Inverse Problem for a Mathematical Model of Adsorption Dynamics

A mixed problem is considered for a system of partial differential equations modeling the process of adsorption dynamics. An existence and uniqueness theorem is proved for this problem, and the solution properties are investigated. The inverse problem is posed, involving the determination of the system coefficient given additional information about the solution. A uniqueness theorem is proved for the solution of the inverse problem.__________Translated from Prikladnaya Matematika i Informatika, No. 16, pp. 5 – 14, 2004.     

Representations of Positive Projections II

In this paper we obtain a number of Maharam-type slice integral representations, with respect to scalar measures, for positive projections in Dedekind complete vector lattices and f-algebras. AMS Classification: 47B65, 46A40, 06F25     

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

A Mini-Max Location Problem with Demand Points Arbitrarily Distributed in a Compact Connected Space

Consider a finite set of demand points which exist anywhere on the boundary of a rectangle contained in the two-dimensional Euclidean space. This paper considers the problem of finding an optimal location (on the boundary of the rectangle) which minimizes the maximum average Euclidean distance to the demand points. The method presented is independent of the number of demand points.     

Some general divergence measures for probability distributions

Summary General divergence measures for probability distributions are introduced and their main properties established. Connections with f-divergence corresponding to a convex function fare explored.     

Liquid–gas critical phenomena under confinement: small-angle neutron scattering studies of CO2 in aerogel

Small angle neutron scattering (SANS) is a well-established technique for investigating the behavior of confined binary liquid solutions, as it can probe the correlation length and susceptibility in pores on length scales 1 – 100 nm. We applied SANS to explore the influence of confinement on critical behavior of an individual fluid carbon dioxide (CO₂) in a highly porous aerogel. The results demonstrate that quenched disorder induced by aerogel significantly depresses density fluctuations. Despite the negligible volume occupied by aerogel (< 4%), the macroscopic phase separation of confined CO₂ into coexisting liquid and gaseous phases is suppressed and below the critical temperature of the bulk fluid frozen methastable microdomains are formed. Experimental data show that critical adsorption is as important as the effect of confinement in defining the behavior of confined fluids.     

Study of a Microwave Radar Signal Backscattered at Small Incidence Angles: In-Situ Measurements

We present the results of data processing of the field experiment devoted to a study of a microwave signal backscattered by a rough water surface and compare them with the theoretical estimates. The measurements were conducted sequentially using a radar with parabolic and knife-beam antennas. The radar was mounted on the Molitovsky bridge at a height of 40 m across the Oka river in Nizhny Novgorod, Russia. For the radar with knife-shaped antenna pattern, we examined the reflected-signal power and the shift and width of the Doppler spectrum as functions of the azimuthal angle for the nadir sounding. For the parabolic antenna, we studied the reflected-signal power as a function of the incidence angle. Comparison with the experimental data shows that the developed theoretical model of a Doppler spectrum is in good agreement with the observations. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 8, pp. 661–673, August 2005.     

Leptonic constant of the pseudoscalar <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> meson

We calculate the leptonic constant for the pseudoscalar ground state of the B _c meson in the framework of a QCD-motivated potential model taking into account the two-loop anomalous dimension for the heavy quark current in nonrelativistic QCD as matched with full QCD.