DSpace Collection: Volume 21 Number 3
http://hdl.handle.net/10525/530
Serdica Mathematical Journal Volume 21, Number 3, 1995The Collection's search engineSearch the Channelsearch
http://sci-gems.math.bas.bg/jspui/simple-search
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).