Boundary Problems for the Quantum Bose Gas

A relaxation kinetic equation that describes the behavior of a Bose gas is derived. The Kramers half-space problem on isothermal slip is treated. An analytical solution and the number-of-particle distribution function for particles flying toward a wall, in explicit form, are obtained. The dependence of the slip velocity on the parameter that is the ratio of the chemical potential to the product of Boltzmann's constant by the absolute temperature is analyzed. The influence of the quantum effects on the isothermal slip coefficient is evaluated for He⁴.     

The effect of geoacoustic characteristics of the bottom on the long-range sound propagation in an inhomogeneous ocean

The long-range sound propagation from a deep ocean to a receiving system located on the shelf is modeled. The waveguide model is constructed on the basis of the data of an acoustic-oceanographic experiment carried out in the northwestern Pacific. The sensitivity and the frequency dependence of the difference in the sound field levels at the crossing of the frontal zone on the geoacoustic characteristics of the bottom of the shelf and the continental slope are investigated. It is shown that the level difference decreases by 8.2 dB as the velocity of longitudinal waves increases by 100 m/s in the range within 1490–1820 m/s.     

Wave biomechanics of the skeletal muscle

Results of acoustic measurements in skeletal muscle are generalized. It is shown that assessment of the pathologies and functional condition of the muscular system is possible with the use of shear waves. The velocity of these waves in muscles is much smaller than the velocity of sound; therefore, a higher symmetry type is formed for them. In the presence of a preferential direction (along muscle fibers), it is characterized by only two rather than five (as in usual media with the same anisotropy) moduli of elasticity. A covariant form of the corresponding wave equation is presented. It is shown that dissipation properties of skeletal muscles can be controlled by contracting them isometrically. Pulsed loads (shocks) and vibrations are damped differently, depending on their frequency spectrum. Characteristic frequencies on the order of tens and hundreds of hertz are attenuated due to actin-myosin bridges association/dissociation dynamics in the contracted muscle. At higher (kilohertz) frequencies, when the muscle is tensed, viscosity of the tissue increases by a factor of several tens because of the increase in friction experienced by fibrillar structures as they move relative to the surrounding liquid; the tension of the fibers changes the hydrodynamic conditions of the flow around them. Finally, at higher frequencies, the attenuation is associated with the rheological properties of biological molecules, in particular, with their conformational dynamics in the wave field. Models that describe the controlled shock dissipation mechanisms are proposed. Corresponding solutions are found, including those that allow for nonlinear effects.     

On a Modified Subgradient Algorithm for Dual Problems via Sharp Augmented Lagrangian*

We study convergence properties of a modified subgradient algorithm, applied to the dual problem defined by the sharp augmented Lagrangian. The primal problem we consider is nonconvex and nondifferentiable, with equality constraints. We obtain primal and dual convergence results, as well as a condition for existence of a dual solution. Using a practical selection of the step-size parameters, we demonstrate the algorithm and its advantages on test problems, including an integer programming and an optimal control problem. *Partially Supported by 2003 UniSA ITEE Small Research Grant Ero2. Supported by CAPES, Brazil, Grant No. 0664-02/2, during her visit to the School of Mathematics and Statistics, UniSA.     

On the construction of samples for testing approximate optimization methods for estimate calculation algorithms

To validate approximate optimization schemes for estimate calculation algorithms (ECAs), it is necessary to compute the optimal height, which cannot be done in a reasonable amount of time. A variety of samples are built for which the optimal height of the ECAs is known by construction.     

Factor and term ranks for matrix union over semirings

We consider the arithmetic properties of the factor-rank and term-rank functions for matrices over semirings. In particular, we investigate the sets of matrices that satisfy the extremes of inequalities for these rank functions of matrix union. The classification of the linear transformations that keep these sets invariant is obtained. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 175–197, 2003.     

On the scales of computability potentials of finite algebras: Results and problems

We give a review of general known results on problems concerning the structure of scales of computability potentials of n-element algebras. We also formulate a number of natural open problems. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 145–164, 2003.