No 4 (2008)

This paper presents the conditions of optimality for a problem with linear phase constraints in an infinite dimensional normal space with separated locally convex topology demonstrated using the works of M.F. Sukhinin in infinite dimensional normal spaces, his theory of differential equations in these spaces when functions are not Bochner-integrable and have no derivative of Gateaux. Problems with phase constraints were analyzed in finite spaces by many authors like L.S. Pontryagin, L. Graves, V.G. Boltyanskiy, R.V. Gamkrelidze, A.A. Milyutin, A.V. Dmitruk, N.P. Osmolovskij and others. Using the theory of differential equations of Prof. M.F. Sukhinin published in his monograph [1], applying the Gamkrelidze and Pontryagin's method illustrated in book [2], we enounced and proved theorems for linear mixed constraint in the separated locally convex space X.

The procedure of constructing a differential equations set for a regulator providing quasiinvariant stabilization of a manipulator with proportional navigation is proposed.

Object-oriented approach provides essential advantages in multidimensional modeling. The question of information analytical system multidimensional metamodel development is considered in this paper very closely. It is offered to use widely the methods based on standards in the field of the multidimensional analysis: Meta Object Facility (MOF), Common Warehouse Metamodel (CWM), Unified Modeling Language (UML).

In the paper we are presenting a heuristic approach to solve the problem of changing network topology by minimally extending a digraph G′ through adding edges from a given spanning supergraph G of G', such that the sum of the costs of the new edges is minimum, and in the new graph the end-to-end delay between two distinguished vertices s and t meets a predefined time constraint (ME problem). We develop a heuristic based upon the Genetictype algorithm technique. Moreover, the application of this heuristic is justified and is shown that the solution of ME problem belongs to the NP-hard computational class.

Application of numerical functional integration method to solving some problems of mathematical physics is described. The recent publications related to calculation of functional integrals in various branches of science are reviewed. The analysis of modern trends and directions of functional integral applications is given.

The purpose of our work consists in simulation of forming of a progressive morphological structure during sympatric speciation. This progressive structure is described by an unique set of «1»s in two non-parallel bit-strings. Individuals with this structure will be better adapted to the current environment. We show that the appearance of a stable progressive structure can occur in case of low probability of negative mutations and, therefore, it is a very rare evolutionary event.

The equations for spinodal and quasispinodal of a liquid phase are obtained; the area of existence of an unstable liquid phase on the phase diagram is certain. The established process of homogeneous nucleation of a vapor nuclei in overheated liquids in a spinodal area is considered, the formula for definition of characteristic time of development of this process is obtained. Velocity of heating of a liquid at which to pass through the spinodal in area of an unstable phase is possible is certain. Prominent features of spinodal disintegration of unstable liquid metal phases are considered.