way. c © 2004 Published by Elsevier B.V.