Approximate Conditions and Passage to the Limit in Sobolev Spaces over Thin and Composite Structures

Approximate properties of variable measures compose a base of the two-scale convergence method with respect to a variable measure, which is used in averaging on periodic thin and composite structures. The paper gives a survey of methods for verifying approximate properties. The main focus is on studying composite measures, which have been little studied. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 16, Partial Differential Equations, 2004.     

Propagation of Electromagnetic Pulses in an Inhomogeneous Scattering Absorbing Medium. Invariant Temporal Properties

We present analytical solutions of the Ishimaru parabolic equation for the coherence function of electromagnetic field. The equation describes the temporal properties of the pulse at the output of an inhomogeneous dissipative scattering medium. An explicit expression for the Green's function of the problem is found. It is shown that the temporal part of the Green's function has an invariant Laguerre form. Numerical results describing the shapes of the studied temporal pulses at the output of the pass interval of the medium are also given. Time scales characterizing the shapes of the Laguerre output pulses are proposed and the influence of the parameters of the medium on the properties of the resulting pulses is analyzed.     

ACTIVE CONTROL OF ENVIRONMENTAL NOISE, VII: PERFORMANCE OF MULTI-FREQUENCY, MULTI-CHANNEL, FREEFIELD SOUND CANCELLING SYSTEMS

The paper considers the performance of multi-frequency, multi-channel, free field sound cancelling systems for the reduction of discrete frequency and periodic noise. The approach uses a method of directional active noise control. Large sound reductions from these systems have been made possible through: (a) synthetically generating the cancelling sound and synchronizing with the primary source; (b) automatic alignment of all stability regions of the control system and; (c) avoiding instability produced by these multi-channel systems.     

Symmetric normal wave spectrum in an orthotropic layer

A solution is constructed for an orthotropic layer with free plane faces, that corresponds to the plane elastic waves symmetric over the thickness. The dynamical reconstruction of the normal wave spectrum during rotation of the wave vector from one to another elastically equivalent direction is investigated on the basis of a numerical analysis of the dispersion equation.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 116–121, 1988.     

Effects of stenosis on arterial rheology through a mathematical model

The paper presents an analytical study of blood flow through a stenosed artery using a suitable mathematical model. The artery is modelled as an anisotropic viscoelastic cylindrical tube containing a non-Newtonian viscous incompressible fluid representing blood. The blood flow is assumed to be characterized by the Herschel–Bulkley model. The effect of the surrounding connective tissues on the motion of the arterial wall has been incorporated. Initially, the relevant solutions of the boundary value problem are obtained in the Laplace transform space, through the use of a suitable finite difference technique. Laplace inversion is carried out by employing suitable numerical techniques. Finally, the variations of the vascular wall displacements, the velocity distribution of the blood flow, the flux, the resistance to flow and the wall shear stress in the stenotic region are quantified through numerical computations and presented graphically.     

Representations of symmetric groups with maximal dimension

Results of numerical modeling connected with the study of the asymptotics of representations of the symmetric group S_N for largeN which are of maximal dimension are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Akad. Nauk SSSR, Vol. 172, pp. 160–166, 1989.     

Mutual coupling of elements in finite microstrip antennas

The mutual coupling of the radiating elements in microstrip antennas is studied using a rigorous electrodynamic approach in which the field singularities at the radiator edges are taken into account with analytic accuracy. A spectral method is employed in combination with a method of semi-inversion by extraction of the Green-function singularity. The degree of interaction of the elements of microstrip structures at the fundamental and higher current harmonicsis determined, and the applicability of various approximations is assessed.Radio-Astronomy Institute, Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, No. 8, pp. 688–701, August, 1992.