DSpace Collection: Volume 34, Number 2 http://hdl.handle.net/10525/2576 Serdica Mathematical Journal Volume 34, Number 2, 2008 The Collection's search engine Search the Channel search http://sci-gems.math.bas.bg/jspui/simple-search Test for Independence of the Variables with Missing Elements in One and the Same Column of the Empirical Correlation Matrix http://hdl.handle.net/10525/2603 Title: Test for Independence of the Variables with Missing Elements in One and the Same Column of the Empirical Correlation Matrix<br/><br/>Authors: Veleva, Evelina<br/><br/>Abstract: We consider variables with joint multivariate normal distribution and suppose that the sample correlation matrix has missing elements, located in one and the same column. Under these assumptions we derive the maximum likelihood ratio test for independence of the variables. We obtain also the maximum likelihood estimations for the missing values.<br/><br/>Description: 2000 Mathematics Subject Classification: 62H15, 62H12. Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier http://hdl.handle.net/10525/2602 Title: Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier<br/><br/>Authors: Gourdin, D.; Kamoun, H.; Ben Khalifa, O.<br/><br/>Abstract: We give here examples of equations of type (1) ∂tt2 y -p(t, Dx) y = 0, where p is a singular pseudo-differential operator with regular global solutions when the Cauchy data are regular, t ∈ R, x ∈ R5.<br/><br/>Description: 2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99. Limit Theorems for Non-Critical Branching Processes with Continuous State Space http://hdl.handle.net/10525/2601 Title: Limit Theorems for Non-Critical Branching Processes with Continuous State Space<br/><br/>Authors: Kurbanov, S.<br/><br/>Abstract: In the paper a modification of the branching stochastic process with immigration and with continuous states introduced by Adke S. R. and Gadag V. G. (1995) is considered. Limit theorems for the non-critical processes with or without non-stationary immigration and finite variance are proved. The subcritical case is illustrated with examples.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99. Zeros of Sequences of Partial Sums and Overconvergence http://hdl.handle.net/10525/2600 Title: Zeros of Sequences of Partial Sums and Overconvergence<br/><br/>Authors: Kovacheva, Ralitza K.<br/><br/>Abstract: We are concerned with overconvergent power series. The main idea is to relate the distribution of the zeros of subsequences of partial sums and the phenomenon of overconvergence. Sufficient conditions for a power series to be overconvergent in terms of the distribution of the zeros of a subsequence are provided, and results of Jentzsch-Szegö type about the asymptotic distribution of the zeros of overconvergent subsequences are stated.<br/><br/>Description: 2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15. Steffensen Methods for Solving Generalized Equations http://hdl.handle.net/10525/2599 Title: Steffensen Methods for Solving Generalized Equations<br/><br/>Authors: Argyros, Ioannis K.; Hilout, Saïd<br/><br/>Abstract: We provide a local convergence analysis for Steffensen's method in order to solve a generalized equation in a Banach space setting. Using well known fixed point theorems for set-valued maps  and Hölder type conditions introduced by us in  for nonlinear equations, we obtain the superlinear local convergence of Steffensen's method. Our results compare favorably with related ones obtained in .<br/><br/>Description: 2000 Mathematics Subject Classification: 65G99, 65K10, 47H04. An Iterative Procedure for Solving Nonsmooth Generalized Equation http://hdl.handle.net/10525/2598 Title: An Iterative Procedure for Solving Nonsmooth Generalized Equation<br/><br/>Authors: Marinov, Rumen Tsanev<br/><br/>Abstract: In this article, we study a general iterative procedure of the following form 0 ∈ f(xk)+F(xk+1), where f is a function and F is a set valued map acting from a Banach space X to a linear normed space Y, for solving generalized equations in the nonsmooth framework. We prove that this method is locally Q-linearly convergent to x* a solution of the generalized equation 0 ∈ f(x)+F(x) if the set-valued map [f(x*)+g(·)−g(x*)+F(·)]−1 is Aubin continuous at (0,x*), where g:X→ Y is a function, whose Fréchet derivative is L-Lipschitz.<br/><br/>Description: 2000 Mathematics Subject Classification: 47H04, 65K10. q-Leibniz Algebras http://hdl.handle.net/10525/2597 Title: q-Leibniz Algebras<br/><br/>Authors: Dzhumadil'daev, A. S.<br/><br/>Abstract: An algebra (A,ο) is called Leibniz if aο(bοc) = (a ο b)ο c-(a ο c) ο b for all a,b,c ∈ A. We study identities for the algebras A(q) = (A,οq), where a οq b = a ο b+q b ο a is the q-commutator. Let Char K ≠ 2,3. We show that the class of q-Leibniz algebras is defined by one identity of degree 3 if q2 ≠ 1, q ≠−2, by two identities of degree 3 if q = −2, and by the commutativity identity and one identity of degree 4 if q = 1. In the case of q = −1 we construct two identities of degree 5 that form a base of identities of degree 5 for −1-Leibniz algebras. Any identity of degree < 5 for −1-Leibniz algebras follows from the anti-commutativity identity.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 17A32, Secondary 17D25. Oscillation Criteria for Nonlinear Differential Equations of Second Order with Damping Term http://hdl.handle.net/10525/2596 Title: Oscillation Criteria for Nonlinear Differential Equations of Second Order with Damping Term<br/><br/>Authors: Elabbasy, E. M.; Elhaddad, W. W.<br/><br/>Abstract: Some new criteria for the oscillation of all solutions of second order differential equations of the form(d/dt)(r(t)ψ(x)|dx/dt|α−2(dx/dt))+ p(t)φ(|x|α−2x,r(t) ψ(x)|dx/dt|α−2(dx/dt))+q(t)|x|α−2 x=0,and the more general equation (d/dt)(r(t)ψ(x)|dx/dt|α−2(dx/dt))+p(t)φ(g(x),r(t) ψ(x)|dx/dt|α−2 (dx/dt))+q(t)g(x)=0,are established. our results generalize and extend some known oscillation criterain in the literature.<br/><br/>Description: 2000 Mathematics Subject Classification: 34C10, 34C15. Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines http://hdl.handle.net/10525/2595 Title: Régularité Lipschitzienne des Géodésiques Minimisantes pour Quelques Distributions Affines<br/><br/>Authors: Bensalem, Naceurdine<br/><br/>Abstract: In the context of sub-Riemannian geometry and the Lipschitzian regularity of minimizers in control theory, we investigate some properties of minimizing geodesics for certain affine distributions. In particular, we consider the case of a generalized H2-strong affine distribution and the case of an affine Plaff system of maximal class.<br/><br/>Description: 2000 Mathematics Subject Classification: 49J15, 49J30, 53B50. A Unified Group-Theoretic Method on Improper Partial Semi-Bilateral Generating Functions http://hdl.handle.net/10525/2594 Title: A Unified Group-Theoretic Method on Improper Partial Semi-Bilateral Generating Functions<br/><br/>Authors: Sarkar, Asit Kumar<br/><br/>Abstract: A unifed group-theoretic method of obtaining more general class of generating functions from a given class of improper partial semi-bilateral generating functions involving Laguerre and Gegenbauer polynomials are discussed.<br/><br/>Description: 2000 Mathematics Subject Classification: 33A65, 33C20.