2017
Том 69
№ 9

Volume 60, № 5, 2008

Article (Ukrainian)

On Sidon-Telyakovskii-type conditions for the integrability of multiple trigonometric series

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 579–585

For the trigonometric series $$\sum_{k=0}^{\infty}a_k\sum_{l\in kV \setminus (k-1)V}e^{i(l, x)}, \quad a_k\rightarrow 0,\quad k\rightarrow \infty,$$ given on $[-\pi, \pi)^m$, where $V$ is some polyhedron in $R^m$, we prove that the inequality $$\int\limits_{T^m}\left|\sum^{\infty}_{k=0} a_k \sum_{l\in kV\setminus(k-1)V}e^{i(l, x)} \right| dx \leq C \sum^{\infty}_{k=0} (k+1) |\Delta A_k|,$$ holds if the coefficients $a_k$ satisfy the following conditions of the Sidon - Telyakovskii type: $$A_k\rightarrow\infty,\quad |\Delta a_k| \leq A_k, \quad \forall k \geq 0, \quad \sum^{\infty}_{k=0}(k+1) |\Delta A_k|<\infty.$$

Article (Ukrainian)

Cauchy problem for a semilinear Éidel’man parabolic equation

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 586–602

Article (English)

Basic properties and applications of graded fractal bundles related to Clifford structures: An introduction

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 603–618

Using the central extension of the Cuntz C*-algebra, we study the periodicity for corresponding fractals.

Article (Russian)

Piecewise-smooth+ version of the implicit-function theorem

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 619–625

We introduce a class of piecewise-smooth + mappings and prove the implicit-function theorem for this class. The proof is based on the theorem on global homeomorphism, which follows from the well-known Chernavskii theorem.

Article (Ukrainian)

On the asymptotic equilibrium and asymptotic equivalence of differential equations in Banach spaces

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 626–635

We present some conditions for the asymptotic equilibrium of nonlinear differential equations and, in particular, a linear inhomogeneous equation in Banach spaces. We also discuss analogous problems for a linear equation with unbounded operator. Some obtained results are applied to problems of asymptotic equivalence.

Article (Ukrainian)

Best linear methods of approximation and optimal orthonormal systems of the Hardy space

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 636–646

We construct the best linear methods of the approximation of functions from the Hardy space Hp on compact subsets of the unit disk. We show that the Takenaka - Malmquist systems are such systems of functions that are orthonormal on the unit circle and optimal for the construction of the best linear methods of approximation.

Article (Ukrainian)

Best M-term orthogonal trigonometric approximations of the classes B Ωp,θ of periodic functions of many variables

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 647 – 656

Order estimates of the best M-term orthogonal trigonometric approximations of the classes B Ωp,θ of multivariable functions in the metric of the space Lq are obtained for the case 1 < q < p < ∞.

Article (Russian)

On the application of some concepts of ring theory to the study of the influence of systems of subgroups of a group

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 657–668

We study the groups, in which the family Lnon-nn(G) of all not nearly normal subgroups has the Krull dimension. A subgroup H of the group G is said to be nearly normal if H has finite index in its normal closure.

Article (Ukrainian)

Approximation of functions from the class $\hat{C}^{\psi}_{\beta, \infty}$ by Poisson biharmonic operators in the uniform metric

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 669 – 693

We obtain asymptotic equalities for upper bounds of approximations of functions from the class $\hat{C}^{\psi}_{\beta, \infty}$ by the Poisson biharmonic operators in the uniform metric.

Article (English)

Oscillation criteria for nonlinear second-order differential equations with damping

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 694–700

Some new oscillation criteria are given for general nonlinear second-order ordinary differential equations with damping of the form x?+?p?(?t?)?x?+?q?(?t?)?f?(?x?) = 0, where f is monotone or nonmonotone. Our results generalize and extend some earlier results of Deng.

Anniversaries (Ukrainian)

Yuri Yurievich Trokhimchuk (on his 80th birthday)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 701 – 703

Brief Communications (Ukrainian)

On the defect of nondenseness of continuous imbeddings in the scale of Hilbert spaces

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 704–708

We obtain a formula for the determination of a defect under a continuous imbedding of subspaces in the scale of Hilbert spaces.

Brief Communications (Russian)

Criterion for convexity of a domain of a Euclidean space

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 709–711

We establish an external criterion for the convexity of a domain of a Euclidean space.

Brief Communications (English)

On fuzzy semi δ - V continuity in fuzzy δ - V topological space

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 709–711

New concepts of fuzzy semi δ - V and fuzzy semi δ - Λ sets were introduced in the work „On fuzzy semi δ - Λ sets and fuzzy semi δ - V sets V - 6" by the authors (J. Trip. Math. Soc., 6, 81 - 88 (2004)). It was shown that the family of all fuzzy semi δ - V sets forms a fuzzy supra topological space on X denoted by ( X, FS δ V ). The aim of this paper is to introduce the concept of fuzzy semi δ - V continuity in a fuzzy δ - V topological space. Finally, some properties, preservation theorems, etc., are studied.

Brief Communications (Ukrainian)

Denjoy problems

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 718–720

We solve Denjoy problems concerning the elimination of singularities of analytic functions of measure zero.