This paper presents a symmetry analysis based on Lie groups of a system of ordinary differential equations (ODEs) modelling the p53mdm2 regulatory pathway. This pathway is being investigated across several research groups as a biological system from which to extract dynamical and algebraic characteristics relevant to the emerging concept of Interaction Computing. After providing a conceptual mo...

This paper is a personal look at some issues in the representation theory of Lie groups having to do with the role of commutative hypergroups, bi-modules, and the construction of representations. We begin by considering Frobenius’ original approach to the character theory of a finite group and extending it to the Lie group setting, and then introduce bi-modules as objects intermediate between c...

Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite–difference equations approximating ordinary differential equations. Finite–difference equations are viewed as a system of algebraic equations with a small parameter, introduced through the definitions of finite–difference derivatives. I...

In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations with functional derivatives. In order to perform the group analysis and deal with the functional derivatives we extend the quantities such as infinitesimal transformations, prolongations and invariant solutions. For the sake of example the procedure is applied to...

`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method h...

this article concerned on the study of signature submanifolds for curves under lie group actions se(2), sa(2) and for surfaces under se(3). signature submanifold is a regular submanifold which its coordinate components are dierential invariants of an associated manifold under lie group action, and therefore signature submanifold is a key for solving equivalence problems.