The series ∑n≥1τnP(|Sn|≥ εnα) is studied, where Sn are the sums of independent equally distributed random variables, τn is a sequence of nonnegative numbers, α>0, and ε>0 is an arbitrary positive number. For a broad class ...
The expressions for partial scattering matrices Sl(λ) are obtained for any natural l by vising V. M. Adamyan's result which establishes the universal relationship between the scattering matrix for a wave equation with ...
Conditions are established under which the unital divisor extracted from a matrix polynomial over an arbitrary field is determined uniquely by its characteristic polynomial. The result obtained is applied to the problem ...
The notion of a generalized y-derivative of a function of complex variable is introduced and applied to classifying the functions analytic in Jordan domains. The approximations of functions from thus introduced classes are ...
The linear stochastic differential equations with a deviating neutral type argument are considered. The sufficient conditions for stability are obtained. The functions that give the initial perturbations of the solutions ...
The transformation of Wiener's process ξt in ℝm is considered by using the multiplicative functional αt=u(ξt)/u(ξ0), where the function u is similar to a local time type functional on a surface. It is proved that such a ...
By using both the Pólya theorem on the connection between the growth of an entire exponential function and the location of singularities of its Borel transform and the analog of this result for finite-order entire functions ...
The necessary and sufficient conditions for existence on manifolds of the dynamical systems having non-wandering set consisting of disconnected union of 2-dimensional tori with hyperbolic structure are given
У всьому просторі R" реалізується метод дослідження диференціальних рівнянь з імпульсною дією на поверхню, застосований в [1] для обмеженої частини фазового простору. Доведені теореми про існування інтегральних поверхонь ...
A method of study of differential equations with an impulse action on a surface, applied in [1] for a bounded part of the phase space, is now being extended to the whole space
We obtain existence criteria and describe the commuting maximal proper extensions of a closed Hermite operator and a dual pair of continuous operators in a Hilbeit space.