Статьи журнала - Владикавказский математический журнал
Все статьи: 930
Positive isometries of Orlicz-Kantorovich spaces
Статья научная
Let B be a complete Boolean algebra, Q(B) the Stone compact of B, and let C∞(Q(B)) be the commutative unital algebra of all continuous functions x:Q(B)→[-∞,+∞], assuming possibly the values ±∞ on nowhere-dense subsets of Q(B). We consider the Orlicz-Kantorovich spaces (LΦ(B,m),∥⋅∥Φ)⊂C∞(Q(B)) with the Luxembourg norm associated with an Orlicz function Φ and a vector-valued measure m, with values in the algebra of real-valued measurable functions. It is shown, that in the case when Φ satisfies the (Δ2)-condition, the norm ∥⋅∥Φ is order continuous, that is, ∥xn∥Φ↓0 for every sequence {xn}⊂LΦ(B,m) with xn↓0. Moreover, in this case, the norm ∥⋅∥Φ is strictly monotone, that is, the conditions |x|≨|y|, x,y∈LΦ(B,m), imply ∥x∥Φ≨∥y∥Φ. In addition, for positive elements x,y∈LΦ(B,m), the equality ∥x+y∥Φ=∥x-y∥Φ is valid if and only if x⋅y=0. Using these properties of the Luxembourg norm, we prove that for any positive linear isometry V:LΦ(B,m)→LΦ(B,m) there exists an injective normal homomorphisms T:C∞(Q(B))→C∞(Q(B)) and a positive element y∈LΦ(B,m) such that V(x)=y⋅T(x) for all x∈LΦ(B,m).
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Q-полиномиальных графах Шилла с b=6
Статья научная
Графом Шилла называется дистанционно регулярный граф Γ диаметра 3, имеющий второе собственное значение θ1, равное a=a3. В этом случае a делит k и полагают b=b(Γ)=k/a. Далее, a1=a-b и Γ имеет массив пересечений {ab,(a+1)(b-1),b2;1,c2,a(b-1)}. И. Н. Белоусов и А. А. Махнев нашли допустимые массивы пересечений Q-полиномиальных графов Шилла с b=6: {42t,5(7t+1),3(t+3);1,3(t+3),35t}, где t∈{7,12,17,27,57}, {312,265,48;1,24,260}, {372,315,75;1,15,310}, {624,525,80;1,40,520}, {744,625,125;1,25,620}, {930,780,150;1,30,775}, {1794,1500,200;1,100,1495} или {5694,4750,600;1,300,4745}. В работе доказано, что графы с массивами пересечений {372,315,75;1,15,310}, {744,625,125;1,25,620} и {1794,1500,200;1,100,1495} не существуют.
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Quasi-complete q-groups are bounded
Статья научная
We prove that any p-torsion quasi-complete abelian Q-group is bounded. This extends a recent statement of ours in [6, Corollary~8] to an arbitrary large cardinality, thus also answering in the negative a conjecture from [6]. Some other related assertions are established as well.
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Randic type additive connectivity energy of a graph
Статья научная
The Randic type additive connectivity matrix of the graph G of order n and size m is defined as RA(G)=(Rij), where Rij=√di+√dj if the vertices vi and vj are adjacent, and Rij=0 if vi and vj are not adjacent, where di and dj be the degrees of vertices vi and vj respectively. The purpose of this paper is to introduce and investigate the Randic type additive connectivity energy of a graph. In this paper, we obtain new inequalities involving the Randic type additive connectivity energy and presented upper and lower bounds for the Randic type additive connectivity energy of a graph. We also report results on Randic type additive connectivity energy of generalized complements of a graph.
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Remarks on first Zagreb indices
Статья научная
The necessary and sufficient condition for optimality in the form of the Pontryagin maximum principle in optimal control problem with variable linear structure, described by linear difference and integral-differential equations of Volterra type, is obtained. Under some additional assumptions sufficient optimality conditions are also derived.
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Representation and extension of orthoregular bilinear operators
Статья научная
In this paper we study some important structural properties of orthosymmetric bilinear operators using the concept of the square of an Archimedean vector lattice. Some new results on extension and analytical representation of such operators are presented.
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Статья научная
The main result states that every special AJW-algebra can be decomposed into the direct sum of totally irreversible and reversible subalgebras. In turn, every reversible special AJW-algebra decomposes into a~direct sum of two subalgebras, one of which has purely real enveloping real von Neumann algebra, and the second one contains an ideal, whose complexification is a C*-algebra and the annihilator of this complexification in the enveloping C*-algebra of this subalgebra is equal to zero.
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Sergei Sobolev a genius of natural sciences
Персоналии
This is a short tribute to Sergei Sobolev on the occasion of the 105 years of his birth.
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Some asymptotic properties of a kernel spectrum estimate with different multitapers
Статья научная
Let X(t), t=0,\pm 1,..., be a zero mean real-valued stationary time series with spectrum f_{XX}(\lambda ), -\pi \leq \lambda \leq \pi. Given the realization X(1), X(2),...,X(N), we construct L different multitapered periodograms I_{XX}^{(mt)_j}(\lambda ), j=1,2,...,L, on non-overlapped and overlapped segments X^(j)(t), 1\leq t
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Статья научная
In the classical theory of approximation of functions on R+, the modulus of smoothness are basically built by means of the translation operators f→f(x+y). As the notion of translation operators was extended to various contexts (see [2] and [3]), many generalized modulus of smoothness have been discovered. Such generalized modulus of smoothness are often more convenient than the usual ones for the study of the connection between the smoothness properties of a function and the best approximations of this function in weight functional spaces (see [4] and [5]). In [1], Abilov et al. proved two useful estimates for the Fourier transform in the space of square integrable functions on certain classes of functions characterized by the generalized continuity modulus, using a translation operator. In this paper, we also discuss this subject. More specifically, we prove some estimates (similar to those proved in [1]) in certain classes of functions characterized by a generalized continuity modulus and connected with the generalized Fourier transform associated with the differential-difference operator T(α,β) in L2α,β(R). For this purpose, we use a generalized translation operator.
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Some isomorphism results on commutative group algebras
Статья научная
We prove certain results pertaining to some isomorphism properties of commutative modular group algebras and briefly review a paper by pointing out some obvious mistakes and essential incorrectness.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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