DSpace Collection: Volume 23 Number 3-4
http://hdl.handle.net/10525/521
Serdica Mathematical Journal Volume 23, Number 3-4, 1997The Collection's search engineSearch the Channelsearch
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Coincidence of Vietoris and Wijsman Topologies: A New Proof
http://hdl.handle.net/10525/593
Title: Coincidence of Vietoris and Wijsman Topologies: A New Proof<br/><br/>Authors: Holá, L’.<br/><br/>Abstract: Let (X, d) be a metric space and CL(X) the family of allnonempty closed subsets of X. We provide a new proof of the fact that thecoincidence of the Vietoris and Wijsman topologies induced by the metricd forces X to be a compact space. In the literature only a more involvedand indirect proof using the proximal topology is known. Here we do notneed this intermediate step. Moreover we prove that (X, d) is boundedlycompact if and only if the bounded Vietoris and Wijsman topologies onCL(X) coincide.Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms
http://hdl.handle.net/10525/592
Title: Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms<br/><br/>Authors: Fabian, Marián; Hájek, Petr; Zizler, Václav<br/><br/>Abstract: It is shown that the dual unit ball BX∗ of a Banach space X∗in its weak star topology is a uniform Eberlein compact if and only if Xadmits a uniformly Gâteaux smooth norm and X is a subspace of a weaklycompactly generated space. The bidual unit ball BX∗∗ of a Banach spaceX∗∗ in its weak star topology is a uniform Eberlein compact if and only ifX admits a weakly uniformly rotund norm. In this case X admits a locallyuniformly rotund and Fréchet differentiable norm. An Eberlein compactK is a uniform Eberlein compact if and only if C(K) admits a uniformlyGˆateaux differentiable norm.<br/><br/>Description: * Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada).Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps
http://hdl.handle.net/10525/591
Title: Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps<br/><br/>Authors: Plichko, Anatolij<br/><br/>Abstract: The main results of the paper are:Theorem 1. Let a Banach space E be decomposed into a direct sum ofseparable and reflexive subspaces. Then for every Hausdorff locally convextopological vector space Z and for every linear continuous bijective operatorT : E → Z, the inverse T^(−1) is a Borel map.Theorem 2. Let us assume the continuum hypothesis. If a Banach space Ecannot be decomposed into a direct sum of separable and reflexive subspaces,then there exists a normed space Z and a linear continuous bijective operatorT : E → Z such that T^(−1) is not a Borel map.<br/><br/>Description: * This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions
http://hdl.handle.net/10525/590
Title: Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions<br/><br/>Authors: Kirchev, K.; Borisova, G.<br/><br/>Abstract: In this paper we present some generalizations of results of M.S. Livšic [4,6], concerning regular colligations (A1, A2, H, Φ, E, σ1, σ2, γ, ˜γ)(σ1 > 0) of a pair of commuting nonselfadjoint operators A1, A2 with ﬁnitedimensional imaginary parts, their complete characteristic functions and aclass Ω(σ1, σ2) of operator-functions W(x1, x2, z): E → E in the case ofan inner function W(1, 0, z) of the class Ω(σ1). ...<br/><br/>Description: * Partially supported by Grant MM-428/94 of MESC.On the Structure of Spatial Branching Processes
http://hdl.handle.net/10525/589
Title: On the Structure of Spatial Branching Processes<br/><br/>Authors: Matthes, Klaus; Nawrotzki, Kurt; Siegmund-Schultze, Rainer<br/><br/>Abstract: The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. Wecharacterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments.This enables us to classify the clans of (Φk) into the regular part and thecompletely non-regular part. It turns out that the completely non-regularbranching processes are built up from single-line processes, whereas the regular ones are mixtures of left-tail trivial processes with a Poisson familystructure.On Typical Compact Convex Sets in Hilbert Spaces
http://hdl.handle.net/10525/588
Title: On Typical Compact Convex Sets in Hilbert Spaces<br/><br/>Authors: De Blasi, F.<br/><br/>Abstract: Let E be an infinite dimensional separable space and for e ∈ Eand X a nonempty compact convex subset of E, let qX(e) be the metricantiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shownthat for a typical (in the sence of the Baire category) compact convex setX ⊂ E the metric antiprojection qX(e) has cardinality at least n for everye in a dense subset of E.Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations
http://hdl.handle.net/10525/587
Title: Oscillation Theorems for Second Order Sublinear Ordinary Differential Equations<br/><br/>Authors: Elabbasy, E.<br/><br/>Abstract: Oscillation criteria are given for the second order sublinearnon-autonomous differential equation.(r(t) (x)x′(t))′ + q(t)g(x(t)) = (t).These criteria extends and improves earlier oscillation criteria of Kamenev,Kura, Philos and Wong. Oscillation criteria are also given for second ordersublinear damped non-autonomous differential equations.Functionally Countable Spaces and Baire Functions
http://hdl.handle.net/10525/586
Title: Functionally Countable Spaces and Baire Functions<br/><br/>Authors: Choban, M.<br/><br/>Abstract: The concept of the distinguished sets is applied to the investigationof the functionally countable spaces. It is proved that every Bairefunction on a functionally countable space has a countable image. This is apositive answer to a question of R. Levy and W. D. Rice.Involutivity and Symple Waves in R^2
http://hdl.handle.net/10525/585
Title: Involutivity and Symple Waves in R^2<br/><br/>Authors: Kolev, Dimitar<br/><br/>Abstract: A strictly hyperbolic quasi-linear 2×2 system in two independentvariables with C2 coefficients is considered. The existence of a simplewave solution in the sense that the solution is a 2-dimensional vector-valuedfunction of the so called Riemann invariant is discussed. It is shown, througha purely geometrical approach, that there always exists simple wave solutionfor the general system when the coefficients are arbitrary C^2 functionsdepending on both, dependent and independent variables.Isomorphism of Commutative Modular Group Algebras
http://hdl.handle.net/10525/584
Title: Isomorphism of Commutative Modular Group Algebras<br/><br/>Authors: Danchev, P.<br/><br/>Abstract: Let K be a field of characteristic p > 0 and let G be a directsum of cyclic groups, such that its torsion part is a p-group. If there existsa K-isomorphism KH ∼= KG for some group H, then it is shown thatH ∼= G.Let G be a direct sum of cyclic groups, a divisible group or a simplypresented torsion abelian group. Then KH ∼= KG as K-algebras for allfields K and some group H if and only if H ∼= G.<br/><br/>Description: ∗ The work was supported by the National Fund “Scientific researches” and by the Ministryof Education and Science in Bulgaria under contract MM 70/91.Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function
http://hdl.handle.net/10525/583
Title: Existence and Uniqueness of Solutions for Partial Differential-Functional Equations of the First Order with Deviating Argument of the Derivative of Unknown Function<br/><br/>Authors: Augustynowicz, A.<br/><br/>Abstract: We consider the existence and uniqueness problem for partialdifferential-functional equations of the first order with the initial conditionfor which the right-hand side depends on the derivative of unknown functionwith deviating argument.The Fiftieth Anniversary of the Institute of Mathematics and Informatics
http://hdl.handle.net/10525/582
Title: The Fiftieth Anniversary of the Institute of Mathematics and Informatics<br/><br/>Authors: Yanev, N.<br/><br/>Abstract: In October 1997 we celebrate the fiftieth anniversary of the founding ofthe Institute for Mathematics and Informatics (IMI) of the Bulgarian Academyof Sciences (BAS).