Vol. 35 No. 2 (195) (2001)

Let $0<t_0<t_1<...,\lim\limits_{n\rightarrow +\infty}t_n=+\infty, \sup\limits_{n}(t_{n+1}-t-n)<+\infty.$ For an upward convex slowly varying function $L(t)>0$ an equivalent slowly varying function $L_1(t)$ has been constructed that is convex, infinitely differentiable, and that coincides with $L(t)>0$ on a beforehand given numerical sequence ${t_n}$.

This paper investigates the convolution polynomials and identities of vector spaces on the field. These results are based on tensor convolutions.

In this work matriciant, matrix of monodromy are defined, their properties are considered and Floke–Liapunov's theorem is proved for Dirac's two-parameter system with periodical coefficients.

In this paper generalizations of "modus ponens" rules are defined on the basis of which a certain system of propositional logics calculus is constructed to which both the Frege systems and the Frege systems with substitutions are polynomially brought.

The paper considers the problem of stability of nonlinear differential equations systems with retardation when small integral perturbations effect the system in finite interval of time. Sufficient conditions are obtained, under which such systems are stable according to the acting force.

The paper is devoted to the factorization of stress strain state of elastic space including half infinitive inclusion. Supposing that elastic inclusion is too thin the problem is reduced to the solution of boundary problem of harmonic wave diffraction on the half infinitive interval. Using the method of Wiener-Hopf and circulant method the boundary problem is reduced to the Wiener-Hopf matrix equation, which is completely solved. This solution allows to get analytical solution of the boundary problem.

The phenomenon of intersubband absorption of x-polarized light in quantum well with double δ-like barriers, caused by the electron effective mass coordinate dependence is considered. Analytical expressions for the oscillator strength for intersubband transitions and quantum efficiency of the optical absorption of photons under the enfluence of x-polarized light are obtained. It is shown that the absorption decreases with the increase of the opacity of surrounding δ-like barriers.

In the given paper the equivariant analogue of Freudenthal’s theorem in finite G-group is proved, which allows to generalize some results attained by Bogaty on n-mobility of topological distance.