2. Articole
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Item LINEAR SINGULAR PERTURBATIONS OF HYPERBOLIC-PARABOLIC TYPE(Academia de Ştiinţe a Moldovei, 2003) Perjan, AndreiWe study the behavior of solutions of the problem εu′′(t)+u′(t)+Au(t) =f (t), u(0) = u0, u′(0) = u1 in the Hilbert space H as ε → 0, where A is a linear,symmetric, strong positive operator.Item SINGULAR PERTURBATIONS OFHYPERBOLIC-PARABOLIC TYPE(Institutul de Matematică şi Informatică al AŞM, 2003) Perjan, AndreiWe study the behavior of solutions of the problemεu′′(t)+u′(t)+Au(t) =f(t), u(0) =u0, u′(0) =u1in the Hilbert spaceHasε→0, whereAis a linear,symmetric, strong positive operator.Item ERGODIC SETS AND MIXING EXTENSIONS OF TOPOLOGICAL TRANSFORMATION SEMIGROUPS(Institutul de Matematică şi Informatică al AŞM, 2003) Gerco, AnatolieWe extend the concept of the ergodic set [1] – [2] from topological trans-formation groups to topological transformation semigroups. We investigate, in par-ticular, connections between ergodicity, weak ergodicity, topological transitivity andminimality of the Whitney’s sum of extensions of topological transformation semi-groupsItem THE PACKING KNAPSACK PROBLEM, AND THE K-OPTIMAL TREE IN A WEIGHTED DIGRAPH(2003) Lozovanu, DumitruWe consider the packing knapsack problem, which generalizes the classical knapsack problem. A dynamic programming algorithm for solving this problem and its applicationto find the k-optimal tree in a weighted directed graph are discussed.Item ON STRONG STABILITY OF LINEAR POISSON ACTIONS(Institutul de Matematică şi Informatică al AŞM, 2003) Glavan, Vasile; Rzeszotko, Z.Linear Poisson actions of the groupRmare considered. Conditions on thejoint spectrum of the generators and on the centralizers assuring stability and strongstability of the action are given. We give also some examplesof Poisson actions usingCAS”Mathematica”.Item GLOBAL ATTRACTORS FOR V -MONOTONE NONAUTONOMOUS DYNAMICAL SYSTEMS(Institutul de Matematică şi Informatică al AŞM, 2003) Cheban, David; Kloeden, Peter-E.; Schmalfuss, BjornThis article is devoted to the study of the compact global atrractors of Vmomotone nonautonomous dynamical systems.We give a description of the structure of compact global attractors of this class of systems. Several applications of general results for different classes of differential equations (ODEs, ODEs with impulse, some classes of evolutionary partial differential equations) are given.Item THE OPTIMAL FLOW IN DYNAMIC NETWORKSWITH NONLINEAR COST FUNCTIONS ON EDGES(Institutul de Matematică şi Informatică al AŞM, 2004) Fonoberova, Maria; Lozovanu, DmitriiIn this paper we study the dynamic version of the nonlinear minimum- cost flow problem on networks. We consider the problem on dynamic networks with nonlinear cost functions on edges that depend on time and flow. Moreover, we assume that the demand function and capacities of edges also depend on time. To solve the problem we propose an algorithm, which is based on reducing the dynamic problem to the classical minimum-cost problem on a time-expanded network. We also study some generalization of the proposed problem.Item THE SCHAUDER BASIS IN SYMMETRICALLY NORMED IDEALSOF OPERATORS(Institutul de Matematică şi Informatică al AŞM, 2004) Spinu, EfimiiIn this paper we build a basis in a separable symmetrically normed ideal.Item B-STABLE SUBGRAPHS IN UNDIRECTED GRAPHS(Valines SRL, 2004) Grigoriu, NicolaeIn this article special structures of stable subgraphs and some of their most important properties that will be necessary for calculation of the number of transitive orientations of an undirected graph are described.Item ALMOST PERIODIC SOLUTIONS AND GLOBAL ATTRACTORS OF NON-AUTONOMOUS NAVIER–STOKES EQUATIONS(Springer, 2004) Cheban, David; Duan, JinqiaoThe article is devoted to the study of non-autonomous Navier–Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier–Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic, almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier–Stokes equations is given. Finally, the authors have derived a global averaging principle for non-autonomous Navier–Stokes equations.Item INVARIANT MANIFOLDS, GLOBAL ATTRACTORS AND ALMOST PERIODIC SOLUTIONS OF NONAUTONOMOUS DIFFERENCE EQUATIONS(Elsevier, 2004) Cheban, David; Mammana, CristianaThe article is devoted to the study of quasi-linear nonautonomous difference equations: invariant manifolds, compact global attractors, almost periodic and recurrent solutions and chaotic sets. First, we prove that such equations admit an invariant continuous section (an invariant manifold). Then, we obtain the conditions for the existence of a compact global attractor and characterize its structure. Third, we derive a criterion for the existence of almost periodic and recurrent solutions of the quasi-linear nonautonomous difference equations. Finally, we prove that quasi-linear maps with chaotic base admit a chaotic compact invariant set. The obtained results are applied while studying triangular maps: invariant manifolds, compact global attractors, almost periodic and recurrent solutions and chaotic sets.Item ASYMPTOTIC STABILITY OF AUTONOMOUSAND NON-AUTONOMOUS DISCRETE LINEAR INCLUSIONS(Institutul de Matematică şi Informatică al AŞM, 2004) Cheban, David; Mammana, CristianaThe article is devoted to the study of absolute asymptotic stability ofdiscrete linear inclusions (both autonomous and non-autonomous) in Banach space.We establish the relation between absolute asymptotic stability, uniform asymptoticstability and uniform exponential stability. It is proved that for compact (completelycontinuous) discrete linear inclusions these notions of stability are equivalent. Westudy this problem in the framework of non-autonomous dynamical systems (cocyles).Item NUMERICAL TREATMENT OF THE KENDALL EQUATIONIN THE ANALYSIS OF PRIORITY QUEUEING SYSTEMS(Institutul de Matematică şi Informatică al AŞM, 2006) Bejan, AndreiWe investigate here how to treat numerically the Kendall functional equa-tion occuring in the theory of branching processes and queueing theory. We discussthis question in the context of priority queueing systems with switchover times. Innumerical analysis of such systems one deals with functional equations of the Kendalltype and efficient numerical treatment of these is necessary in order to estimate im-portant system performance characteristics.Item LIMITS OF SOLUTIONS TO THE SEMILINEAR WAVE EQUATION WITH SMALL PARAMETER(Academia de Ştiinţe a Moldovei, 2006) Perjan, AndreiWe study the existence of the limits of solution to singularly perturbed initial boundary value problem of hyperbolic - parabolic type with boundary Dirichlet condition for the semilinear wave equation. We prove the convergence of solutions and also the convergence of gradients of solutions to perturbed problem to the corresponding solutions to the unperturbed problem as the small parameter tends to zero. We show that the derivatives of solution relative to time-variable possess the boundary layer function of the exponential type in the neighborhood of t = 0Item A TEST FOR COMPLETENESS WITH RESPECT TO IMPLICIT REDUCIBILITY IN THE CHAIN SUPER-INTUTIONISTIC LOGICS(Institutul de Matematică şi Informatică al AŞM, 2006) Cucu, Ion V.We examine chain logicsC2, C3, . . . ,which are intermediary betweenclassical and intuitionistic logics. They are also the logics of pseudo-Boolean algebrasof type< Em,&,∨,⊃,¬>, whereEmis the chain 0< τ1< τ2<···< τm−2<1 (m= 2,3, . . .).The formulaFis called to be implicitly expressible in logicLbythe system Σ of formulas if the relationL⊢(F∼q)∼((G1∼H1) &. . .& (Gk∼Hk))is true, whereqdo not appear inF, and formulasGiandHi, fori= 1, . . . , k, areexplicitly expressible inLvia Σ. The formulaFis said to be implicitly reducible inlogicLto formulas of Σ if there exists a finite sequence of formulasG1, G2, . . . , GlwhereGlcoincides withFand forj= 1, . . . , lthe formulaGjis implicitly expressibleinLby Σ∪{G1, . . . , Gj−1}. The system Σ is called complete relative to implicitreducibility in logicLif any formula is implicitly reducible inLto Σ.The paper contains the criterion for recognition of completeness with respect to im-plicit reducibility in the logicCm, for anym= 2,3, . . .. The criterion is based on 13closed pre-complete classes of formulas.Item COLLOCATION AND QUADRATURE METHODS FOR SOLVING SINGULAR INTEGRAL EQUATIONS WITH PIECEWISE CONTINUOUS COEFFICIENTS(Institutul de Matematică şi Informatică al AŞM, 2006) Capcelea, TituThe computation schemes of collocation and mechanical quadraturemethods for approximate solving of the complete singular integral equations withpiecewise continuous coefficients and a regular kernel with weak singularity are elab-orated. The case when the equations are defined on the unit circumference of thecomplex plane is examined. The sufficient conditions for the convergence of thesemethods in the spaceL2are obtained.Item THE MULTIDIMENSIONAL DIRECTED EULER TOUROF CUBIC MANIFOLD(Institutul de Matematică şi Informatică al AŞM, 2006) Bujac, Marianan the paper [3] we tried to generalize the problem of existence of a di-rected (n−1)-dimensional Euler tour for the abstract directedn-dimensional manifold,which is acomplex of multi-ary relations[5], namely by means of abstract simplexes.In the paper [3] we show the existence of such kind of tour onlyfor manifolds of odddimension because we have not enough conditions to do more. In the present paperwe will show conditions of existence for a directed Euler tour of abstract manifoldswith even dimensions. In this purpose, we will introduce some new definitions whichpermit us to define manifolds by so-calledabstract cubes.Item ON THE DIVISION OF ABSTRACT MANIFOLDS IN CUBES(Institutul de Matematică şi Informatică al AŞM, 2006) Bujac, Mariana; Cataranciuc, Sergiu; Soltan, PetruWe prove that in the class of abstract multidimensional manifolds withoutborders only torusVn1of dimensionn≥1 can be divided in abstract cubes with theproperty: every faceImfromVn1is shared by 2n−mcubes,m= 0,1, . . . , n−1. Theabstract torusVn1is realized inEd, n+1≤d≤2n+1, so it results that in the class ofalln-dimensional combinatorial manifolds [1]onlytorus respects this propriety. Torusis autodual because of this propriety.Item ABSOLUTE ASYMPTOTIC STABILITY OF DISCRETE LINEAR INCLUSIONS(Institutul de Matematică şi Informatică al AŞM, 2006) Cheban, David; Mammana, CristianaThe article is devoted to the study of absolute asymptotic stability of discrete linear inclusions in Banach (both finite and infinite dimensional) space. We establish the relation between absolute asymptotic stability, asymptotic stability, uniform asymptotic stability and uniform exponential stability. It is proved that for asymptotical compact (a sum of compact operator and contraction) discrete linear inclusions the notions of asymptotic stability and uniform exponential stability are equivalent. It is proved that finite-dimensional discrete linear inclusion, defined by matrices {A1,A2, ...,Am}, is absolutely asymptotically stable if it does not admit nontrivial bounded full trajectories and at least one of the matrices {A1,A2, ...,Am} is asymptotically stable. We study this problem in the framework of non-autonomous dynamical systems (cocyles).Item JUNIOR SPATIAL GROUPS OF (221)-SYMMETRY(Institutul de Matematică şi Informatică al AŞM, 2006) Shenesheutskaia, AllaThe connection between junior groups of three independent kinds ofantisymmetry transformations and junior groups of (221)-symmetry, derived fromspace Fedorov groups was established. This connection allowed us to find all thesegroups.