DSpace Community: 2009
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Fractional Korovkin Theory Based on Statistical Convergence
http://hdl.handle.net/10525/2677
Title: Fractional Korovkin Theory Based on Statistical Convergence<br/><br/>Authors: Anastassiou, George A.; Duman, Oktay<br/><br/>Abstract: In this paper, we obtain some statistical Korovkin-type approximation theorems including fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.<br/><br/>Description: 2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.Thu, 01 Jan 2009 00:00:00 GMTEstimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast
http://hdl.handle.net/10525/2676
Title: Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast<br/><br/>Authors: Dia, Galaye; Kone, Abdoulaye<br/><br/>Abstract: We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the nth arrival, the regression curve of R on S predicts ruin arrival time when the premium intensity c is less than rm whatever be the initial reverve.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.Thu, 01 Jan 2009 00:00:00 GMTPotapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators
http://hdl.handle.net/10525/2675
Title: Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators<br/><br/>Authors: Zolotarev, Vladimir A.; Hatamleh, Raéd<br/><br/>Abstract: A relation between an arbitrary bounded operator A and dissipative operator A+, built by A in the following way A+ = A+ij*Q-j, where A-A* = ij*Jj, (J = Q+-Q- is involution), is studied. The characteristic functions of the operators A and A+ are expressed by each other using the known Potapov-Ginsburg linear-fractional transformations. The explicit form of the resolvent (A-lI)-1 is expressed by (A+-lI)-1 and (A+*-lI)-1 in terms of these transformations. Furthermore, the functional model [10, 12] of non-dissipative operator A in terms of a model for A+, which evolves the results, was obtained by Naboko, S. N. [7]. The main constructive elements of the present construction are shown to be the elements of the Potapov-Ginsburg transformation for corresponding characteristic functions. A relation between an arbitrary bounded operator A and dissipative operator A+, built by A in the following way A+ = A + iϕ<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.Thu, 01 Jan 2009 00:00:00 GMTProbabilistic Approach to the Neumann Problem for a Symmetric Operator
http://hdl.handle.net/10525/2673
Title: Probabilistic Approach to the Neumann Problem for a Symmetric Operator<br/><br/>Authors: Benchérif-Madani, Abdelatif<br/><br/>Abstract: We give a probabilistic formula for the solution of a non-homogeneous Neumann problem for a symmetric nondegenerate operator of second order in a bounded domain. We begin with a g-Hölder matrix and a C^1,g domain, g > 0, and then consider extensions. The solutions are expressed as a double layer potential instead of a single layer potential; in particular a new boundary function is discovered and boundary random walk methods can be used for simulations. We use tools from harmonic analysis and probability theory.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.Thu, 01 Jan 2009 00:00:00 GMTA Note About the Nowicki Conjecture on Weitzenböck Derivations
http://hdl.handle.net/10525/2670
Title: A Note About the Nowicki Conjecture on Weitzenböck Derivations<br/><br/>Authors: Bedratyuk, Leonid<br/><br/>Abstract: We reduce the Nowicki conjecture on Weitzenböck derivations of polynomial algebras to a well known problem of classical invariant theory.<br/><br/>Description: 2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.Thu, 01 Jan 2009 00:00:00 GMTCompound Compound Poisson Risk Model
http://hdl.handle.net/10525/2668
Title: Compound Compound Poisson Risk Model<br/><br/>Authors: Minkova, Leda D.<br/><br/>Abstract: The compound Poisson risk models are widely used in practice. In this paper the counting process in the insurance risk model is a compound Poisson process. The model is called Compound Compound Poisson Risk Model. Some basic properties and ruin probability are given. We analyze the model under the proportional reinsurance. The optimal retention level and the corresponding adjustment coefficient are obtained. The particular case of the Pólya-Aeppli risk model is discussed.<br/><br/>Description: 2000 Mathematics Subject Classification: 60K10, 62P05.Thu, 01 Jan 2009 00:00:00 GMTClass Number Two for Real Quadratic Fields of Richaud-Degert Type
http://hdl.handle.net/10525/2666
Title: Class Number Two for Real Quadratic Fields of Richaud-Degert Type<br/><br/>Authors: Mollin, R. A.<br/><br/>Abstract: This paper contains proofs of conjectures made in [16] on class number 2 and what this author has dubbed the Euler-Rabinowitsch polynomial for real quadratic fields. As well, we complete the list of Richaud-Degert types given in [16] and show how the behaviour of the Euler-Rabinowitsch polynomials and certain continued fraction expansions come into play in the complete determination of the class number 2 problem for such types. For some values the determination is unconditional, and for others, the wide Richaud-Degert types, the determination is conditional on the generalized Riemann hypothesis (GRH).<br/><br/>Description: 2000 Mathematics Subject Classification: Primary: 11D09, 11A55, 11C08, 11R11, 11R29; Secondary: 11R65, 11S40; 11R09.Thu, 01 Jan 2009 00:00:00 GMTGeometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold
http://hdl.handle.net/10525/2664
Title: Geometry of Warped Product Semi-Invariant Submanifolds of a Locally Riemannian Product Manifold<br/><br/>Authors: Atçeken, Mehmet<br/><br/>Abstract: In this article, we have studied warped product semi-invariant submanifolds in a locally Riemannian product manifold and introduced the notions of a warped product semi-invariant submanifold. We have also proved several fundamental properties of a warped product semi-invariant in a locally Riemannian product manifold.<br/><br/>Description: 2000 Mathematics Subject Classification: 53C42, 53C15.Thu, 01 Jan 2009 00:00:00 GMTOn the Vertex Folkman Numbers Fv(2,...,2;q)
http://hdl.handle.net/10525/2662
Title: On the Vertex Folkman Numbers Fv(2,...,2;q)<br/><br/>Authors: Nenov, Nedyalko<br/><br/>Abstract: In this paper we shall compute the Folkman numbers ... We provealso new bounds for some vertex and edge Folkman numbers.<br/><br/>Description: 2000 Mathematics Subject Classification: 05C55.Thu, 01 Jan 2009 00:00:00 GMTIndice de Point Fixe pour les Morphismes de Chaînes
http://hdl.handle.net/10525/2659
Title: Indice de Point Fixe pour les Morphismes de Chaînes<br/><br/>Authors: Cauty, Robert<br/><br/>Abstract: The aim of this paper is to define a fixed point index for compact maps in the class of algebraic ANRs. This class, which we introduced in [2], contains all open subsets of convex subsets of metrizable topological vector spaces. In this class, it is convenient to study the fixed points of compact maps with the help of the chain morphisms that they induce on the singular chains. For this reason, we first define a fixed point index for a certain class of chain morphisms, and then define the fixed point index of compact maps as the fixed point index of the induced chain morphism. This fixed point index has all the usual properties of an index, including the mod p-theorem. The results of this paper are thus, in the metrizable case, a vast generalization of the Schauder conjecture.<br/><br/>Description: 2000 Mathematics Subject Classification: 54H25, 55M20.Thu, 01 Jan 2009 00:00:00 GMTMultipliers on a Hilbert Space of Functions on R
http://hdl.handle.net/10525/2657
Title: Multipliers on a Hilbert Space of Functions on R<br/><br/>Authors: Petkova, Violeta<br/><br/>Abstract: For a Hilbert space H ⊂ L1loc(R) of functions on R we obtaina representation theorem for the multipliers M commuting with the shiftoperator S. This generalizes the classical result for multipliers in L2(R) aswell as our previous result for multipliers in weighted space L2ω(R). Moreover,we obtain a description of the spectrum of S.<br/><br/>Description: 2000 Mathematics Subject Classification: 42A45.Thu, 01 Jan 2009 00:00:00 GMTCourbure et Polygone de Newton
http://hdl.handle.net/10525/2656
Title: Courbure et Polygone de Newton<br/><br/>Authors: Hannachi M, M.; Mezaghcha, K.<br/><br/>Abstract: The object of this article relates to the study of the complex algebraic curves by using the concept of envelope convex. One proposes to characterize the points of a holomorphic complex curve (C) and to associate a metric invariant to them ( generalized curvature), by using the equations of the various segments constituting the polygon of Newton associated with (C).<br/><br/>Description: 2000 Mathematics Subject Classification: 26E35, 14H05, 14H20.Thu, 01 Jan 2009 00:00:00 GMTRelationship between Extremal and Sum Processes Generated by the same Point Process
http://hdl.handle.net/10525/2655
Title: Relationship between Extremal and Sum Processes Generated by the same Point Process<br/><br/>Authors: Pancheva, E.; Mitov, I.; Volkovich, Z.<br/><br/>Abstract: We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^das well as for the associated with it sum and extremal processes on an open subset S . The complementof S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and studysum processes over explosion area. Finally we generalize the model of u.n.t.a. to random sample size processes.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.Thu, 01 Jan 2009 00:00:00 GMTDensity of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space
http://hdl.handle.net/10525/2652
Title: Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space<br/><br/>Authors: Klotz, Lutz; Zagorodnyuk, Sergey M.<br/><br/>Abstract: In this paper we consider an L^2 type space of scalar functions L^2 M, A (R u iR) which can be, in particular, the usual L^2 space of scalar functions on R u iR. We find conditions for density of polynomials in this space using a connection with the L^2 space of square-integrable matrix-valued functions on R with respect to a non-negative Hermitian matrix measure. The completness of L^2 M, A (R u iR ) is also established.<br/><br/>Description: 2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.Thu, 01 Jan 2009 00:00:00 GMTBayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size
http://hdl.handle.net/10525/2651
Title: Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size<br/><br/>Authors: Ellah, A. H. Abd<br/><br/>Abstract: We consider the problem of predictive interval for future observations from Weibull distribution. We consider two cases they are: (i) fixed sample size (FSS), (ii) random sample size (RSS). Further, we derive the predictive function for both FSS and RSS in closed forms. Next, the upper and lower 1%, 2.5%, 5% and 10% critical points for the predictive functions are calculated. To show the usefulness of our results, we present some simulation examples. Finally, we apply our results to some real data set in life testing given in Lawless [16].<br/><br/>Description: 2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.Thu, 01 Jan 2009 00:00:00 GMTOn Quasi-Normality of Two-Sided Multiplication
http://hdl.handle.net/10525/2648
Title: On Quasi-Normality of Two-Sided Multiplication<br/><br/>Authors: Amouch, M.<br/><br/>Abstract: In this note, we characterize quasi-normality of two-sided multiplication, restricted to a norm ideal and we extend this result, to an important class which contains all quasi-normal operators. Also we give some applications of this result.<br/><br/>Description: 2000 Mathematics Subject Classification: 47B47, 47B10, 47A30.Thu, 01 Jan 2009 00:00:00 GMT