## No 4 (2008)

**Year:**2008**Articles:**14**URL:**http://journals.rudn.ru/miph/issue/view/520

Articles

Pontryagin's Principle of Maximum for Linear Optimal Control Problems with Phase Constraints in Infinite Dimensional Spaces

###### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):5-19

On dimKer and dimCoker for an Elliptic Operator with Discontinuous Coefficients

###### Abstract

For divergence form of elliptic operator with discontinuous piecewise smooth coefficients we analyzed questions of the uniqueness and the existence of generalized solutions for BVP with the divergent right-hand part from the class with first derivatives from in a bounded plain domains with smooth and nonsmooth borders. We calculate dimKer and dimCoker for an elliptic operator for all indices depending on parameters of critical points.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):20-29

The Quasiinvariant Stabilization of a Pursuit Motion of a Manipulator by Proportional Navigation

###### Abstract

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

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):30-36

Research of Stability of Integral Variety for Perturbation of Constraints with Constant Coefficients

###### Abstract

The method of constructing of mathematical model of dynamics of operated mechanical system is offered. The algorithm of updating of the equations of dynamics which allows to solve a problem of stabilization of communications is under construction and to provide demanded accuracy of the numerical decision of corresponding system of the differential-algebraic equations describing imposed on communication system, its kinematics and dynamics. The offered method can be used for research of dynamics of systems of the various physical nature.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):37-41

On Some Aspects of Information Analytical SystemConceptual Object-Oriented Multidimensional Metamodel Development

###### Abstract

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).

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):42-49

Automatic Generation of Logical Knowledge

###### Abstract

We study problems which arise deriving generating automatically logical knowledge in systems of artificial intellect, first of all in systems of automatic theorem proving. Three necessary conditions for a generator of logical knowledge are proposed and a verification of these ones is presented.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):50-60

Heuristic Approach to the Problem ofMinimal Extension of a Communication Network and Its AssessmentBased on a Specialized Class of Weighted Digraphs

###### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):61-67

Transition Probabilities in Quantum Mechanics of Kuryshkin

###### Abstract

The method of calculating probabilities of radiation transitions in hydrogen-like atoms in quantum mechanics with nonnegative distribution function is proposed. Galerkin method using Sturmian functions of the hydrogen atom as basis functions allows to reduce the computations to algebraic operations with matrix elements calculated analitically.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):68-74

Application of Functional Integration Method inSome Problems of Mathematical Physics

###### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):75-83

On New Conditional Heteroskedasticity Model withCorrelation of Autoregressive Type

###### Abstract

New econometric model of stock indexes joint dynamics has been introduced in this paper. The distinctive feature of the model is description of conditional correlation between time series using autoregressive type random process. Efficient calculation algorithm for parameters estimation has been developed for suggested model.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):84-88

Computer Simulation of Appearance of Animal Organ

###### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):89-92

Simple Two-Oscillators Model of C. Bjerknes'sVibrating Spheres Problem

###### Abstract

The simple two-oscillators model is suggested to illustrate the phase dependent interaction of vibrating spheres in hydrodynamics (the C. Bjerknes's problem). The integrability of this model is shown. Correspondence with the Fermi-Bose statistics in quantum mechanics is underlined.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):93-95

Conditions of Excitation of a Spinodal Decay of Unstable Liquid Phase in the Process of Metals Pulse Heating

###### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):96-103

Use of Natural Syrian Zeolitic Tuff in Solar Thermal Applications

###### Abstract

We focus our attention in this work, from experimental point of view, on the applicability of natural Syrian zeolitic tuff in storing thermal solar energy. Several samples of different zeolitic content were taken from different heights of the borehole. These samples were used in this study. It was found that, when the heating temperature is below C, the effect of Syrian natural zeolitic tuff' storing energy is quite good. The obtained results clearly show that the tentative idea of utilizing natural zeolitic tuff to store solar heat energy is feasible. Zeolitic content and grain sizes are the main affecting factors. As the operating temperature of the conventional flat-plate solar collectors generally is below C, the aforementioned conclusion has important significance.

**Discrete and Continuous Models and Applied Computational Science**. 2008;(4):104-108