Статьи журнала - Владикавказский математический журнал

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One general method in operator theory

One general method in operator theory

Kutateladze Semen Samsonovich

Статья научная

An order bounded operator with target a Dedekind complete vector lattice is determined up to an orthomorphism from the kernels of its strata. Some applications to 2-disjoint operators are briefly discussed.

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One property of the weak covergence of operators iterations in von Neumann algebras

One property of the weak covergence of operators iterations in von Neumann algebras

Katz Alexander A.

Статья научная

Conditions are given for *-weak convergence of iterations for an ultraweak continuous fuctional in von Neumann algebra to imply norm convergence.

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Operators on injective banach lattices

Operators on injective banach lattices

Kusraev Anatoly Georgievich

Статья научная

The paper deals with some properties of bounded linear operators on injective Banach lattice using a Boolean-valued transfer principle from AL-spaces to injectives stated in author's previous work.

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Order bornological locally convex lattice cones

Order bornological locally convex lattice cones

Ayaseh Davood, Ranjbari Asghar

Статья научная

In this paper, we introduce the concepts of $us$-lattice cones and order bornological locally convex lattice cones. In the special case of locally convex solid Riesz spaces, these concepts reduce to the known concepts of seminormed Riesz spaces and order bornological Riesz spaces, respectively. We define solid sets in locally convex cones and present some characterizations for order bornological locally convex lattice cones.

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Partial integral operators of Fredholm type on Kaplansky-Hilbert module over L0

Partial integral operators of Fredholm type on Kaplansky-Hilbert module over L0

Eshkabilov Yusup Kh., Kucharov Ramziddin R.

Статья научная

The article studies some characteristic properties of self-adjoint partially integral operators of Fredholm type in the Kaplansky--Hilbert module L0[L2(Ω1)] over L0(Ω2). Some mathematical tools from the theory of Kaplansky--Hilbert module are used. In the Kaplansky--Hilbert module L0[L2(Ω1)] over L0(Ω2) we consider the partially integral operator of Fredholm type T1 (Ω1 and Ω2 are closed bounded sets in Rν1 and Rν2, ν1,ν2∈N, respectively). The existence of L0(Ω2) nonzero eigenvalues for any self-adjoint partially integral operator T1 is proved; moreover, it is shown that T1 has finite and countable number of real L0(Ω2)-eigenvalues. In the latter case, the sequence L0(Ω2)-eigenvalues is order convergent to the zero function. It is also established that the operator T1 admits an expansion into a series of ∇1-one-dimensional operators.

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Pluriharmonic definable functions in some O-minimal expansions of the real field

Pluriharmonic definable functions in some O-minimal expansions of the real field

Berraho Mourad

Статья научная

In this paper, we first try to solve the following problem: If a pluriharmonic function f is definable in an arbitrary o-minimal expansion of the structure of the real field R:=(R,+,-,.,0,1,

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Positive isometries of Orlicz-Kantorovich spaces

Positive isometries of Orlicz-Kantorovich spaces

Zakirov B.S., Chilin V.I.

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

Q-полиномиальных графах Шилла с b=6

Махнев Александр Алексеевич, Ван Чжиган

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

Quasi-complete q-groups are bounded

Danchev Peter V.

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

Randic type additive connectivity energy of a graph

Madhusudhan Krishnarajapete Venkatarama, Reddy Polaepalli Siva Kota, Rajanna Karpenahalli Ranganathappa

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

Remarks on first Zagreb indices

Milovanovic Emina I., Milovanovic Igor Z.

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

Representation and extension of orthoregular bilinear operators

Gerard Buskes , Kusraev Anatoly G.

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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Reversible AJW-algebras

Reversible AJW-algebras

Ayupov Shavkat Abdullayevich, Arzikulov Farhodjon Nematjonovich

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

Sergei Sobolev a genius of natural sciences

Kutateladze Semen Samsonovich

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

Some asymptotic properties of a kernel spectrum estimate with different multitapers

Teamah A.A.M., Hassan Salah Bakouch

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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Some estimates for the generalized Fourier transform associated with the Cherednik-Opdam operator on r

Some estimates for the generalized Fourier transform associated with the Cherednik-Opdam operator on r

El Ouadih Salah, Daher Radouan, Lafdal Hamad Sidi

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

Some isomorphism results on commutative group algebras

Danchev Peter V.

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

Some open questions on positive operators in Banach lattices

Emelyanov Eduard Yu.

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

Some remarks about nonstandard methods in analysis. I

Gordon Evgeny 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

Some stability results for Picard iterative process in uniform space

Olatinwo M.O.

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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