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Vol 52, No 3 (2017)
- Year: 2017
- Articles: 6
- URL: https://journals.rcsi.science/1068-3623/issue/view/14070
Algebra
Periodic products of groups
Abstract
In this paper we provide an overview of the results relating to the n-periodic products of groups that have been obtained in recent years by the authors of the present paper, as well as some results obtained by other authors in this direction. The periodic products were introduced by S.I. Adian in 1976 to solve the Maltsev’s well-known problem. It was shown that the periodic products are exact, associative and hereditary for subgroups. They also possess some other important properties such as the Hopf property, the C*-simplicity, the uniform non-amenability, the SQ-universality, etc. It was proved that the n-periodic products of groups can uniquely be characterized by means of certain quite specific and simply formulated properties. These properties allow to extend to n-periodic products of various families of groups a number of results previously obtained for free periodic groups B(m, n). In particular,we describe the finite subgroups of n-periodic products, Also, we analyze and extend the simplicity criterion of n-periodic products obtained previously by S.I. Adian.
111-117
Differential Equations
The radius of convexity of particular functions and applications to the study of a second order differential inequality
Abstract
In this paper we determine the radius of convexity of particular functions. The obtained results are used to deduce sharp estimates regarding functions which satisfy a second order differential subordination. A lemma regarding starlikeness that involves the notion of convolution is established, and is used in order to obtain a sharp starlikeness condition.
118-127
A note on solutions of some differential-difference equations
Abstract
This research is a continuation of the recent paper by X. Qi and L. Yang [15]. In this paper, we continue our study concerning existence of solutions of a Fermat type differentialdifference equation, and improve the results obtained by K. Liu et al. in [8, 10].
128-133
Functional Analysis
Commutators of homogeneous fractional integrals on Herz-type Hardy spaces with variable exponent
Abstract
Let Ω ∈ Ls(Sn−1), s ≥ 1, be a homogeneous function of degree zero, and let σ (0 < σ < n) and b be Lipschitz or BMO functions. In this paper, we establish the boundedness of the commutators [b, TΩ,σ], generated by a homogeneous fractional integral operator TΩ,σ and function b, on the Herz-type Hardy spaces with variable exponent.
134-143
Real and Complex Analysis
144-148
On Haar series of A–integrable functions
Abstract
In this paper we obtain a necessary and sufficient condition on the sequence of natural numbers {qn} such that the almost everywhere convergence of the cubic partial sums Sqn(x) of the multiple Haar series Σnanχn(x) and the condition lim inf \(\lambda \cdot mes\left\{ {x:\begin{array}{*{20}{c}} {\sup } \\ n \end{array}\left| {S{}_{qn}\left( x \right)} \right| \succ \lambda } \right\} = 0\) , imply that the coefficients an can be uniquely determined by the sum of the series. Also, we have obtained a necessary and sufficient condition for the series \(\sum\limits_{n = 1}^\infty {{\varepsilon _n}{a_n}} {\chi _n}\left( x \right)\) with an arbitrary bounded sequence {εn} to be a Fourier-Haar series of an A-integrable function.
149-160