Статьи журнала - Владикавказский математический журнал
Все статьи: 995
On the Gehring type condition and properties of mappings
Статья научная
The goal of this work is to obtain an analytical description of mappings satisfying some capacity inequality (so called Gp-condition): we study mappings for which the Gp-condition holds for a cubical ring. In other words, we replace rings with concentric spheres in the Gp-condition by rings with concentric cubes. We obtain new analytic properties of homeomophisms in Rn meeting Gehring type capacity inequality. In this paper the capacity inequality means that the capacity of the image of a cubical ring is controlled by the capacity of the given ring. From the analytic properties we conclude some geometric properties of mappings under consideration. The method is new and is based on an equivalent analytical description of such mappings previously established by the author. Our arguments are based on assertions and methods discovered in author's recent papers [1] and [2] (see also some references inside). Then we obtain geometric properties of these mappings.
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On the balanced subgroups of modular group rings
Статья научная
The balanced property of certain subgroups of the group of all normalized p-torsion invertible elements in a modular group ring of characteristic p is explored.
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On the expansions of analytic functions on convex locally closed sets in exponential series
Статья научная
Let Q be a bounded, convex, locally closed subset of CN with nonempty interior. For N>1 sufficient conditions are obtained that an operator of the representation of analytic functions on Q by exponential series has a continuous linear right inverse. For N=1 the criterions for the existence of a continuous linear right inverse for the representation operator are proved
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On the rate of convergence of ergodic averages for functions of Gordin space
Статья научная
For an automorphisms with non-zero Kolmogorov-Sinai entropy, a new class of L2-functions called the Gordin space is considered. This space is the linear span of Gordin classes constructed by some automorphism-invariant filtration of σ-algebras Fn. A function from the Gordin class is an orthogonal projection with respect to the operator I-E(⋅|Fn) of some Fm-measurable function. After Gordin's work on the use of the martingale method to prove the central limit theorem, this construction was developed in the works of Voln\'{y}. In this review article we consider this construction in ergodic theory. It is shown that the rate of convergence of ergodic averages in the L2 norm for functions from the Gordin space is simply calculated and is O(1n√). It is also shown that the Gordin space is a dense set of the first Baire category in L2(Ω,F,μ)⊖L2(Ω,Π(T,F),μ), where Π(T,F) is the Pinsker σ-algebra.
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On the theory of spaces of generalized bessel potentials
Статья научная
The purpose of the article is to introduce norms in the space of generalized Bessel potentials based on the weighted Dirichlet integrals. First, we define weighted Dirichlet integral and show that this integral can be represented using multidimensional generalised translation. Next, we demonstrate that this norm does not allow to define function spaces of arbitrary fractional order of smoothness. The potential theory originates from the theory of electrostatic and gravitational potentials and the Laplace, wave, Helmholtz, and Poisson equations. The famous Riesz potentials are known to be realizations of the real negative powers of the Laplace and wave operators. In the meantime, a lot of attention in the potential theory is given to the Bessel potential. Generalization in the article is achieved by considering the Laplace-Bessel operator which is constructed on the basis of the singular Bessel differential operator. The theory of singular differential equations containing the Bessel operator and the theory of the corresponding weighted function spaces belong to those mathematical areas, the theoretical and applied significance of which can hardly be overestimated.
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On the weak convergence of operators iterations in von Neumann algebras
Статья научная
Equivalent conditions are obtained for the weak convergence of iterations of the positive contractions in the pre-conjugate spaces of von Neumann algebras.
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Статья научная
We study topological structures of the sets $(0,1/2)^3 \cap \Omega$ and $(0,1/2)^3 \setminus \Omega$, where $\Omega$ is one special algebraic surface defined by a symmetric polynomial of degree $12$. These problems arise in studying of general properties of degenerate singular points of dynamical systems obtained from the~normalized Ricci flow on generalized Wallach spaces. Our main goal is to prove the connectedness of $(0,1/2)^3 \cap \Omega$ and to determine the number of connected components of $(0,1/2)^3 \setminus \Omega$.
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One Application of Ptolemy's Theorem
Статья научная
In this paper, we present a simple proof of one result from a recent paper by Yu. G. Nikonorov and O. Yu. Nikonorova, the original proof of which is rather cumbersome and based on the study of polynomial ideals and symbolic computations using a computer. The new proof is based on Ptolemy's theorem on inscribed quadrilaterals. In addition, other properties of inscribed quadrilaterals and related problems are considered.
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One functional-analytical idea by Alexandrov in convex geometry
Статья научная
The functional-analytical approach by A. D. Alexandrov is discussed to the Minkowski and Blaschke structures making the set of convex compact figures into a vector space. The resulting analytical possibilities are illustrated by the isoperimetric type problems of finding convex figures separated by current hyperplanes similar to the Urysohn and double bubble problems.
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One general method in operator theory
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
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
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
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
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
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
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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