2017
Том 69
№ 6

All Issues

Volume 63, № 4, 2011

Article (Russian)

Conditions of smoothness for the distribution density of a solution of a multidimensional linear stochastic differential equation with levy noise

Bodnarchuk S. V., Kulik A. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 435-447

A sufficient condition is obtained for smoothness of the density of distribution for a multidimensional Levy-driven Ornstein-Uhlenbeck process, i.e., a solution to a linear stochastic differential equation with Levy noise.

Article (Russian)

On the mean value of the function $\overline{S}_k(n)$

Kirbat S. A., Varbanets P. D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 448-458

An asymptotic formula is constructed for a mean value of the function $\overline{S}_k(n)$ which is dual to the Smarandache function $S_k(n)$. $O$- and $\Omega$-estimates for the second moment of the remainder term are obtained.

Article (Ukrainian)

On hyperholomorphic functions of the space variable

Gerus O. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 459-465

For quaternionic-differentiable functions of a spatial variable, we prove a theorem on an integral over a closed surface. This theorem is an analog of the Cauchy theorem from complex analysis.

Article (Ukrainian)

On some criteria of convexity for compact sets

Tkachuk M. V., Vyhovs'ka I. Yu., Zelinskii Yu. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 466-471

We establish some criteria of convexity of compact sets in the Euclidean space. Analogs of these results are extended to complex and hypercomplex cases.

Article (Ukrainian)

On positive solutions of one class of evolutionary inclusions of the subdifferential type

Kapustyan O. V., Shklyar T. B.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 472-480

Sufficient conditions of the existence of a nonnegative solution are obtained for an evolution inclusion of subdifferential type with multivalued non-Lipschitz perturbation. Under the additional condition of dissipativity, the existence of the global attractor in the class of nonnegative functions is proved.

Article (Russian)

Asymptotic behavior of generalized quasiisometries at a point

Kovtonyuk D. A., Salimov R. R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 481-488

We consider $Q$-homeomorphisms with respect to the $p$-modulus. An estimate for a measure of a ball image is obtained under such mappings and the asymptotic behavior at zero is investigated.

Article (English)

On some imbedding relations between certain sequence spaces

Mursaleen M., Noman A. K.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 489-501

In the present paper, we introduce the sequence space $l^{\lambda}_p$ of non-absolute type which is a $p$-normed space and a $BK$-space in the cases of $0 < p < 1$ and $0 < p < 1$ i $1 \leq p < \infty$, respectively. Further, we derive some imbedding relations and construct the basis for the space $l^{\lambda}_p$, where $1 \leq p < \infty$.

Article (English)

Properties of a certain product of submodules

Heidari S., Nikandish R., Nikmehr M. J.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 502-512

Let $R$ be a commutative ring with identity, $M$ an $R$-module and $K_1,..., K_n$ submodules of $M$. In this article, we construct an algebraic object, called product of $K_1,..., K_n$. We equipped this structure with appropriate operations to get an $R(M)$-module. It is shown that $R(M)$-module $M^n = M... M$ and $R$-module $M$ inherit some of the most important properties of each other. For example, we show that $M$ is a projective (flat) $R$-module if and only if $M^n$ is a projective (flat) $R(M)$-module.

Article (Russian)

Resonance elliptic variational inequalities with discontinuous nonlinearities of linear growth

Pavlenko V. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 513-522

We consider resonance elliptic variational inequalities with second-order differential operators and discontinuous nonlinearity of linear grows. The theorem on the existence of a strong solution is obtained. The initial problem is reduced to the problem of the existence of a fixed point in a compact multivalued mapping and then, with the use of the Leray - Schauder method, the existence of the fixed point is established.

Article (Ukrainian)

On the reconstruction of the variation of the metric tensor of a surface on the basis of a given variation of christoffel symbols of the second kind under infinitesimal deformations of surfaces in the euclidean space $E_3$

Potapenko I. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 523-530

We investigate the problem of reconstruction of variation of a metric tensor of a surface on the basis of given variation of the sekond-kind Christoffel symbols for infinitesimal deformations of surfaces in the Euclidean space $E_3$.

Article (Russian)

Landau-Kolmogorov problem for a class of functions absolutely monotone on a finite interval

Skorokhodov D. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 531-548

We solve the Landau - Kolmogorov problem for the class of functions absolutely monotone on a finite interval. For this class of functions, a new exact additive inequalities of the Kolmogorov type are obtained.

Article (Russian)

Best $m$-term approximation of the classes $B ^{r}_{\infty, \theta}$ of functions of many variables by polynomials in the haar system

Stasyuk S. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 549-555

We obtain the exact-order estimate for the best $m$-term approximation of the classes $B ^{r}_{\infty, \theta}$ of periodic functions of many variables by polynomials with respect to the Haar system in the metric of the space $L_q,\quad 1 < q < \infty$.

Article (English)

On uniqueness theorems for holomorphic curves sharing hypersurfaces without counting multiplicity

Phuong Ha Tran

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 556-565

We prove some uniqueness theorems for algebraically nondegenerate holomorphic curves sharing hyper-surfaces ignoring multiplicity.

Brief Communications (Russian)

On the fredholm theory of a planar problem with shift for a pair of functions

Lysenko Z. M., Matviyuk L. V., Nechaev L. V., Shvets V. T.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 566-571

We obtain necessary and sufficient conditions of the Fredholm properties and the formula for the calculation of index of a planar problem with shift and conjugation for a pair of functions.

Brief Communications (English)

Multidimensional random motion with uniformly distributed changes of direction and Erlang steps

Pogorui A. О., Rodriguez-Dagnino R. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 572-577

In this paper we study transport processes in $\mathbb{R}^n,\quad n \geq 1$, having non-exponential distributed sojourn times or non-Markovian step durations. We use the idea that the probabilistic properties of a random vector are completely determined by those of its projection on a fixed line, and using this idea we avoid many of the difficulties appearing in the analysis of these problems in higher dimensions. As a particular case, we find the probability density function in three dimensions for 2-Erlang distributed sojourn times.