Existence and approximation of slow integral manifolds in some degenerate cases

We consider singularly perturbed differential systems whose degenerate equations have an isolated but not simple solution. In that case, the standard theory to establish a slow integral manifold near this solution does not work. Applying scaling transformations and using the technique of gauge functions we reduce the original singularly perturbed problem to a regularized one such that the existence of slow integral manifolds can be established by means of the standard theory of singular perturbations. We illustrate our method by several examples

Integral manifolds for slow-fast differential systems loosing their attractivity in time

The work is devoted to the investigation of the integral manifolds of the nonautonomous slow-fast systems, which change their attractivity in time. The method used here is based on gluing attractive and repulsive integral manifolds by using an additional function

A new type of travelling wave solutions

We study the existence of combustion waves for an autocatalytic reaction in the non-adiabatic case. Basing on the fact that the reaction system has canard solutions separating the slow combustion regime from the explosive one, we prove by applying the geometric theory of singularly perturbed differential equations the existence of a new type of travelling waves solutions, the so-called canard travelling waves

SPACE: a suite of tools for protein structure prediction and analysis based on complementarity and environment

We describe a suite of SPACE tools for analysis and prediction of structures of biomolecules and their complexes. LPC/CSU software provides a common definition of inter-atomic contacts and complementarity of contacting surfaces to analyze protein structure and complexes. In the current version of LPC/CSU, analyses of water molecules and nucleic acids have been added, together with improved and expanded visualization options using Chime or Java based Jmol. The SPACE suite includes servers and programs for: structural analysis of point mutations (MutaProt); side chain modeling based on surface complementarity (SCCOMP); building a crystal environment and analysis of crystal contacts (CryCo); construction and analysis of protein contact maps (CMA) and molecular docking software (LIGIN). The SPACE suite is accessed at

Research of the thorium purification at monazite refinement processes

This paper is aimed to the research of the thorium purification processes at monazite refinement processes. We have investigated different solution containing thorium with different mix of rare-earth elements. It was found that the application of cation resin is well- recommended if we want to reach the highest yields of thorium purification process