Coset extensions of <Emphasis Type=”Italic”>S</Emphasis>-sets

Summary Three weak variants of compactness which lie strictly between compactness and quasicompactness, are introduced. Their basic properties are studied. The interplay with mapping and their direct and inverse preservation under mappings are investigated. In the process three decompositions of compactness are observed.     

The semi‐iterative method applied to the hyper‐power iteration

The semi‐iterative method (SIM) is applied to the hyper‐power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi‐iterative–hyper‐power (SIM–HP) iteration. The root convergence rate is computed for both the HP and SIM–HP methods, and the quotient convergence rate is given for the HP iteration. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

Vascular morphology by three-dimensional magnetic resonance imaging

A three-dimensional examination of blood vessels is provided using MR data from seven cases. The vascular surfaces are constructed with an algorithm that automatically follows the selected artery or vein and generates a projected three-dimensional gradient shaded image. Fast 3DFT pulse sequences were optimized to enhance the time-of-flight contrast of the intravascular region. By increasing the surface threshold value in a three-dimensional head study, the flesh of a patient's face was peeled away to demonstrate the superfacial temporal artery. Gated cardiac images show the great vessels and cardiac chambers. A three-dimensional view of the aorta shows an irregular surface in the vicinity of an adrenal tumor. 3D MR exams provide a non-invasive technique for assessing vascular morphology in a clinical setting.     

Calculation of diatomic molecules with the lctoc method. Excited states of some homonuclear molecules and ions

Calculations are performed, using a basis of two-center functions described previously, for excited states of the following three-and four-electron compounds: H₂ ^–, He₂ ⁺, He₂, Li₂ ⁺². High efficiency is demonstrated for the frozen ionic core approximation and the nonorthogonal orbital method in such calculations. For four-electron systems the practical feasibility of the frozen hybrid core approximation is demonstrated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 53–56, August, 1987.     

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.