On general relations in relativistic kinematics and some of their applications

Two vector fields are considered, a timelike one,u , and an arbitrary one, . The relative expansion and rotation are defined with respect to these fields, their mutual relations are studied, and some general formulas obtained. Applications are made, first to vector fields which are mutually nonrotating in a plane-symmetric metric, then to the electromagnetic field of an arbitrary magnetohydrodynamic fluid.     

The effect of LH wave on the peripheral plasma of TM-1-MH tokamak

The work is devoted to the study of the LH wave effect on the peripheral plasma of the TM-1-MH tokamak. The observed enhancement of the ion saturated current in the limiter shadow is interpreted as heating of the peripheral ions by absorption of decay waves generated in this region due to the nonlinear wave-plasma interaction.     

Some Landau's type inequalities for infinitesimal generators

Summary Lett T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx D(A ³), the following inequalities hold true: Ax³ 243/8 x²A ³ x, A ² x 24 xA ³ x². Ift T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions.     

Numerical solution of a singularly perturbed problem via exponential splines

It is proved that a spline difference scheme for a singularly perturbed self-adjoint problem, derived by using exponential cubic splines at mid-points, has second order uniform convergence in a small parameter . Numerical experiments are presented to confirm the theoretical predictions.     

Test for the existence of finite-dimensional Chebyshev subspaces in Lϕ spaces

Vilnius University. Translated from Lietuvos Matematikos Rinkinys (Litovskii Matematicheskii Sbornik), Vol. 30, No. 1, pp. 44–55, January–March, 1990.     

Invariance Principle Under Self-Normalization for Nonidentically Distributed Random Variables

Let V _n ^–1 _n be the adaptive process of self-normalized partial sums S _k of independent random variables X _i , defined by linear interpolation between the points (V _k ²/V _n ²,S _k /V _n ), kn, where V _k ²= _ik X _i ². We prove that if the X _k 's are symmetric, V _n ^–1 _n converges weakly to the Brownian motion W in each Hölder space supporting W if and only if V _n ^–1 max _kn |X _k |=o _P (1). We give some partial extension to the non symmetric case.     

On Hadamard Inequality for Log-Concave Functions

Some improvements and generalizations of Finks results about Hadamards inequality for log-concave functions are given.AMS Subject Classification: 26D07, 26D15, 26A51.     

nvolutorial Płonka sums

The construction of the sum of a direct (semilattice ordered) system of algebras introduced by J. Plonka – later known as the Plonka sum – is one of the most important methods of composition in universal algebra, having a number of applications in different algebraic theories, such as semigroup theory, semiring theory, etc. In this paper we present a more general way for constructing algebras with involution, that is, algebraic systems equipped with a unary involutorial operation which is at the same time an antiautomorphism of the underlying algebra. It is the sum – involutorial Plonka sum, as we call it – of an involution semilattice ordered system of algebras. We investigate its basic properties, as well as the problem of its subdirect decomposition.     

Theorems of Large Deviations in the Approximation by the Compound Poisson Distribution

The paper is devoted to the research of large deviation probabilities in the approximation by compound Poisson law.