Статьи журнала - Владикавказский математический журнал
Все статьи: 907
Topological aspects boron triangular nanotube and boron- nanotube
Статья научная
Topological graph indices have been used in a lot of~areas to study required properties of different objects such as atoms and molecules. Such indices have been described and studied by many mathematicians and chemists since most graphs are generated from molecules by replacing each atom with a vertex and each chemical bond with an edge. These indices are also topological graph invariants measuring several chemical, physical, biological, pharmacological, pharmaceutical, etc. properties of graphs corresponding to real life situations. The degree-based topological indices are used to correlate the physical and chemical properties of a molecule with its chemical structure. Boron nanotubular structures are high-interest materials due to the presence of multicenter bonds and have novel electronic properties. These materials have some important issues in nanodevice applications like mechanical and thermal stability. Therefore, they require theoretical studies on the other properties. In this paper, we compute the third Zagreb index, harmonic index, forgotten index, inverse sum index, modified Zagreb index and symmetric division deg index by applying subdivision and semi total point graph for boron triangular and boron-α nanotubes.
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Topological lattice rings with the AM-property
Статья научная
Motivated by the recent definition of the AM-property in locally solid vector lattices [O. Zabeti, doi: 10.1007/s41980-020-00458-7], in this note, we try to investigate some counterparts of those results in the category of all locally solid lattice rings. In fact, we characterize locally solid lattice rings in which order bounded sets and bounded sets agree. Furthermore, with the aid of the AM-property, we find conditions under which order bounded group homomorphisms and different types of bounded group homomorphisms coincide. Moreover, we show that each class of bounded order bounded group homomorphisms on a locally solid lattice ring X has the Lebesgue or the Levi property if and only if so is X.
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Topological unified (r,s)-entropy of continuous maps on quasi-metric spaces
Статья научная
The category of metric spaces is a subcategory of quasi-metric spaces. It is shown that the entropy of a map when symmetric properties is included is greater or equal to the entropy in the case that the symmetric property of the space is not considered. The topological entropy and Shannon entropy have similar properties such as nonnegativity, subadditivity and conditioning reduces entropy. In other words, topological entropy is supposed as the extension of classical entropy in dynamical systems. In the recent decade, different extensions of Shannon entropy have been introduced. One of them which generalizes many classical entropies is unified (r,s)-entropy. In this paper, we extend the notion of unified (r,s)-entropy for the continuous maps of a quasi-metric space via spanning and separated sets. Moreover, we survey unified (r,s)-entropy of a map for two metric spaces that are associated with a given quasi-metric space and compare unified (r,s)-entropy of a map of a given quasi-metric space and the maps of its associated metric spaces. Finally we define Tsallis topological entropy for the continuous map on a quasi-metric space via Bowen's definition and analyze some properties such as chain rule.
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Tosha-degree equivalence signed graphs
Статья научная
The Tosha-degree of an edge α in a graph Γ without multiple edges, denoted by T(α), is the number of edges adjacent to α in Γ, with self-loops counted twice. A signed graph (marked graph) is an ordered pair Σ=(Γ,σ) (Σ=(Γ,μ)), where Γ=(V,E) is a graph called the underlying graph of Σ and σ:E→{+,-} (μ:V→{+,-}) is a function. In this paper, we define the Tosha-degree equivalence signed graph of a given signed graph and offer a switching equivalence characterization of signed graphs that are switching equivalent to Tosha-degree equivalence signed graphs and kth iterated Tosha-degree equivalence signed graphs. It is shown that for any signed graph Σ, its Tosha-degree equivalence signed graph T(Σ) is balanced and we offer a structural characterization of Tosha-degree equivalence signed graphs.
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Trace class and Lidskii trace formula on Kaplansky - Hilbert modules
Статья научная
In this paper, we introduce and study the concepts of the trace class operators and global eigenvalue of continuous $\Lambda$-linear operators in Kaplansky--Hilbert modules. In particular, we give a variant of Lidskii trace formula for cyclically compact operators in Kaplansky--Hilbert modules.
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Transversal domination in double graphs
Статья научная
Let G be any graph. A subset S of vertices in G is called a dominating set if each vertex not in S is adjacent to at least one vertex in S. A dominating set S is called a transversal dominating set if S has nonempty intersection with every dominating set of minimum cardinality in G. The minimum cardinality of a transversal dominating set is called the transversal domination number denoted by γtd(G). In this paper, we are considering special types of graphs called double graphs obtained through a graph operation. We study the new domination parameter for these graphs. We calculate the exact value of domination and transversal domination number in double graphs of some standard class of graphs. Further, we also estimate some simple bounds for these parameters in terms of order of a graph.
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Two measure-free versions of the Brezis - Lieb lemma
Статья научная
We present two measure-free versions of the Brezis-Lieb lemma for uo-convergence in Riesz spaces.
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Статья научная
Fractional calculus is considered to be a powerful tool in describing complex systems with a wide range of applicability in many fields of science and engineering. The behavior of many systems can be described by using fractional differential equations with boundary conditions. In this sense, the study on the stability of fractional boundary value problems is of high importance. The main goal of this paper is to investigate the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of a class of fractional four-point boundary value problem involving Caputo derivative and with a given parameter. By using contraction principles, sufficient conditions are obtained to guarantee the uniqueness of solution. Therefore, we obtain sufficient conditions for the stability of that class of nonlinear fractional boundary value problems on the space of continuous functions. The presented results improve and extend some previous research. Finally, we construct some examples to illustrate the theoretical results.
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Unbounded convergence in the convergence vector lattices: a survey
Статья научная
Various convergences in vector lattices were historically a subject of deep investigation which stems from the begining of the 20th century in works of Riesz, Kantorovich, Nakano, Vulikh, Zanen, and many other mathematicians. The study of the unbounded order convergence had been initiated by Nakano in late 40th in connection with Birkhoff's ergodic theorem. The idea of Nakano was to define the almost everywhere convergence in terms of lattice operations without the direct use of measure theory. Many years later it was recognised that the unbounded order convergence is also rathe useful in probability theory. Since then, the idea of investigating of convergences by using their unbounded versions, have been exploited in several papers. For instance, unbounded convergences in vector lattices have attracted attention of many researchers in order to find new approaches to various problems of functional analysis, operator theory, variational calculus, theory of risk measures in mathematical finance, stochastic processes, etc. Some of those unbounded convergences, like unbounded norm convergence, unbounded multi-norm convergence, unbounded τ-convergence are topological. Others are not topological in general, for example: the unbounded order convergence, the unbounded relative uniform convergence, various unbounded convergences in lattice-normed lattices, etc. Topological convergences are, as usual, more flexible for an investigation due to the compactness arguments, etc. The non-topological convergences are more complicated in genelal, as it can be seen on an example of the a.e-convergence. In the present paper we present recent developments in convergence vector lattices with emphasis on related unbounded convergences. Special attention is paid to the case of convergence in lattice multi pseudo normed vector lattices that generalizes most of cases which were discussed in the literature in the last 5 years.
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Unbounded order convergence and the Gordon theorem
Статья научная
The celebrated Gordon's theorem is a natural tool for dealing with universal completions of Archimedean vector lattices. Gordon's theorem allows us to clarify some recent results on unbounded order convergence. Applying the Gordon theorem, we demonstrate several facts on order convergence of sequences in Archimedean vector lattices. We present an elementary Boolean-Valued proof of the Gao-Grobler-Troitsky-Xanthos theorem saying that a sequence xn in an Archimedean vector lattice X is uo- (uo-Cauchy) in X if and only if xn is o- (o-convergent) in Xu. We also give elementary proof of the theorem, which is a result of contributions of several authors, saying that an Archimedean vector lattice is sequentially uo-complete if and only if it is σ-universally complete. Furthermore, we provide a comprehensive solution to Azouzi's problem on characterization of an Archimedean vector lattice in which every uo-Cauchy net is o-convergent in its universal completion.
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Unicity on entire functions concerning their difference operators and derivatives
Статья научная
In this paper we study the uniqueness of entire functions concerning their difference operator and derivatives. The idea of entire and meromorphic functions relies heavily on this direction. Rubel and Yang considered the uniqueness of entire function and its derivative and proved that if f(z) and f′(z) share two values a,b counting multilicities then f(z)≡f′(z). Later, Li Ping and Yang improved the result given by Rubel and Yang and proved that if f(z) is a non-constant entire function and a,b are two finite distinct complex values and if f(z) and f(k)(z) share a counting multiplicities and b ignoring multiplicities then f(z)≡f(k)(z). In recent years, the value distribution of meromorphic functions of finite order with respect to difference analogue has become a subject of interest. By replacing finite distinct complex values by polynomials, we prove the following result: Let Δf(z) be trancendental entire functions of finite order, k≥0 be integer and P1 and P2 be two polynomials. If Δf(z) and f(k) share P1 CM and share P2 IM, then Δf≡f(k). A non-trivial proof of this result uses Nevanlinna's value distribution theory.
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Статья научная
In the fall of 1990 a small colloquium on nonstandard analysis was arranged at the request of a group of graduate and postgraduate students of Novosibirsk State University. At the meetings many unsolved problems were formulated stemming from various branches of analysis and seemingly deserving attention of the novices of nonstandard analysis. In 1994 some discussion took place on combining nonstandard methods at the international conference "Interaction Between Functional Analysis, Harmonic Analysis and Probability" (Missouri University, Columbia USA). The same topics were submitted to the international conference "Analysis and Logic" held in Belgium in 1997. In 1998 an INTAS research project was submitted. The problems raised in the framework of these projects are the core of this article. The list of the problems contains not only simple questions for drill but also topics for serious research intended mostly at the graduate and post graduate level. Some problems need creative thought to clarify and specify them.
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Upper semilattices of finite-dimensional gauges
Статья научная
This is a brief overview of some applications of the ideas of abstract convexity to the upper semilattices of gauges in finite dimensions.
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Персоналии
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Weakly N1-separable quasi-complete Abelian p-groups are bounded
Статья научная
We prove that each weakly N1-separable quasi-complete abelian p-group is bounded, thus extending recent results of ours in (Vladikavkaz Math. J., 2007 and 2008).
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Weakly compact-friendly operators
Статья научная
We introduce weak compact-friendliness as an extension of compact-friendliness, and and prove that if a non-zero weakly compact-friendly operator B: E→ E on a Banach lattice is quasi-nilpotent at some non-zero positive vector, then B has a non-trivial closed invariant ideal. Relevant facts related to compact-friendliness are also discussed.
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When all separately band preserving bilinear operators are symmetric?
Статья научная
A purely algebraic characterization of universally complete vector lattices in which all separately band preserving bilinear operators are symmetric is obtained: this class consists of universally complete vector lattices with \sigma-distributive Boolean algebra of bands.
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When are the nonstandard hulls of normed lattices discrete or continuous?
Статья научная
This note is a nonstandard analysis version of the paper "When are ultrapowers of normed lattices discrete or continuous?" by W. Wnuk and B. Wiatrowski.
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ξ-лиевы дифференцирования на алгебрах локально измеримых операторов
Статья научная
Изучаются ξ-лиевы дифференцирования на алгебрах локально измеримых операторов LS(M), где M - алгебра фон Неймана, не содержащая прямых абелевых слагаемых
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