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Vol 52, No 4 (2017)
- Year: 2017
- Articles: 6
- URL: https://journals.rcsi.science/1068-3623/issue/view/14073
Algebra
The unique trace property of n-periodic product of groups
Abstract
In this paper we prove the unique trace property of C*-algebras of n-periodic products of arbitrary family of groups without involutions. We show that the free Burnside groups B(m, n) and their automorphism groups also possess the unique trace property. Also, we show that every countable group is embedded into some 3-generated group with the unique trace property, while every countable periodic group of bounded period and without involutions is embedded into some 3- generated periodic group G of bounded period with the unique trace property. Moreover, as a group G can be chosen both simple and not simple group.
161-165
Generalized (Jordan) left derivations on rings associated with an element of rings
Abstract
In this paper, we introduce a new notion of generalized (Jordan) left derivation on rings as follows: let R be a ring, an additive mapping F : R → R is called a generalized (resp. Jordan) left derivation if there exists an element w ∈ R such that F(xy) = xF(y) + yF(x) + yxw (resp. F(x2) = 2xF(x) + x2w) for all x, y ∈ R. Then, some related properties and results on generalized (Jordan) left derivation of square closed Lie ideals are obtained.
166-174
Differential Equations
Nonlocal semi-linear fractional-order boundary value problems with strip conditions
Abstract
This paper is concerned with the question of existence of solutions for one-dimensional higher-order semi-linear fractional differential equations supplemented with nonlocal strip type boundary conditions. The nonlocal strip condition addresses a situation where the linear combination of the values of unknown function at two nonlocal points, located to the left and right hand sides of the strip, respectively, is proportional to its strip value. The case of Stieltjes type strip condition is also discussed. Our results, relying on some standard fixed point theorems are supported with illustrative examples.
175-183
On a general nonlinear problem with distributed delays
Abstract
The paper considers a general system of ordinary differential equations appearing in the neural network theory. The activation functions are assumed to be continuous and bounded by power type functions of the states and distributed delay terms. These activation functions are not necessarily Lipschitz continuous as it is commonly assumed in the literature. We obtain sufficient conditions for exponential decay of solutions.
184-190
Functional Analysis
Weyl-type theorems for unbounded posinormal operators
Abstract
For bounded linear operators, the study ofWeyl-type theorems and properties has been of significant interest for several non-normal classes of operators. In this paper, we extend this study to a class of unbounded posinormal operators. We define and study the spectral properties of unbounded posinormal and totally posinormal operators defined on an infinite dimensional complex Hilbert space H. For this class, under certain conditions several Weyl-type theorems and related properties are obtained.
191-197
Real and Complex Analysis
The Gibbs phenomenon for general Franklin systems
Abstract
The paper is devoted to the Gibbs phenomenon for series by general Franklin systems. The general Franklin system corresponding to a given dense sequence of points T = (tn, n ≥ 0) in [0, 1] is a sequence of orthonormal piecewise linear functions with knots from T, that is, the nth function from the system has knots t0,..., tn. The main result of this paper is that the Gibbs phenomenon for Fourier series by general Franklin systems occurs for almost all points of [0, 1].
198-210