Vol 15, No 2 (2011)

We present new integral transforms, generalized the classical Laplace, Stieltjes and Widder integral transforms in the potential theory. The (τ, β)-generalized confluent hypergeometric functions are the kernels of these integral transforms. Inverse formulas for new integral transforms are proved. Relations of the Parseval-Goldstein type are established. Some examples of applications of the new integral transforms are given.

This article contains proving the convergence of numerical solving of optimal control problem for degenerate linear systems of ordinary differential equations with constant coefficients. Considering different appendixes of such systems, they belong to Leontief type system, as in the first time such systems were investigated as a dynamic Leontief input-output model with noninvertible operator on derivative. By using the initial condition of Showalter-Sidorov we gain an ability to extend the range of practical applicability for this model. The article includes existence and uniqueness theorem of numerical solution of investigated problem, his kind, and results of numerical experiment for dynamic input-output model, which was offered by W. Leontief.

Non-local boundary value problem for loaded equation of parabolic type with the sign- variable characteristic form is solved. Common representation of solution is constructed. The theorems of common representation, existence and uniqueness of solution for boundary value problems set in rectangular domain are proved.

The paper presents a study of wavenumbers of coupled harmonic thermoelastic waves propagating via an infinite circular cylinder for higher azimuthal order. Heat interchanging between sidewall of the waveguide and environment is assumed. The analysis is carried in the frameworks of coupled generalized thermoelasticity theory of type III (GNIII-thermoelasticity). This theory synthesizes thermodiffusion and wave mechanisms of heat transfer in solids including as limiting cases both the theories: classical thermoelasticity (GNI/CTE) and the theory of hyperbolic thermoelasticity (GNII). The latter permits field-theoretic formulation and leads to the field equations of hyperbolic analytical type. The two principal problems: separation of 32 independent single-valued square radicals involved in the frequency equation and more accurate computation of the real-valued wavenumbers are resolved and discussed.

The stochastic boundary-value problem of elasticity theory for two-phase polydisperse composites is stated. The solution method with using high order moment functions is described. Algorithm of synthesis of n-order moment functions for 3D structures is presented. Approximating expression for moment functions is suggested. Examples of calculation of high-order moment functions for polydisperse structures are given.

Parallelization of deformation-damage coupling boundary value problem solution is considered. In definition the equations of the strength we used the principle of equivalence of deformations in a real and relatively undamaged structures. Principle of real and hypothetical undamaged structure strain equivalence is applied. An iterative procedure characterized by successive solutions of plasticity and damage problems at each iteration step, is proposed. The approach to parallelization of softening plasticity boundary value problem solution is based on the conception of generalized nonlinear structural models and on the method of decomposition.

The results of the study of static and dynamic magnetic properties of single-crystal spinel ferrites films. It is shown that the magnetic properties of films depend on the chemical composition, degree of structural defects and technological conditions of synthesis. We conclude that decreasing the cooling rate of the films on the synthesis temperature may change the valence of iron that significantly affects the magnetic parameters of the films.

The paper describes the main results of thermodynamic calculations of aluminoferric themit combustion reaction, including combustion reaction of thermit, pelletized with cellulose nitrate. Based on the calculations results, the presence of gas phase during combustion is approved. The reason of gas phase presence is determined, what allowed to develop recommendations of its reducing. The effect of cellulose nitrate on thermit combustion reaction temperature is also estimated.

The peculiarities of atom-field entanglement in the model of two nonidentical atoms interacting with one-mode coherent electromagnetic field in lossless cavity via degenerate two-photon Raman transitions have been investigated. The times of atoms and field states disentanglement have been calculated on the basis of time-dependent wave function behavior and the linear atomic entropy concept.

The group-theoretical justification is presented for the original approach by Kirznits and Chechin which allows for the primary protons of ultra-high energy cosmic rays to overcome the energetic limit (about 50 EeV) of Greisen-Zatsepin-Kuzmin remaining in the scope of the usual ideas about the nature of the extra-galactic sources of the cosmic rays. It is shown that the explicit form of the factor deforming the Lorentz invariant in the energy-momentum space may be found on the grounds of the approximate transition from Lorentz symmetry to the conformal values of the Lorentz-factor of the order 1010÷1011.

We consider the hierarchical model of financial crashes introduced by A. Johansen and D. Sornette which reproduces the log-periodic power law behavior of the price before the critical point. In order to build the generalization of this model we introduce the dependence of an influence exponent on an ultrametric distance between agents. Much attention is being paid to a problem of critical point universality which is investigated by comparison of probability density functions of the crash times corresponding to systems with various total numbers of agents.

We consider self-adjoint generalized Friedrichs model h(p), p ∈ T3 (T3 is the threedimensional torus), in the case where the parameter functions w1 and w2 of this operator has the special forms. These functions has non-degenerate minimum at the several different points. Threshold effects for the considering operator are studied depending on the minimum points of w2.

This paper investigates properties of Parseval frames in finite dimensional vector spaces, namely, the possibility of representing some frames as sums of others. A new approach in constructing arbitrary Parseval frames and the decomposition arbitrary frame into the sum are described. Besides there is a number of special properties of equiangular tight frames.

The application of the method of super-potential to the solution of the problems of cosmology with the tachyon fields is examined. The classes of exact solutions are found and the periods of time with the predominance of dark energy are established.

A new quantum-mechanical model of the two-slit experiment is presented, in which the wave properties of a particle are compatible with its corpuscular ones. The model is based on the idea which also underlies our previous model of a one-dimensional completed scattering. Its essence is that quantum processes, in which the systems state represents a coherent superposition of microscopically distinct substates (CSMDS), must be considered as complex random processes consisting of alternative subprocesses. Only with a new approach to CSMDSs quantum theory admits a consistent statistical interpretation and becomes free from the paradoxes associated at present with CSMDSs.

Homogeneous closed PDO are constructed which are analogous to the powers of (absolute value of ) infinite dimensional Laplacian and acting in Banach spaces of complexvalued functions defined on function spaces over a field of p-adic numbers. For elements of semigroups, for which these PDOs are generators, Feynman formulas and Feynman-Kac ones are obtained.

A mathematical model of the dynamical system of the two elastic tandem type plates, flowing along of the subsonic flow of gas (fluid) is proposed. The solution of aerohydrodynamic part of problem based on the methods of complex variable functions theory is given. The bound system of the equations allowing to investigate the plates dynamic is obtained. The numerical-analytical method of solution of this equation is offered.

The technique of exact non-stationary dynamic calculation of compound designed systems of in steps-variable thickness a method initial parameters is offered. The settlement scheme considers displacement of median surfaces of interfaced elements. As an example calculation of base plate of a dam GES and matrices of explosive punching is resulted at pulse influence.

A model describing the process of destruction of granular materials was developed. The regularities of formation and development of cracks in discrete environment were determined. The results of numerical calculation of stress intensity factors of the first kind, taking into account the elastic characteristics of grain boundary core are presented.

In this paper a new mathematical model of the disk motion on the basis of the Kelvin body is constructed. Accepting the hypothesis of a point contact with the drive base, a system of differential equations of the disk motion is derived in the form of modified Chaplygin equations involving generalized rheological response force, as well as three stationary constraint equations, two of which are nonholonomic. The analysis of the drive permanent movements stability was carried out. It is shown that the rectilinear motion of the disk and spinning around a vertical diameter are unstable in relation to the nutation angle θ.