Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics
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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 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 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 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 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 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 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.Item 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 QUEUING SYSTEM EVOLUTION IN PHASE MERGING SCHEME(Institutul de Matematică şi Informatică al AŞM, 2008) Korolyk, V.; Mishkoy, Gheorghe; Mamonova, A.; Griz, Iu.We study asymptotic average scheme for semi-Markov queuingsystemsusing compensating operator of the corresponding extendedMarkov process. Thepeculiarity of our queuing system is that the series scheme is considered with phasemerging procedure.Item THE EULER TOUR OFN-DIMENSIONAL MANIFOLDWITH POSITIVE GENUS(Institutul de Matematică şi Informatică al AŞM, 2008) Cataranciuc, Sergiu; Bujac-Leisz, Mariana; Soltan, PetruIn the paper [1] it is proved that abstract cubicn-dimensional torus[2] possesses a directed Euler tour of the same dimension. The result prompts toa new (virtual) device for transmission and reception of information. In the presentpaper it is shown that every abstract cubicn-dimensional manifold without borders, ofpositive genus possesses an-dimensional directed Euler tour. This result has practicalapplication.