Mathematical Model of a Social Insurance Fund with Random Expenditures for Social Programs (the Diffusion Approximation)

In the present work, the diffusion approximation of the capital is constructed for the mathematical model of a social insurance fund with random expenditures for social programs. The discontinuous hysteresis control of the fund capital is considered.     

Diffraction of the Electromagnetic Wave on a Small Obstacle of Elliptic Form in a Layer

The problem on the diffraction of the electromagnetic plane wave on a small obstacle included in a layer is investigated. The obstacle is assumed to be an elliptic cylinder whose diameter and focal distance are small in comparison with the length of the incident wave. It is proved that the small obstacle radiates as a point source, and its amplitude is proportional to the area of the cross-section and the jumps of the dielectric and magnetic constants on the interfaces. Bibliography: 5 titles.     

Pyroelectric effect in lead-magnoniobate-based solid solutions

A coordinated study of the dielectric, electrostriction, and pyroelectric properties of the lead-magnoniobate-based ceramic solid solutions 0.9PbMg_1/3Nb_2/3O₃-0.1PbTiO₃ and 0.55PbMg_1/3Nb_2/3O₃-0.45PbSc_1/2Nb_1/2O₃ conducted at the relaxor transition temperatures is reported. Electromechanical coupling stimulated by the giant electrostriction effect is shown to play an essential part in the pyroelectric effect.     

Effect of diffraction on the electrodynamic characteristics of two-dimensional coaxial Bragg resonators

The electrodynamic properties of coaxial two-dimensional Bragg resonators with two-dimensional distributed feedback are analyzed. These resonators are made of coaxial waveguide sections with doubly periodic corrugation, which provides coupling and mutual scattering of four partial waves. Two of them propagate along the waveguide, while the other two propagate in the transverse (azimuthal) direction. It is shown that the high azimuthal index selectivity of two-dimensional Bragg resonators may be related to a qualitative difference in topology of the dispersion characteristics of azimuth-symmetric and asymmetric normal waves propagating in infinite waveguides of such a geometry. For the finite-length systems used as two-dimensional Bragg resonators, the eigenmode spectrum is found for two types of boundary conditions that correspond to the limiting cases of perfectly matched (open) systems and, conversely, of systems closed for the extraction of transverse electromagnetic fluxes. Perimeter-to-length ratios of the resonator at which the Q factor of the fundamental azimuth-symmetric mode is greater than those of the other modes are determined. The applicability domain of the geometrical approach, which was earlier applied to two-dimensional Bragg resonators, is discussed.     

Axisymmetric Collision Problem for Two Identical Elastic Solids of Revolution

A direct central collision of two identical bodies of revolution is studied. A nonstationary mixed boundary-value problem with an unknown moving boundary is formulated. Its solution is represented by a series in term of Bessel functions. An infinite system of Volterra equations of the second kind for the unknown expansion coefficients is derived by satisfying the boundary conditions. The basic characteristics of the collision process are determined depending on the curvature of the frontal surface of the bodies     

Shape sensitivity of a plane crack front

The 3D‐elasticity model of a solid with a plane crack under the stress‐free boundary conditions at the crack is considered. We investigate variations of a solution and of energy functionals with respect to perturbations of the crack front in the plane. The corresponding expansions at least up to the second‐order terms are obtained. The strong derivatives of the solution are constructed as an iterative solution of the same elasticity problem with specified right‐hand sides. Using the expansion of the potential and surface energy, we consider an approximate quadratic form for local shape optimization of the crack front defined by the Griffith criterion. To specify its properties, a procedure of discrete optimization is proposed, which reduces to a matrix variational inequality. At least for a small load we prove its solvability and find a quasi‐static model of the crack growth depending on the loading parameter. Copyright © 2003 John Wiley & Sons, Ltd.     

Chaos-controlling technique for suppressing self-modulation in backward-wave tubes

A method for suppressing self-modulation in backward-wave tubes is proposed. Additional delay is introduced into the feedback circuit, owing to which the output signal amplitude affects the electron beam current that enters into the interaction space. Numerical simulations demonstrate that the operating current in the single-frequency oscillation mode may be increased roughly twofold.     

Effects of Moisture and Stresses on the Structure and Properties of Polyester Resin

The results of a complex study of structural changes in a cured Norpol 440 polyester resin under the action of damp environment and mechanical loading are presented. A considerable effect of absorbed moisture on the structure and some characteristics of the material is revealed by using thermophysical methods and X-ray diffractometry. The joint effect of moisture and mechanical stress is estimated by investigating the creep in stationary and nonstationary moisture conditions. The anisotropy of the material structure formed during creep is evaluated from the results of dilatometric measurements. It is found that the degree of anisotropy of the material after creep accompanied by moisture sorption is higher than that after creep in the conditions of moisture equilibrium with atmosphere. It is established that the aftercure and relaxation of the residual creep deformation come to an end at heating to 80-85°C. At a further rise in temperature and repeated heating, changes in the material structure are not observed.     

Improved tabu search algorithm for the handling of route duration constraints in vehicle routing problems with time windows

This note introduces a refinement to a previously proposed tabu search algorithm for vehicle routing problems with time windows. This refinement yields new best known solutions on a set of benchmark instances of the multi-depot, the periodic and the site-dependent vehicle routing problems with time windows.