Volume 61, № 1, 2009
Integral group ring of Rudvalis simple group
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 3-13
Using the Luthar–Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Rudvalis sporadic simple group Ru . As a consequence, for this group we confirm the Kimmerle conjecture on prime graphs.
Algebraic-geometric operators and Galois differential theory
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 14-27
We show that, by using the Galois differential theory, one can substantially improve the description of algebraic-geometric operators. In particular, we give a complete description of all elementary algebraic-geometric operators, present simple relations for the construction of all second-order operators of this type, and give a criterion for testing the algebraic-geometric properties of a linear differential operator with meromorphic coefficients.
Inverse problem for the strongly degenerate heat equation in a domain with free boundary
Hryntsiv N. M., Ivanchov N. I.
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 28-43
In a domain with free boundary, we establish conditions for the existence and uniqueness of a solution of the inverse problem of finding the time-dependent coefficient of heat conductivity. We study the case of strong degeneration where the unknown coefficient tends to zero as $t → +0$ as a power function $t^{β}$, where $β ≥ 1$.
On one class of modules over integer group rings of locally solvable groups
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 44-51
We study a $Z G$-module $A$ in the case where the group $G$ is locally solvable and satisfies the condition min–naz and its cocentralizer in A is not an Artinian $Z$-module. We prove that the group G is solvable under the conditions indicated above. The structure of the group $G$ is studied in detail in the case where this group is not a Chernikov group.
Structure of a Munn semigroup of finite rank every stable order of which is fundamental or antifundamental
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 52-60
We describe the structure of a Munn semigroup of finite rank every stable order of which is fundamental or antifundamental.
On one extremal problem of Pompeiu sets
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 61-72
We determine upper bounds for the least radius of a ball in which a given set is a Pompeiu set (the set considered is a half right circular cone). The obtained estimates significantly improve known results.
Approximation of conjugate differentiable functions by their Abel–Poisson integrals
Kharkevych Yu. I., Zhyhallo K. M.
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 73-82
We obtain the exact values of upper bounds of approximations of classes of periodic conjugate differentiable functions by their Abel–Poisson integrals in uniform and integral metrics.
Full measure of a set of singular continuous measures
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 83-91
On the space of structurally similar measures, we construct a nontrivial measure m such that the subclass of all purely singular continuous measures is a set of full m-measure.
Exact constants in Jackson-type inequalities for $L_2$-approximation on an axis
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 92-98
We investigate exact constants in Jackson-type inequalities in the space $L_2$ for the approximation of functions on an axis by the subspace of entire functions of exponential type.
Exact constants in Jackson-type inequalities for $L_2$-approximation on an axis
Doronin V. G., Ligun A. A., Serdyuk A. S., Shydlich A. L.
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 92-98
We investigate exact constants in Jackson-type inequalities in the space $L_2$ for the approximation of functions on an axis by the subspace of entire functions of exponential type.
On Γ-convergence of integral functionals defined on various weighted Sobolev spaces
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 99-115
We consider weighted Sobolev spaces correlated with a sequence of $n$-dimensional domains. We prove a theorem on the choice of a subsequence $Γ$-convergent to an integral functional defined on a “limit” weighted Sobolev space from a sequence of integral functionals defined on the spaces indicated.
Removal of singularities and analogs of the Sokhotskii–Weierstrass theorem for Q-mappings
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 116-126
We prove that an open discrete Q-mapping \( f:D \to \overline {{\mathbb{R}^n}} \) has a continuous extension to an isolated boundary point if the function Q(x) has finite mean oscillation or logarithmic singularities of order at most n – 1 at this point. Moreover, the extended mapping is open and discrete and is a Q-mapping. As a corollary, we obtain an analog of the well-known Sokhotskii–Weierstrass theorem on Q-mappings. In particular, we prove that an open discrete Q-mapping takes any value infinitely many times in the neighborhood of an essential singularity, except, possibly, for a certain set of capacity zero.
Almost critical branching processes and limit theorems
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 127-133
We study almost critical branching processes with infinitely increasing immigration and prove functional limit theorems for these processes.
Classification of topologically conjugate affine mappings
Ukr. Mat. Zh. - 2009. - 61, № 1. - pp. 134-139
We consider affine mappings from $ℝ^n$ into $ℝ^n, n ≥ 1$. We prove a theorem on the topological conjugacy of an affine mapping that has at least one fixed point to the corresponding linear mapping. We give a classification, up to topological conjugacy, for affine mappings from $ℝ$ into $ℝ$ and also for affine mappings from $ℝ^n$ into $ℝ^n, n > 1$, having at least one fixed point and the nonperiodic linear part.