Mathematical Model of Re-Structuring Complex Technical and Economic Structures

Research and development of mathematical model of optimum distribution of resources (basically financial) for maintenance of the new (raised) quality (reliability) of complex system concerning, which the decision on its re-structuring is accepted, is stated. The final model gives answers (algorithm of calculation) to questions: how many elements of system to allocate on modernization, which elements, up to what level of depth modernization of each of allocated is necessary, and optimum answers are by criterion of minimization of financial charges.

e-Course of Theoretical Mechanics

The concept, structure and contents of the Internet textbook on classical mechanics intended for Higher Technical Institutions are presented in this work. Aspects of program realization of textbook applications and the technology of elaborating the textbook in the “Hecadem” Internet-teaching environment are given too.

Applied Aspects of Mathematical Modeling and Optimization of Dynamics of Charged Beams

The complex of questions connected with the analysis, estimation and structural-parametrical optimization of dynamic system is considered in this article. Connection of such problems with tasks of control by beams of trajectories is emphasized. The special attention is concentrated on the review and analysis of spent scientific researches, the attention is stressed to their constructability and applied directedness. Efficiency of the developed algorithmic and software is demonstrated on the tasks of modeling and optimization of output beam characteristics in linear resonance accelerators.

On the Mathematical Modelling of Microbial Growth: Some Computational Aspects

We propose a new approach to the mathematical modelling of microbial growth. Our approach differs from familiar Monod type models by considering two phases in the physiological states of the microorganisms and makes use of basic relations from enzyme kinetics. Such an approach may be useful in the modelling and control of biotechnological processes, where microorganisms are used for various biodegradation purposes and are often put under extreme inhibitory conditions. Some computational experiments are performed in support of our modelling approach.

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Research partially supported by INTAS grant 97-1644

Partial Ovoids and Partial Spreads of Classical Finite Polar Spaces

2000 Mathematics Subject Classification: 05B25, 51E20.