On the convergence to zero of solutions of a second-order differential equation with complex-valued potential

We consider the second-order linear differential equation y" + A(t)y = 0 on the semiaxis with complex-valued potential function. Sufficient conditions for the potential function assuring that all solutions of the equation converge to zero at infinity are obtained. It is shown that the conditions imposed on the potential function are close to the necessary ones. One of the results seems to be new even in the case of real-valued function A(·).     

Equation of a shock wave front

Second-order differential equations of the hyperbolic type are derived for describing the local law of shock wave propagation. The shock waves are assumed to be two-dimensional unsteady in a stationary gas flow and three-dimensional steady in a supersonic flow. The behavior of the characteristics of these equations is investigated as a function of the governing flow parameters and their relative position with respect to the typical bicharacteristics of the characteristic cone behind the shock is analyzed. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 159–165, May–June, 2000.     

On Spectral Synthesis for Dissipative Dirac Type Operators

The paper is concerned with the spectral synthesis for general dissipative boundary value problems for n × n first order systems of ordinary differential equations on a finite interval. We show that the resolvent of any complete dissipative Dirac type operator with summable potential admits the spectral synthesis in \({L^2([0,1]; \mathbb{C}^n)}\) . Moreover, we provide explicit sufficient conditions for Dirac type operator to be complete and dissipative.     

Calculation and experimental study of a unidirectional rubber-cord composite in tension and compression

Calculation and experimental study of transverse tension and compression of a rubber-cord composite with a unidirectional scheme of reinforcement is presented. The calculation results for components of the composite and for the composite as a whole are compared with the experimental data. The loss of stability of the deformed rubber-cord composite in transverse tension is analyzed.Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 325–334, 1999.     

Impact of pairing on the heat capacity of systems with an isolated level bunch near the Fermi surface

Canonical heat capacity vs. the temperature for systems with an isolated level bunch near the Fermi surface is calculated using exact eigenvalues of the effective Bardeen–Cooper–Schrieffer Hamiltonian (H _BCS). Two degenerate levels separated by energy spacing Δε in spherical systems can produce two maxima in C at low values of G/Δε, where G is the pairing strength of H _BCS. These two maxima become one as G/Δε grows and the system deforms.     

Calculation and Experimental Study of a Two-Way Reinforced Rubber-Cord Composite in Tension

A rubber-cord composite, reinforced in two directions with fibers of polyamide cord, under large tensile deformations is investigated based on calculations of a rubber-cord composite material and on tensile tests of specimens made of the casing of a diagonal truck tire. A method of the experimental tensile testing of rubber-cord composite specimens is described. The calculations are based on the carcass theory of composite materials. The calculated and experimental parameters of the macroscopic strains of the rubber tire cord and of its structure in a deformed configuration are given. The manifestation of edge effects in relation to the reinforcement angle is described.     

Averaging thermodynamic quantities over pairing fluctuations

Discrepancies in BCS theory results for finite Fermi systems with exact values of thermodynamic quantities are eliminated by means of averaging over pairing fluctuations. A form of the averaging function is proposed and its parameters are considered.