DSpace Community: 1999
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Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions
http://hdl.handle.net/10525/455
Title: Alternative Characterization of the Class k-UCV and Related Classes of Univalent Functions<br/><br/>Authors: Kanas, Stanislawa<br/><br/>Abstract: In this paper an alternative characterization of the class offunctions called k -uniformly convex is found. Various relations concerningconnections with other classes of univalent functions are given. Moreover anew class of univalent functions, analogous to the ’Mocanu class’ of functions,is introduced. Some results concerning this class are derived.Null Condition for Semilinear Wave Equation with Variable Coefficients
http://hdl.handle.net/10525/454
Title: Null Condition for Semilinear Wave Equation with Variable Coefficients<br/><br/>Authors: Catalano, Fabio<br/><br/>Abstract: In this work we analyse the nonlinear Cauchy problem (∂tt − ∆)u(t, x) = ( λg + O(1/(1 + t + |x|)^a) ) ) ∇t,x u(t, x), ∇t,x u(t, x) ), whit initial data u(0, x) = e u0 (x), ut (0, x) = e u1 (x). We assume a ≥ 1,x ∈ R^n (n ≥ 3) and g the matrix related to the Minkowski space. It can beconsiderated a pertubation of the case when the quadratic term has constantcoefficient λg (see Klainerman [6])We prove a global existence and uniqueness theorem for very regular initialdata. The proof avoids a direct application of Klainermann method (Nullcondition, energy conformal method), because the result is obtained by acombination beetwen the energy estimate (norm L^2 ) and the decay estimate(norm L^∞ ).<br/><br/>Description: ∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...”A Cauchy Integral Related to a Robot-safety Device System
http://hdl.handle.net/10525/453
Title: A Cauchy Integral Related to a Robot-safety Device System<br/><br/>Authors: Vanderperre, E.; Makhanov, S.<br/><br/>Abstract: We introduce a robot-safety device system attended by twodifferent repairmen. The twin system is characterized by the natural featureof cold standby and by an admissible “risky” state. In order to analyse therandom behaviour of the entire system (robot, safety device, repair facility)we employ a stochastic process endowed with probability measures satisfyinggeneral Hokstad-type differential equations. The solution procedure isbased on the theory of sectionally holomorphic functions, characterized bya Cauchy-type integral defined as a Cauchy principal value in double sense.An application of the Sokhotski-Plemelj formulae determines the long-runavailability of the robot-safety device. Finally, we consider the particularbut important case of deterministic repair.Topological Dichotomy and Unconditional Convergence
http://hdl.handle.net/10525/452
Title: Topological Dichotomy and Unconditional Convergence<br/><br/>Authors: Lefevre, Pascal<br/><br/>Abstract: In this paper, we give a criterion for unconditional convergencewith respect to some summability methods, dealing with the topological sizeof the set of choices of sign providing convergence. We obtain similar resultsfor boundedness. In particular, quasi-sure unconditional convergence impliesunconditional convergence.Representations and Positive Definite Functions on Hypergroups
http://hdl.handle.net/10525/451
Title: Representations and Positive Definite Functions on Hypergroups<br/><br/>Authors: Nasr-Isfahani, A.<br/><br/>Abstract: Some relationships between representations of a hypergroup X,its algebras, and positive definite functions on X are studied. Also, varioustypes of convergence of positive definite functions on X are discussed.A Differential Game Described by a Hyperbolic System
http://hdl.handle.net/10525/450
Title: A Differential Game Described by a Hyperbolic System<br/><br/>Authors: Souroujon, Diko<br/><br/>Abstract: An antagonistic differential game of hyperbolic type with aseparable linear vector pay-off function is considered. The main result isthe description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to findthe optimal program strategies of two multicriterial problems of hyperbolictype. The application of approximation enables us to relate these problemsto a problem of optimal program control, described by a system of ordinarydifferential equations, with a scalar pay-off function. It is found that theresult of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting thatthe ε-Slater saddle points are not equivalent and there exist two ε-Slatersaddle points for which the values of all components of the vector pay-offfunction at one of them are greater than the respective components of theother ε-saddle point.A Remark On S.M. Bates' Theorem
http://hdl.handle.net/10525/449
Title: A Remark On S.M. Bates' Theorem<br/><br/>Authors: Hájek, Petr<br/><br/>Abstract: In his paper [1], Bates investigates the existence of nonlinear, but highlysmooth, surjective operators between various classes of Banach spaces. Modifyinghis basic method, he obtains the following striking results.Geometric Stable Laws Through Series Representations
http://hdl.handle.net/10525/448
Title: Geometric Stable Laws Through Series Representations<br/><br/>Authors: Kozubowski, Tomasz; Podgórski, Krzysztof<br/><br/>Abstract: Let (Xi ) be a sequence of i.i.d. random variables, and letN be a geometric random variable independent of (Xi ). Geometric stabledistributions are weak limits of (normalized) geometric compounds, SN =X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain seriesrepresentation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi ,and derive series representations of the limiting geometric stable processand the corresponding stochastic integral. We also obtain strong invarianceprinciples for stable and geometric stable laws.The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points
http://hdl.handle.net/10525/447
Title: The General Differential Operators Generated by a Quasi-Differential Expressions with their Interior Singular Points<br/><br/>Authors: El-sayed Ibrahim, Sobhy<br/><br/>Abstract: The general ordinary quasi-differential expression M of n-th order with complex coefficients and its formal adjoint M + are considered overa regoin (a, b) on the real line, −∞ ≤ a < b ≤ ∞, on which the operatormay have a finite number of singular points. By considering M over varioussubintervals on which singularities occur only at the ends, restrictions of themaximal operator generated by M in L2|w (a, b) which are regularly solvablewith respect to the minimal operators T0 (M ) and T0 (M + ). In addition todirect sums of regularly solvable operators defined on the separate subintervals,there are other regularly solvable restrications of the maximal operatorwhich involve linking the various intervals together in interface like style.On the Uniform Decay of the Local Energy
http://hdl.handle.net/10525/446
Title: On the Uniform Decay of the Local Energy<br/><br/>Authors: Vodev, Georgi<br/><br/>Abstract: It is proved in [1],[2] that in odd dimensional spaces any uniform decay of the local energy implies that it must decay exponentially. Weextend this to even dimensional spaces and to more general perturbations(including the transmission problem) showing that any uniform decay of thelocal energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the timeand n being the space dimension.New Binary Extremal Self-Dual Codes of Lengths 50 and 52
http://hdl.handle.net/10525/445
Title: New Binary Extremal Self-Dual Codes of Lengths 50 and 52<br/><br/>Authors: Buyuklieva, Stefka<br/><br/>Abstract: New extremal binary self-dual codes of lengths 50 and 52 areconstructed. Some of them are the first known codes with such weightenumerators. The structure of their automorphisms groups are shown.<br/><br/>Description: * This work was partially supported by the Bulgarian National Science Fund under Contract No. MM – 503/1995.Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
http://hdl.handle.net/10525/444
Title: Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem<br/><br/>Authors: De Schepper, H.<br/><br/>Abstract: We consider a model eigenvalue problem (EVP) in 1D, withperiodic or semi–periodic boundary conditions (BCs). The discretization ofthis type of EVP by consistent mass finite element methods (FEMs) leads tothe generalized matrix EVP Kc = λ M c, where K and M are real, symmetricmatrices, with a certain (skew–)circulant structure. In this paper we fix ourattention to the use of a quadratic FE–mesh. Explicit expressions for theeigenvalues of the resulting algebraic EVP are established. This leads to anexplicit form for the approximation error in terms of the mesh parameter,which confirms the theoretical error estimates, obtained in [2].On the Maximum of a Branching Process Conditioned on the Total Progeny
http://hdl.handle.net/10525/443
Title: On the Maximum of a Branching Process Conditioned on the Total Progeny<br/><br/>Authors: Kerbashev, Tzvetozar<br/><br/>Abstract: The maximum M of a critical Bienaymé-Galton-Watson processconditioned on the total progeny N is studied. Imbedding of the process ina random walk is used. A limit theorem for the distribution of M as N → ∞is proved. The result is trasferred to the non-critical processes. A corollaryfor the maximal strata of a random rooted labeled tree is obtained.An Example Concerning Valdivia Compact Spaces
http://hdl.handle.net/10525/442
Title: An Example Concerning Valdivia Compact Spaces<br/><br/>Authors: Kalenda, Ondrej<br/><br/>Abstract: We prove that the dual unit ball of the space C0 [0, ω1 ) endowedwith the weak* topology is not a Valdivia compact. This answers a questionposed to the author by V. Zizler and has several consequences. Namely, ityields an example of an affine continuous image of a convex Valdivia compact(in the weak* topology of a dual Banach space) which is not Valdivia,and shows that the property of the dual unit ball being Valdivia is not anisomorphic property. Another consequence is that the space C0 [0, ω1 ) has nocountably 1-norming Markusevic basis.<br/><br/>Description: ∗ Supported by Research grants GAUK 190/96 and GAUK 1/1998On The Brill-noether Theory of Spanned Vector Bundles on Smooth Curves
http://hdl.handle.net/10525/441
Title: On The Brill-noether Theory of Spanned Vector Bundles on Smooth Curves<br/><br/>Authors: Ballico, E.<br/><br/>Abstract: Here we study the integers (d, g, r) such that on a smoothprojective curve of genus g there exists a rank r stable vector bundle withdegree d and spanned by its global sections.Paracompact Spaces and Radon Spaces
http://hdl.handle.net/10525/440
Title: Paracompact Spaces and Radon Spaces<br/><br/>Authors: Rodriguez-Salinas, Baltasar<br/><br/>Abstract: We prove that if E is a subset of a Banach space whose densityis of measure zero and such that (E, weak) is a paracompact space, then(E, weak) is a Radon space of type (F ) under very general conditions.