DSpace Community: 1998
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Generalized Problem of Sratlikeness for Products of P-Valent Starlike Functions
http://hdl.handle.net/10525/566
Title: Generalized Problem of Sratlikeness for Products of P-Valent Starlike Functions<br/><br/>Authors: Dimkov, Georgi; Dziok, Jacek<br/><br/>Abstract: We consider functions of the type, j=1 ... n, F(z) = z^p ∏ [ fj (z)/(z^p) ] ^αjwhere fj are p-valent functions starlike of order αj and aj are complexnumbers. The problem we solve is to find conditions for the centre and theradius of the disc {z : |z − ω| < r}, contained in the unit disc {z : |z| < 1}and containing the origin, so that its transformation by the function F be adomain starlike with respect to the origin.<br/><br/>Description: ∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45Integer Points Close to a Smooth Curve
http://hdl.handle.net/10525/565
Title: Integer Points Close to a Smooth Curve<br/><br/>Authors: Trifonov, Ognian<br/><br/>Abstract: We review the existing estimates for the number of integer points close to a smooth curve and improve on some of these.<br/><br/>Description: ∗ This research is partially supported by the Bulgarian National Science Fund under contract MM-403/9La Classe Borélienne Ne Détermine Pas Le Type Topologique De Cp(x)
http://hdl.handle.net/10525/564
Title: La Classe Borélienne Ne Détermine Pas Le Type Topologique De Cp(x)<br/><br/>Authors: Cauty, Robert<br/><br/>Abstract: We prove that, for every countable ordinal α ≥ 3, there existscountable completely regular spaces Xα and Yα such that the spaces Cp (Xα )and Cp (Yα ) are borelian of class exactly Mα , but are not homeomorphic.Directions De Majoration D'une Fonction Quasiconvexe Et Applications
http://hdl.handle.net/10525/563
Title: Directions De Majoration D'une Fonction Quasiconvexe Et Applications<br/><br/>Authors: Amara, Charki<br/><br/>Abstract: We introduce the convex cone constituted by the directionsof majoration of a quasiconvex function. This cone is used to formulate aqualification condition ensuring the epiconvergence of a sequence of generalquasiconvex marginal functions in finite dimensional spaces.On Extension of Functors onto the Kleisli Category of the Inclusion Hyperspace Monad
http://hdl.handle.net/10525/562
Title: On Extension of Functors onto the Kleisli Category of the Inclusion Hyperspace Monad<br/><br/>Authors: Teleiko, Andrii<br/><br/>Abstract: It is proved that there exists no extension of any non-trivial weakly normal functor of finite degree onto the Kleisli category of the inclusion hyperspace monad.On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane
http://hdl.handle.net/10525/561
Title: On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane<br/><br/>Authors: Zagorodniuk, S.<br/><br/>Abstract: Systems of orthogonal polynomials on the real line play animportant role in the theory of special functions [1]. They find applications in numerous problems of mathematical physics and classical analysis.It is known, that classical polynomials have a number of properties, whichuniquely define them.<br/><br/>Description: ∗ Partially supported by Grant MM-428/94 of MESC.Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil
http://hdl.handle.net/10525/560
Title: Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil<br/><br/>Authors: Yordanov, Russi<br/><br/>Abstract: Dubrovin type equations for the N -gap solution of a completelyintegrable system associated with a polynomial pencil is constructed andthen integrated to a system of functional equations. The approach used toderive those results is a generalization of the familiar process of finding the1-soliton (1-gap) solution by integrating the ODE obtained from the solitonequation via the substitution u = u(x + λt).Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations
http://hdl.handle.net/10525/559
Title: Generalization of Ehrlich-Kjurkchiev Method for Multiple Roots of Algebraic Equations<br/><br/>Authors: Iliev, Anton<br/><br/>Abstract: In this paper a new method which is a generalization of theEhrlich-Kjurkchiev method is developed. The method allows to findsimultaneously all roots of the algebraic equation in the case when the roots aresupposed to be multiple with known multiplicities. The offered generalization does not demand calculation of derivatives of order higher than firstsimultaneously keeping quaternary rate of convergence which makes thismethod suitable for application from practical point of view.The Point of Continuity Property: Descriptive Complexity and Ordinal Index
http://hdl.handle.net/10525/558
Title: The Point of Continuity Property: Descriptive Complexity and Ordinal Index<br/><br/>Authors: Bossard, Benoit; López, Ginés<br/><br/>Abstract: Let X be a separable Banach space without the Point ofContinuity Property. When the set of closed subsets of its closed unit ballis equipped with the standard Effros-Borel structure, the set of those whichhave the Point of Continuity Property is non-Borel. We also prove that,for any separable Banach space X, the oscillation rank of the identity onX (an ordinal index which quantifies the Point of Continuity Property) isdetermined by the subspaces of X with a finite-dimensional decomposition.If X does not contain l1 , subspaces with basis suffice. If X ∗ is separable,one can even restrict to subspaces with shrinking basis.<br/><br/>Description: ∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142Fragmentability of the Dual of a Banach Space with Smooth Bump
http://hdl.handle.net/10525/557
Title: Fragmentability of the Dual of a Banach Space with Smooth Bump<br/><br/>Authors: Kortezov, I.<br/><br/>Abstract: We prove that if a Banach space X admits a Lipschitz β-smoothbump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating atopology, which is stronger than the τβ -topology. We also use this to provethat if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X issigma-fragmentable.New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10
http://hdl.handle.net/10525/556
Title: New Symmetric (61,16,4) Designs Invariant Under the Dihedral Group of Order 10<br/><br/>Authors: Landjev, Ivan; Topalova, Svetlana<br/><br/>Abstract: In this note we construct five new symmetric 2-(61,16,4) designs invariant under the dihedral group of order 10. As a by-product weobtain 25 new residual 2-(45,12,4) designs. The automorphism groups of allnew designs are computed.<br/><br/>Description: ∗ This work has been partially supported by the Bulgarian NSF under Contract No. I-506/1995.Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces
http://hdl.handle.net/10525/555
Title: Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces<br/><br/>Authors: Chowdhury, Mohammad<br/><br/>Abstract: Existence theorems of generalized variational inequalities andgeneralized complementarity problems are obtained in topological vectorspaces for demi operators which are upper hemicontinuous along line segments in a convex set X. Fixed point theorems are also given in Hilbertspaces for set-valued operators T which are upper hemicontinuous alongline segments in X such that I − T are demi operators.<br/><br/>Description: ∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses
http://hdl.handle.net/10525/554
Title: Continuous Dependence of Solutions of Quasidifferential Equations with Non-Fixed Time of Impulses<br/><br/>Authors: Plotnikov, V.; Kitanov, P.<br/><br/>Abstract: In this article on quasidifferential equation with non-fixed timeof impulses we consider the continuous dependence of the solutions on theinitial conditions as well as the mappings defined by these equations. Weprove general theorems for quasidifferential equations from which followscorresponding results for differential equations, differential inclusion andequations with Hukuhara derivative.Three Spaces Problem for Lyapunov Theorem on Vector Measure
http://hdl.handle.net/10525/553
Title: Three Spaces Problem for Lyapunov Theorem on Vector Measure<br/><br/>Authors: Kadets, V.; Vladimirskaya, O.<br/><br/>Abstract: It is proved that a Banach space X has the Lyapunov property if its subspace Y and the quotient space X/Y have it.Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations
http://hdl.handle.net/10525/552
Title: Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations<br/><br/>Authors: Stamov, Gani<br/><br/>Abstract: Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.Pseudoradial Spaces: Finite Products and an Example From CH
http://hdl.handle.net/10525/551
Title: Pseudoradial Spaces: Finite Products and an Example From CH<br/><br/>Authors: Simon, Petr; Tironi, Gino<br/><br/>Abstract: Aiming to solve some open problems concerning pseudoradialspaces, we shall present the following: Assuming CH, there are two semiradial spaces without semi-radial product. A new property of pseudoradialspaces insuring the pseudoradiality of a product is presented.<br/><br/>Description: ∗ The first named author’s research was partially supported by GAUK grant no. 350,partially by the Italian CNR. Both supports are gratefully acknowledged. The second authorwas supported by funds of Italian Ministery of University and by funds of the University ofTrieste (40% and 60%).