Volume 11, Issue 3

The 80th Birthday of
Yuri Reshetnyak

September 26 is the 80th birthday of Academician Yuri Reshetnyak, an outstanding Russian mathematician.

Article (rus.) - [pdf] [zip-pdf]

Weakly ℵ 1 -separable quasi-complete abelian p-groups are bounded
Danchev P. V.
MSC (2000): 20K10.

We prove that each weakly ℵ 1 -separable quasi-complete abelian p-group is bounded, so supplementing our recent results in (Vladikavkaz Math. J., 2007 and 2008).

Article (eng.) - [pdf] [zip-pdf]

Interaction of a chain of moving charges with an ideal conductor
Kesaev V. I., Maliev I. N.

We give a new solution of Maxwell's equations, describing the total electrical field that is created by point charges e 0   moving synchonously one after another with time interval τ   and velocity constant V →   at a constant distance z 0   from the flat surface of a massive ideal massive conductor. The eeffect is revealed of amplification of interaction between any charge of the chain and the metal at the small square values of σ  , the ratio of the space interval V⋅τ   to the doubled product of the Lorentz-factor γ   and the distance z 0 .

Article (rus.) - [pdf] [zip-pdf]

On the properties of complemented basic sequences
Kondakov V. P.

The paper contains some remarks on the properties of special basic sequences of the elements which span complemented subspaces in the Fr é chet spaces of the class that can be considered as a generalization of the well-known class of K ö the sequnce spaces. We discuss the question of characterization of these sequences of elements in block-K ö the spaces and survey the available results in this area. Some open problems are posed, and the connection of the topic under study is addressed with the problem of the isomorphic classification of K ö the spaces.

Article (rus.) - [pdf] [zip-pdf]

On the stability criteria in A. M. Lyapunov's article "Analysis of one of the partucular cases of the problem of stability of motion"
Kurakin L. G.

We consider the problem of stability of an equilibrium of an autonomous system of differential equations in the critical case of a double zero root (Jordan cell). Using his first method A. M. Lyapunov [1] found a criterion of stability for any nonlinear degeneration of the system. He addressed most of the subcases of the problem, using his direct method as well. The Lyapunov functions for all remaining subcases were not constructed yet. In this paper we found these functions in a few cases. This enables us to to propose a new algorithm of determination of equilibrium stability for some degenerations of system. This algorithm is specified by some algebraic operations over the Taylor series coefficients of the system whereas the algorithm by A. M. Lyapunov demands the calculation of quadratures.

Article (rus.) - [pdf] [zip-pdf]

Homogeneous functions of regular linear and bilinear operators
Kusraev A. G.
MSC (2000): 46A40, 47A50, 47A60, 47A63, 47B65.

Using envelope representations explicit formulae for computing ϕ ^ ( T 1 ,…, T N )   for any finite sequence of regular linear or bilinear operators T 1 ,…, T N   on vector lattices are derived.

Article (eng.) - [pdf] [zip-pdf]

Boolean models and simultaneous inequalities
Kutateladze S. S.
MSC (2000): 03H10, 47B60, 90C48.

Boolean valued analysis is applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities.

Article (eng.) - [pdf] [zip-pdf]

Estimates for the perturbed Oseen semigroup
Sazonov L. I.

We present a sufficient condition for the perturbed Oseen semigroup which yields the same power-like decay rate as for the unperturbed one. We prove that this phenomenon takes place provided the perturbed Oseen operator has no eigenvalues inside the closed right half-plane. In particular, this result is valid for the perturbations that are small in some sense. The proof is based on the results on invertibility of elements of some Banach algebra of operator-valued functions, which results rests on the Allan-Douglas principle.

Article (rus.) - [pdf] [zip-pdf]