DSpace Community: 1995
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An Iterative Method for the Matrix Principal n-th Root
http://hdl.handle.net/10525/644
Title: An Iterative Method for the Matrix Principal n-th Root<br/><br/>Authors: Lakić, Slobodan<br/><br/>Abstract: In this paper we give an iterative method to compute the principal n-th rootand the principal inverse n-th root of a given matrix. As we shall show thismethod is locally convergent. This method is analyzed and its numerical stabilityis investigated.Radon Measures on Banach Spaces with their Weak Topologies
http://hdl.handle.net/10525/643
Title: Radon Measures on Banach Spaces with their Weak Topologies<br/><br/>Authors: Jayne, J.; Rogers, C.<br/><br/>Abstract: The main concern of this paper is to present some improvementsto results on the existence or non-existence of countably additive Borel measuresthat are not Radon measures on Banach spaces taken with their weak topologies, onthe standard axioms (ZFC) of set-theory. However, to put the results in perspective weshall need to say something about consistency results concerning measurable cardinals.Optimization of Discrete-Time, Stochastic Systems
http://hdl.handle.net/10525/642
Title: Optimization of Discrete-Time, Stochastic Systems<br/><br/>Authors: Papageorgiou, Nikolaos<br/><br/>Abstract: In this paper we study discrete-time, finite horizon stochastic systemswith multivalued dynamics and obtain a necessary and sufficient condition foroptimality using the dynamic programming method. Then we examine a nonlinearstochastic discrete-time system with feedback control constraints and for it, wederive a necessary and sufficient condition for optimality which we then use toestablish the existence of an optimal policy.<br/><br/>Description: * This research was supported by a grant from the Greek Ministry of Industry and Technology.Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds
http://hdl.handle.net/10525/641
Title: Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds<br/><br/>Authors: Ribarska, Nadezhda; Tsachev, Tsvetomir; Krastanov, Mikhail<br/><br/>Abstract: Let M be a complete C1−Finsler manifold without boundary andf : M → R be a locally Lipschitz function. The classical proof of the well knowndeformation lemma can not be extended in this case because integral lines maynot exist. In this paper we establish existence of deformations generalizing theclassical result. This allows us to prove some known results in a more generalsetting (minimax theorem, a theorem of Ljusternik-Schnirelmann type, mountainpass theorem). This approach enables us to drop the compactness assumptionscharacteristic for recent papers in the field using the Ekeland’s variational principleas the main tool.<br/><br/>Description: ∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria.∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.New Upper Bounds for Some Spherical Codes
http://hdl.handle.net/10525/640
Title: New Upper Bounds for Some Spherical Codes<br/><br/>Authors: Boyvalenkov, Peter; Kazakov, Peter<br/><br/>Abstract: The maximal cardinality of a code W on the unit sphere in n dimensions with (x, y) ≤ s whenever x, y ∈ W, x 6= y, is denoted by A(n, s). We use twomethods for obtaining new upper bounds on A(n, s) for some values of n and s.We find new linear programming bounds by suitable polynomials of degrees whichare higher than the degrees of the previously known good polynomials due to Levenshtein [11, 12]. Also we investigate the possibilities for attaining the Levenshteinbounds [11, 12]. In such cases we find the distance distributions of the correspondingfeasible maximal spherical codes. Usually this leads to a contradiction showingthat such codes do not exist.On a Two-Dimensional Search Problem
http://hdl.handle.net/10525/639
Title: On a Two-Dimensional Search Problem<br/><br/>Authors: Kolev, Emil; Landgev, Ivan<br/><br/>Abstract: In this article we explore the so-called two-dimensional tree− searchproblem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) therectangles A(m, n) are all tight, no matter what n is. On the other hand, we provethat there exist infinitely many integers m for which there is an infinite numberof n’s such that A(m, n) is loose. Furthermore, we determine the smallest looserectangle as well as the smallest loose square (A(181, 181)). It is still undecidedwhether there exist infinitely many loose squares.Mean-Periodic Solutions of Retarded Functional Differential Equations
http://hdl.handle.net/10525/638
Title: Mean-Periodic Solutions of Retarded Functional Differential Equations<br/><br/>Authors: Tsvetkov, Dimitar<br/><br/>Abstract: In this paper we present a spectral criterion for existence of mean-periodic solutions of retarded functional differential equations with a time-independent main part.Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities
http://hdl.handle.net/10525/637
Title: Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities<br/><br/>Authors: Ndoutoume, James<br/><br/>Abstract: The author recently introduced a regularity assumption for derivatives of set-valued mappings, in order to obtain first order necessary conditions ofoptimality, in some generalized sense, for nondifferentiable control problems governed by variational inequalities. It was noticed that this regularity assumptioncan be viewed as a symmetry condition playing a role parallel to that of the wellknown symmetry property of the Hessian of a function at a given point. In thispaper, we elaborate this point in a more detailed way and discuss some relatedquestions. The main issue of the paper is to show (using this symmetry condition) that necessary conditions of optimality alluded above can be shown to bealso sufficient if a weak pseudo-convexity assumption is made for the subgradientoperator governing the control equation. Some examples of application to concretesituations are presented involving obstacle problems.<br/><br/>Description: * This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged.Solutions of Analytical Systems of Partial Differential Equations
http://hdl.handle.net/10525/636
Title: Solutions of Analytical Systems of Partial Differential Equations<br/><br/>Authors: Trenčevski, K.<br/><br/>Abstract: In this paper are examined some classes of linear and non-linearanalytical systems of partial differential equations. Compatibility conditions arefound and if they are satisfied, the solutions are given as functional series in aneighborhood of a given point (x = 0).Strong-weak Stackelberg Problems in Finite Dimensional Spaces
http://hdl.handle.net/10525/635
Title: Strong-weak Stackelberg Problems in Finite Dimensional Spaces<br/><br/>Authors: Aboussoror, Abdelmalek; Loridan, Pierre<br/><br/>Abstract: We are concerned with two-level optimization problems called strongweakStackelberg problems, generalizing the class of Stackelberg problems in thestrong and weak sense. In order to handle the fact that the considered two-leveloptimization problems may fail to have a solution under mild assumptions, weconsider a regularization involving ε-approximate optimal solutions in the lowerlevel problems. We prove the existence of optimal solutions for such regularizedproblems and present some approximation results when the parameter ǫ goes tozero. Finally, as an example, we consider an optimization problem associated to abest bound given in [2] for a system of nondifferentiable convex inequalities.On an Extremal Problem concerning Bernstein Operators
http://hdl.handle.net/10525/634
Title: On an Extremal Problem concerning Bernstein Operators<br/><br/>Authors: Gonska, Heinz; Zhou, Ding-Xuan<br/><br/>Abstract: The best constant problem for Bernstein operators with respect tothe second modulus of smoothness is considered. We show that for any1/2 ≤ a < 1, there is an N(a) ∈ N such that for n ≥ N(a),1−a≤k, n≤a, sup | Bn (f, k/n) − f(k/n) | ≤ cω2(f, 1/√n), where c is a constant,0 < c < 1.<br/><br/>Description: * The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.Branching Processes with Immigration and Integer-valued Time Series
http://hdl.handle.net/10525/633
Title: Branching Processes with Immigration and Integer-valued Time Series<br/><br/>Authors: Dion, J.; Gauthier, G.; Latour, A.<br/><br/>Abstract: In this paper, we indicate how integer-valued autoregressive timeseries Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branchingprocesses with immigration. This allows the derivation of a simple criteria for theexistence of a stationary distribution of the time series, thus proving and extendingsome results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour[11]. One can then transfer results on estimation in subcritical multitype branchingprocesses to stationary Ginar(d) and get consistency and asymptotic normality forthe corresponding estimators. The technique covers autoregressive moving averagetime series as well.Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments
http://hdl.handle.net/10525/632
Title: Integral Manifolds and Perturbations of the Nonlinear Part of Systems of Autonomous Differential Equations with Impulses at Fixed Moments<br/><br/>Authors: Stamov, G.<br/><br/>Abstract: Sufficient conditions are obtained for the existence of local integralmanifolds of autonomous systems of differential equations with impulses at fixedmoments. In case of perturbations of the nonlinear part an estimate of the difference between the manifolds is obtained.<br/><br/>Description: * This investigation was supported by the Bulgarian Ministry of Science and Education under Grant MM-7.Perturbations of Systems Describing the Motion of a Particle in Central Fields
http://hdl.handle.net/10525/631
Title: Perturbations of Systems Describing the Motion of a Particle in Central Fields<br/><br/>Authors: Christov, Ognyan; Dragnev, Dragomir<br/><br/>Abstract: The present paper deals with the KAM-theory conditions for systems describing the motion of a particle in central field.Operators Factoring through Banach Lattices and Ideal Norms
http://hdl.handle.net/10525/630
Title: Operators Factoring through Banach Lattices and Ideal Norms<br/><br/>Authors: Reisner, Shlomo<br/><br/>Abstract: A new, unified presentation of the ideal norms of factorization of operators through Banach lattices and related ideal norms is given.Some Comments on Q-Irresolute and Quasi-Irresolute Functions
http://hdl.handle.net/10525/629
Title: Some Comments on Q-Irresolute and Quasi-Irresolute Functions<br/><br/>Authors: Dontchev, Julian; Ganster, Maximilian<br/><br/>Abstract: The aim of this paper is to continue the study of θ-irresolute andquasi-irresolute functions as well as to give an example of a function which is θ-irresolute but neither quasi-irresolute nor an R-map and thus give an answer toa question posed by Ganster, Noiri and Reilly. We prove that RS-compactness ispreserved under open, quasi-irresolute surjections.