Статьи журнала - Владикавказский математический журнал
Все статьи: 907
An EOQ model with time-dependent increasing demand under JIT philosophy for a distributor/agent
Статья научная
This article generalizes an EOQ model for a distributor/agent with Just-in-Time (JIT) philosophy. It is assumed that the demand of seasonal goods is an increasing function of time. The optimality condition of the associated objective function is derived analytically. Also, the model is illustrated with the numerical examples.
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An almost f-algebra multiplication extends from a majorizing sublattice
Статья научная
It is proved that an almost f-algebra multiplication defined on a majorizing sublattice of a Dedekind complete vector lattice can be extended to the whole vector lattice.
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An analysis of convexity and starlikeness attributes for Breaz integro-differential operator
Статья научная
The Geometric Theory of Analytic Functions (GTAF) is the attractive part of complex analysis, which correlates with the rest of the themes in mathematics. Its essential purpose is to formulate numerous classes of geometric analytic functions and to discuss their geometric attributes. In continuation, the association between operator theory and the GTAF area started to take shape and has remained a topic of wide attention today. In the previous century, operator theory was extended to the complex open unit disk and has been applied to propose diverse sorts of generalizations of normalized analytic functions. As a result, the operator theory appears to be a good way to look for things in the GTAF area. Since then, the acquisition of geometric attributes by employing operators has become a significant theme of research studies. The current study centers on and investigates, in the classes of ℓ-uniformly convex and starlike functions of order β, the convexity attribute by utilizing a modified Breaz integro-differential operator in the unit disk. Furthermore, in the class of analytic functions, some conditions that make the Breaz operator look like a star are looked into.
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Статья научная
The main result states that each positive polynomial $p$ in $N$ variables with coefficients in a unital Archimedean $f$-ring $K$ is representable as a sum of squares of rational functions over the complete ring of quotients of $K$ provided that $p$ is positive on the real closure of $K$. This is proved by means of Boolean valued interpretation of Artin's famous theorem which answers Hilbert's 17th problem affirmatively.
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Asymptotic almost automorphy for algebras of generalized functions
Статья научная
The paper aims to to study the concept of asymptotic almost automorphy in the context of generalized functions. We introduce an algebra of asymptotically almost automorphic generalized functions which contains the space of smooth asymptotically almost automorphic functions as a subalgebra. The fundamental importance of this algebra, is related to the impossibility of multiplication of distributions; it also contains the asymptotically almost automorphic Sobolev-Schwartz distributions as a subspace. Moreover, it is shown that the introduced algebra is stable under some nonlinear operations. As a by pass result, the paper gives a Seeley type result on extension of functions in the context of the algebra of bounded generalized functions and the algebra of bounded generalized functions vanishing at infinity, these results are used to prove the fundamental result on the uniqueness of decomposition of an asymptotically almost automorphic generalized function. As applications, neutral difference-differential systems are considered in the framework of the algebra of generalized functions.
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Atomicity in injective banach lattices
Статья научная
This note is aimed to examine a Boolean valued interpretation of the concept of atomic Banach lattice and to give a complete description of the corresponding class of injective Banach lattices.
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Статья научная
The main purpose of this paper is to generalize the Banach--Steinhaus theorem in locally convex spaces for \sigma-locally Lipschitzian operators established by S. Lahrech in [1] to \sigma-locally Lipschitzian convex processes.
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Banach lattices of continuous sections
Статья научная
The aim of this note is to outline some application of ample continuous Banach bundles to the theory of Banach lattices.
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Banach lattices with topologically full centre
Статья научная
After some general background discussion on the notion of a topologically full centre in a Banach lattice, we study two problems in which it has featured. In 1988 Orhon showed that if the centre is topologically full then it is also a maximal abelian algebra of bounded operators and asked if the converse is true. We give a short proof of his result and a counterexample to the converse. After noting that every non scalar central operator has a hyperinvariant band, we show that any hyperinvariant subspace must be an order ideal, provided the centre is topologically full and conclude with a counterexample to this in a general vector lattice setting.
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Bernstein - Nikolskii type inequality in Lorentz spaces and related topics
Статья научная
In this paper we study the Bernstein - Nikolskii type inequality, the inverse Bernstein theorem and some properties of functions and their spectrum in Lorentz spaces L^{p,q}(\R^n).
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Binary correspondences and the inverse problem of chemical kinetics
Статья научная
We show how binary correspondences can be used for simple formalization of the notion of problem, definition of the basic components of problems, their properties, and constructions. In particular, formalization of the following notions is presented: condition, data, unknowns, and solutions of a problem, solvability and unique solvability, inverse problem, composition and restriction of problems, isomorphism between problems. We also consider topological problems and the related notions of stability and correctness. A connection is indicated between the stability and continuity of a uniquely solvable topological problem. The definition of parametrized set is given. The notions are introduced of parametrized problem, the problem of reconstruction of an object by the values of parameters, as well as the notions of locally free set of parameters and stability with respect to a set of parameters. As an illustration, we consider a singularly perturbed system of ordinary differential equations which describe a process in chemical kinetics and burning...
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Статья научная
The block graph of a graph G, written B(G), is the graph whose vertices are the blocks of G and in which two vertices are adjacent whenever the corresponding blocks have a cut-vertex in common. We study the properties of B(G) and present the characterization of graphs whose B(G) are planar, outerplanar, maximal outerplanar, minimally non-outerplanar, Eulerian, and Hamiltonian. A necessary and sufficient condition for B(G) to have crossing number one is also presented.
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Blow-up result for a class of wave p-Laplace equation with nonlinear dissipation in Rn
Статья научная
The Laplace equations has been studied in several stages and has gradually developed over the past decades. Beginning with the well-known standard equation Δu=0, where it has been well studied in all aspects, many results have been found and improved in an excellent manner. Passing to p-Laplace equation Δpu=0 with a constant parameter, whether in stationary or evolutionary systems, where it experienced unprecedented development and was studied in almost exhaustively. In this article, we consider initial value problem for nonlinear wave equation containing the p-Laplacian operator. We prove that a class of solutions with negative initial energy blows up in finite time if p≥r≥m, by using contradiction argument. Additional difficulties due to the constant exponents in Rn are treated in order to obtain the main conclusion. We used a contradiction argument to obtain a condition on initial data such that the solution extinct at finite time. In the absence of the density function, our system reduces to the nonlinear damped wave equation, it has been extensively studied by many mathematicians in bounded domain.
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Boolean models and simultaneous inequalities
Статья научная
Boolean valued analysis is applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities.
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Bounded composition operators on weighted function spaces in the unit disk
Статья научная
We introduce a general class of weighted spaces H(β) of holomorphic functions in the unit disk D, which contains several classical spaces, such as Hardy space, Bergman space, Dirichlet space. We characterize boundedness of composition operators Cφ induced by affine and monomial symbols φ on these spaces H(β). We also establish a sufficient condition under which the operator Cφ induced by the symbol φ with relatively compact image φ(D) in D is bounded on H(β). Note that in the setting of H(β), the characterizations of boundedness of composition operators Cφ depend closely not only on functional properties of the symbols φ but also on the behavior of the weight sequence β.
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Bounded orthomorphisms between locally solid vector lattices
Статья научная
The main aim of the present note is to consider bounded orthomorphisms between locally solid vector lattices. We establish a version of the remarkable Zannen theorem regarding equivalence between orthomorphisms and the underlying vector lattice for the case of all bounded orthomomorphisms. Furthermore, we investigate topological and ordered structures for these classes of orthomorphisms, as well. In particular, we show that each class of bounded orthomorphisms possesses the Levi or the AM-properties if and only if so is the underlying locally solid vector lattice. Moreover, we establish a similar result for the Lebesgue property, as well.
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Статья научная
Let $G=(V,E)$ be a graph. A subset $D$ of $V$ is called common neighbourhood dominating set (CN-do\-mi\-nating set) if for every $v\in V-D$ there exists a vertex $u\in D$ such that $uv\in E(G)$ and $|\Gamma(u,v)|\geq1$, where $|\Gamma(u,v)|$ is the number of common neighbourhood between the vertices $u$ and $v$. The minimum cardinality of such CN-dominating set denoted by $\gamma_{cn}(G)$ and is called common neighbourhood domination number (CN-edge domination) of $G$. In this paper we introduce the concept of common neighbourhood edge domination (CN-edge domination) and common neighbourhood edge domatic number (CN-edge domatic number) in a graph, exact values for some standard graphs, bounds and some interesting results are established.
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Calculus of tangents and beyond
Статья научная
Optimization is the choice of what is most preferable. Geometry and local analysis of nonsmooth objects are needed for variational analysis which embraces optimization. These involved admissible directions and tangents as the limiting positions of the former. The calculus of tangents is one of the main techniques of optimization. Calculus reduces forecast to numbers, which is scalarization in modern parlance. Spontaneous solutions are often labile and rarely optimal. Thus, optimization as well as calculus of tangents deals with inequality, scalarization and stability. The purpose of this article is to give an overview of the modern approach to this range of questions based on non-standard models of set theory. A model of a mathematical theory is usually called nonstandard if the membership within the model has interpretation different from that of set theory. In the recent decades much research is done into the nonstandard methods located at the junctions of analysis and logic. This area requires the study of some new opportunities of modeling that open broad vistas for consideration and solution of various theoretical and applied problems.
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Characterizations of finite dimensional Archimedean vector lattices
Статья научная
In this paper, we give some necessary and sufficient conditions for an Archimedean vector lattice A to be of finite dimension. In this context, we give three characterizations. The first one contains the relation between the vector lattice A to be of finite dimension and its universal completion Au. The second one shows that the vector lattice A is of finite dimension if and only if one of the following two equivalent conditions holds : (a) every maximal modular algebra ideal in Au is relatively uniformly complete or (b) Orth(A,Au)=Z(A,Au) where Orth(A,Au) and Z(A,Au) denote the vector lattice of all orthomorphisms from A to Au and the sublattice consisting of orthomorphisms π with |π(x)|≤λ|x| (x∈A) for some 0≤λ∈R, respectively. It is well-known that any universally complete vector lattice A is of the form C∞(X) for some Hausdorff extremally disconnected compact topological space X. The point x∈X is called σ- isolated if the intersection of every sequence of neighborhoods of x is a neighborhood of x. The last characterization of finite dimensional Archimedean vector lattices is the following. Let A be a vector lattice and let Au(=C∞(X)) be its universal completion. Then A is of finite dimension if and only if each element of X is σ-isolated. Bresar in \cite{4} raised a question to find new examples of zero product determined algebras. Finally, as an application, we give a positive answer to this question.
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