Zaza Sanikidze

The kinetics of oxidation of low-alloyed chromium in air has been investigated over the temperature range of 1300-1400ºC. The net-projection numerical method was proposed for solution of the kinetics equation, taking into account the formation of the oxide film during heating the specimens up to the test temperature.

A matrix of fundamental solutions of the equation of dynamic elasticity theory is constructed for a homogeneous isotropic medium in the case, when a concentrated force changes at time exponentialy-periodicaly. Properties of the indicated matrix and its corresponding stress tensor are investigated. Besides, a way of calculation of their elements is given.

The algorithm of solving the external three-dimensional Dirichlet boundary value problem for a harmonic function by the probabilistic method is given. The algorithm consists of the following stages: 1) transition from an infinite domain to a finite domain by an inversion; 2) consideration of a new boundary problem on the basis of Kelvin’s theorem for the obtained finite domain; 3) application of the probabilistic method to solving a new problem, which in turn is based on a computer simulation of the Wiener process; 4) definition of the solution of the statement problem for the infinite domain by the solution of the new problem. For illustration an example is considered.

An algorithm for the determination of elastico-dynamic state of homogeneous isotropic elastic body with a free surface over finite interval of time is given. In the present paper we consider the case,when the mentioned state of the elastic body is caused by the action of a simple concentrated force applied to a fixed point of the body, with the force varying in time by a non-periodical law. The realization of the algorithm is based on the method of fundamental solutions. The effectiveness of the proposed algorithm in comparison with the methods of integral transformation and Green’s function is shown. For illustration of efficiency, an example has been discussed

In this paper we investigate the question how the method of conformal mapping (MCM) can be applied for approximate solving of the generalized Dirichlet boundary problem for harmonic function. Under the generalized problem is meant the case when a boundary function has a finite number of first kind break points. The problem is considered for finite and infinite simply connected domains. It is shown that the method of fundamental solutions (MFS) is ineffective for solving of the considered problem from the point of view of the accuracy. We propose an efficient algorithm for approximate solving of the generalized problem, which is based on the MCM. Examples of application of the proposed algorithm and the results of numerical experiments are given.

A new way of applying ICT to improve the election process in a biased environment is considered. Namely, VoterBallot - a management information communication system for electoral candidates is suggested. It includes four main components: physical infrastructure, software, structured information and training.

The presented work deals with the new scope of application of information and communication technologies for the improvement of the election process in the biased environment. We are introducing a new concept of construction of the information-communication system for the election participant. It consists of four main components: Software, Physical Infrastructure, Structured Information and the Trained Stuff. The Structured Information is the bases of the whole system and is the collection of all possible events (irregularities among them) at the polling stations, which are structured in special templates, forms and integrated in mobile devices.The software represents a package of analytic modules, which operates with the dynamic database. The application of modern communication technologies facilities the immediate exchange of information and of relevant documents between the polling stations and the Server of the participant. No less important is the training of the staff for the proper functioning of the system. The e-training system with various modules should be applied in this respect.

This paper focuses on the actual practical information regarding boundary problems with the boundary singularities. Dirichlet generalized boundary problem for a Laplace equation is considered for both finite and infinite domains. The case of a boundary function with a limited number of first kind break points is considered under this generalized boundary problem. In this paper, one method is a given ordinary problem for the reduction of the Dirichlet generalized boundary problem with an harmonic function. The method is constructed on the basis of fictitious sources and is applied to finite and infinite domains. From our point of view, this method is characterized by simplicity, stability, and allows for high accuracy. Also, it is oriented for a wide range of users (especially for the researchers in engineering problems). Examples with cusp points in the role of break points are also considered. The results of numerical experiments are given.

An algorithm for the approximate solution of the Dirichlet generalized problem is proposed. The term “generalized” indicates that the boundary function has a finite number of first kind break points. The solution consists of the following stages:

1) the reduction of the Dirichlet generalized problem to an ordinary auxiliary problem for a harmonic function; 2) an approximate solution of the auxiliary problem by the modified version of the MFS (the method of fundamental solutions); 3) the construction of an approximate solution of the generalized problem from the solution of the auxiliary problem. An example is considered in which the break points are the cusp ones.

A Dirichlet generalized harmonic problem for finite right circular cylindrical domains is considered. The term “generalized” indicates that a boundary function has a finite number of first kind discontinuity curves. It is shown that if a finite domain is bounded by several surfaces and the curves are placed in arbitrary form, then the generalized problem has a unique solution depending continuously on the data. The problem is considered for the simple case when the curves of discontinuity are circles with centers situated on the axis of the cylinder. An algorithm of numerical solution by a probabilistic method is given, which in its turn is based on a computer simulation of the Wiener process. A numerical example is considered to illustrate the effectiveness and simplicity of the proposed method.

Some special cases of single-machine problems is considered. In these cases there are many optimal solutions. It is given the formulas of quantity of optimal solutions and calculated the probability of the event that an arbitrary schedule is optimal; the sufficient conditions to increase the value of this probability is given and the corresponding optimal full completion time is calculated.