Vol 18, No 9 (2012)

The article examines some aspects of numerical solution of some problems of antenna electrodynamics, reducible to the integral equations of the second kind with the use of various bases of decomposition of the sought function.

The construction of integral models is necessary for the research on arithmetical properties of algebraic tori. Neron model, having some unique properties, is of special interest among different possible integral models of algebraic tori over local fields. Its definition is not constructive, though. That's why its construction is an important problem. In this paper the problem of explicit construction of Neron model is solved for all two-dimensional anisotropic algebraic tori over local fields.

In this paper, we consider a problem with Saigo operators of fractional differentiation in a boundary condition on a characteristic part of a boundary. The unique solvability of this problem is proved.

An approximate solution of nonlinear eigenvalue problem arising from the Mode I crack problem in a nonlinear power-law medium is obtained. The perturbation technique is used. The method allows to find the analytical formula expressing the eigenvalue as the function of parameters of constitutive law and eigenvalue corresponding to the linear undisturbed problem.

In work the problem of pressure decrease of steam in the closed volume owing to condensation on border of contact to a cold liquid is considered. The nonlinear integrodifferential equations which numerical decision is executed by a method of final differences are received. Influence of an initial condition and the expense of a liquid, the geometrical size of the closed volume on rate of pressure decrease is analysed.

The solution of optimal control problem of the threefold integrator with any boundary conditions by method of moments is considered. It is shown that in case of minimization of total impulse of control influence or control consumption, the solution of L

In this chapter the new results are systematized on study of the equations of motion of dynamically symmetrical four-dimensional (4D—) rigid body which residing in a certain nonconservative field of forces in case of special dynamical symmetry. Its type is unoriginal from dynamics of the real smaller-dimensional rigid bodies of interacting with a resisting medium on the laws of a jet flow, under which the nonconservative tracing force acts onto the body and forces both the value of velocity of a certain typical point of the rigid body and the certain phase variable to remain as constant in all time, that means the presence in system nonintegrable servo-constraints.

In this article phase transitions in the modified two-dimensional Ising model with long-range correlations investigated. This model was studied with Monte-Carlo method and Metropolis algorithm. Critical temperature increase is shown in such model.

The data on some phenotypic features of 40 population groups of Silybum marianum Gaertn, created on the base of seeds with different geographic origin during the field investigations in 1989-2006 in Samara region are given in the article. The problem of possible connection between morphological and quantitative, especially productivity-connected, parameters is discussed.

In this paper the effects of heavy metal ions (Pb2+) and cationic surfactants combination on enzyme activities in water submerged plant Ceratophyllum demersum are considered.

The antioxidant system activity in liver and muscle of rat after bilateral ovaryectomy and allogenic hydroxyapatite injections was investigated. The decrease of antioxidant system activity in rats with removed ovaries was found. Injections of allogenic hydroxyapatite leads to normalization of antioxidant system activity.