Статьи журнала - Владикавказский математический журнал
Все статьи: 883
Some open questions on positive operators in Banach lattices
Статья научная
Recently, some new results on asymptotic behaviour of positive operators in Banach lattices were obtained. Here we discuss some open problems related to these results.
Бесплатно
Some remarks about nonstandard methods in analysis. I
Статья научная
This and forthcoming articles discuss two of the most known nonstandard methods of analysis-the Robinson's infinitesimal analysis and the Boolean valued analysis, the history of their origination, common features, differences, applications and prospects. This article contains a review of infinitesimal analysis and the original method of forcing. The presentation is intended for a reader who is familiar only with the most basic concepts of mathematical logic-the language of first-order predicate logic and its interpretations. It is also desirable to have some idea of the formal proofs and the Zermelo--Fraenkel axiomatics of the set theory. In presenting the infinitesimal analysis, special attention is paid to formalizing the sentences of ordinary mathematics in a first-order language for a superstructure. The presentation of the forcing method is preceded by a brief review of C.~Godel's result on the compatibility of the Axiom of Choice and the Continuum Hypothesis with Zermelo--Fraenkel's axiomatics. The forthcoming article is devoted to Boolean valued models and to the Boolean valued analysis, with particular attention to the history of its origination.
Бесплатно
Some stability results for Picard iterative process in uniform space
Статья научная
We prove some stability results for Picard iteration in uniform space by introducing the concept of an M_e-distance as well as using some contractive conditions. Our results generalize, extend and improve some earlier results.
Бесплатно
Статья научная
The theory of the basic quantum calculus (that is, the basic q-calculus) plays important roles in many diverse areas of the engineering, physical and mathematical science. Making use of the basic definitions and concept details of the q-calculus, Govindaraj and Sivasubramanian [10] defined the Salagean type q-difference (q-derivative) operator. In this paper, we introduce a certain subclass of analytic functions with complex order in the open unit disk by applying the Salagean type q-derivative operator in conjunction with the familiar principle of subordination between analytic functions. Also, we derive some geometric properties such as sufficient condition and several subordination results for functions belonging to this subclass. The results presented here would provide extensions of those given in earlier works.
Бесплатно
Some vector valued multiplier difference sequence spaces defined by a sequence of Orlicz functions
Статья научная
In this article we introduce some new difference sequence spaces with a real 2-normed linear space as base space and which are defined using a sequence of Orlicz functions, a bounded sequence of positive real numbers and a sequence of non-zero reals as multiplier sequence. We show that these spaces are complete paranormed spaces when the base space is a 2-Banach space and investigate these spaces for solidity, symmetricity, convergence free, monotonicity and sequence algebra. Further we obtain some relation between these spaces as well as prove some inclusion results.
Бесплатно
Structure of archimedean f-rings
Статья научная
It is proved that the Boolean valued representation of a Dedekind complete f-ring is either the group of integers with zero multiplication, or the ring of integers, or the additive groups of reals with zero multiplication, or the ring of reals. Correspondingly, the Dedekind completion of an Archimedean f-ring admits a decomposition into the direct sum of for polars: singular ℓ-group and an erased vector lattice, both with zero multiplication, a singular f-rings and an erased f-algebra. A corollary on a functional representation of universally complete f-rings is also given.
Бесплатно
The Gordon theorem: origins and meaning
Статья научная
Boolean valued analysis, the term coined by Takeuti, signifies a branch of functional analysis which uses a special technique of Boolean valued models of set theory. The fundamental result of Boolean valued analysis is Gordon’s Theorem stating that each internal field of reals of a Boolean valued model descends into a universally complete vector lattice. Thus, a remarkable opportunity opens up to expand and enrich the mathematical knowledge by translating information about the reals to the language of other branches of functional analysis. This is a brief overview of the mathematical events around the Gordon Theorem. The relationship between the Kantorovich's heuristic principle and Boolean valued transfer principle is also discussed.
Бесплатно
The order continuous dual of the regular integral operators on Lp
Статья научная
In this paper we give two descriptions of the order continuous dual of the Banach lattics of regular integral operators on Lp. The first description is in terms of a Calderon space, while the second one in terms of the ideal generated by the finite rank operators.
Бесплатно
The stieltjes moment problem in vector lattices
Статья научная
In the present paper the Stieltjes moment problem in vector lattices is briefly outlined. First of all two examples justifying the statement of the moment problem in vector lattices are considered. The first example concerns a stochastic setting of the moment problem (the moment sequence depends on a measurable parameter) and the second one concerns the spectral resolution of a self-adjoint operator in a Hilbert space. Both examples are covered by the Freudenthal spectral theorem, which is one of the most powerful tools in the theory of vector lattices, and can be interpreted as one of the first solutions to the moment problem in vector lattices. In the last section two resulats concerning the general Stieltjes moment problem in vector lattices are formulated. The main difficulty is to find an appropriate measure extension in vector lattices.
Бесплатно
The uuniqueness of the symmetric structure in ideals of compact operators
Статья научная
Let H be a separable infinite-dimensional complex Hilbert space, let L(H) be the C∗-algebra of bounded linear operators acting in H, and let K(H) be the two-sided ideal of compact linear operators in L(H). Let (E,∥⋅∥E) be a symmetric sequence space, and let CE:={x∈K(H):{sn(x)}∞n=1∈E} be the proper two-sided ideal in L(H), where {sn(x)}∞n=1 are the singular values of a compact operator x. It is known that CE is a Banach symmetric ideal with respect to the norm ∥x∥CE=∥{sn(x)}∞n=1∥E. A symmetric ideal CE is said to have a unique symmetric structure if CE=CF, that is E=F, modulo norm equivalence, whenever (CE,∥⋅∥CE) is isomorphic to another symmetric ideal (CF,∥⋅∥CF). At the Kent international conference on Banach space theory and its applications (Kent, Ohio, August 1979), A. Pelczynsky posted the following problem: (P) Does every symmetric ideal have a unique symmetric structure? This problem has positive solution for Schatten ideals Cp, 1≤p
Бесплатно
Titchmarsh-Weyl theory of the singular Hahn-Sturm-Liouville equation
Статья научная
In this work, we will consider the singular Hahn-Sturm-Liouville difference equation defined by -q-1D-ωq-1,q-1Dω,qy(x)+v(x)y(x)=λy(x), x∈(ω0,∞), where λ is a complex parameter, v is a real-valued continuous function at ω0 defined on [ω0,∞). These type equations are obtained when the ordinary derivative in the classical Sturm--Liouville problem is replaced by the ω,q-Hahn difference operator Dω,q. We develop the ω,q-analogue of the classical Titchmarsh-Weyl theory for such equations. In other words, we study the existence of square-integrable solutions of the singular Hahn-Sturm-Liouville equation. Accordingly, first we define an appropriate Hilbert space in terms of Jackson-Norlund integral and then we study families of regular Hahn-Sturm-Liouville problems on [ω0,q-n], n∈N. Then we define a family of circles that converge either to a point or a circle. Thus, we will define the limit-point, limit-circle cases in the Hahn calculus setting by using Titchmarsh's technique.
Бесплатно
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.
Бесплатно
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.
Бесплатно
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.
Бесплатно
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.
Бесплатно
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.
Бесплатно
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.
Бесплатно
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.
Бесплатно
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.
Бесплатно
