The approximate description of the process of interaction between two eddy-flows in sufficiently rarefied gas of hard spheres is obtained. Such the flows rotate and move translationally, besides corresponding Maxwell distributions are exact solutions of the Boltzmann equation. Each of the flows have two different axes - the axis of density and the axis of velocities, whose disposition in the space in a special way is connected with the degree of accuracy of the bimodal approximate solution. 2000 Mathematics Subject Classification: 76P05; 45K05; 82C40; 35Q55. Top of the page.
We consider a Mindlin-Timoshenko thermoelastic plate model with nonlinear feedback forces. We prove the existence of a compact global attractor and study its properties when the shear modulus tends to infinity and to zero. 2000 Mathematics Subject Classification: 35B25. Top of the page.
The functional model for any bounded non-selfadjoint operator in the Hilbert space $H$ is constructed. Operator dissipativness is not supposed. This model is a generalization of the B. S. Pavlov functional model and realized by the operator of multiplication by the independent variable in a weight Hardy space in a strip. 2000 Mathematics Subject Classification: 47A45. Top of the page.
The main part of the operator of the electrostatic problem for a spherical segment which is imbedded into a dielectric rounding of a cone was separated and inversed by the method of regularization. The method is based on the use of the techniques of contour integration and Abel integral transformation. As a result, the Fredholm integral equation of the second kind with a compact operator in Hilbert space $L_2(0,\gamma)$ was obtained. Particular cases of problem formulation are considered. [Full-text pdf]. 2000 Mathematics Subject Classification: 65N12, 35A25,78A45. Top of the page.
The paper concerns the contact interaction of the opposite faces of a penny-shaped crack under oblique incidence of a harmonic tension-compression wave. The problem is solved by the method of boundary integral equations using an iterative algorithm. The dependence of stress intensity factors on the wave frequency and the friction coefficient is studied. 2000 Mathematics Subject Classification: 74R10, 74M99, 45E99. Top of the page.
The criterions of mappabability of nonlinear systems with one-dimensional control to feedforward systems with the change of the control and without change of the control are obtained. 2000 Mathematics Subject Classification: 93B18. Top of the page.
The Azarin's set of subharmonic function is more refined characteristic of growth than the indicator and low indicator. We give example of subharmonic function with extremely nonregular growth. The Azarin's limit set of Riesz' measure of this function consists of single point supported measures. 2000 Mathematics Subject Classification: 31A05. Top of the page.
Small oscillations of ideal fluid in partially filled vessel cavity divided by rigid perforated baffler with large number of holes are studied. Mathematic formulation of problem with averaged conjugated conditions on bafflers was given, solutions of which are asymptotic approximation of precise solutions under unlimited increasing of hole number. Results of studying of evolutional and spectral averaged problems are given. 2000 Mathematics Subject Classification: 74J05. Top of the page.
Stability problem of cylindrical zone of current-carrying liquid interacting with external magnetic field is considered. The method of stability investigation on the base of analysis of free oscillation frequencies is proposed. The boundary of stability region in the space of dimensionless parameters of the system is constructed. 2000 Mathematics Subject Classification: 76W05. Top of the page.
A Banach space is said to have the big slice property if every slice of its unit ball is of diameter 2. Let $K$ be a metric space. We establish some necessary and some sufficient conditions for the big slice property of the space ${\rm Lip}(K)$ of all real-valued Lipschitz functions on $K$. In particular, ${\rm Lip}(K)$ has the big slice property if $K$ is an infinite compact space. In the case of finite set $K$ we find a characterization of extreme points of the unit ball of ${\rm Lip}(K)$. 2000 Mathematics Subject Classification: 46B20. [Full-text pdf]. Top of the page.