DSpace Collection: Volume 34, Number 3
http://hdl.handle.net/10525/2577
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On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density
http://hdl.handle.net/10525/2621
Title: On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density<br/><br/>Authors: Djeddour, Khédidja; Mokkadem, Abdelkader; Pelletier, Mariane<br/><br/>Abstract: Tsybakov [31] introduced the method of stochastic approximation to construct a recursive estimator of the location q of the mode of a probability density. The aim of this paper is to provide a companion algorithm to Tsybakov's algorithm, which allows to simultaneously recursively approximate the size m of the mode. We provide a precise study of the joint weak convergence rate of both estimators. Moreover, we introduce the averaging principle of stochastic approximation algorithms to construct asymptotically efficient algorithms approximating the couple (q,m).<br/><br/>Description: 2000 Mathematics Subject Classification: 62G07, 62L20.Ostrowski Type Inequalities over Spherical Shells
http://hdl.handle.net/10525/2620
Title: Ostrowski Type Inequalities over Spherical Shells<br/><br/>Authors: Anastassiou, George A.<br/><br/>Abstract: Here are presented Ostrowski type inequalities over spherical shells. These regard sharp or close to sharp estimates to the difference of the average of a multivariate function from its value at a point.<br/><br/>Description: 2000 Mathematics Subject Classification: 26D10, 26D15.Convexity around the Unit of a Banach Algebra
http://hdl.handle.net/10525/2619
Title: Convexity around the Unit of a Banach Algebra<br/><br/>Authors: Kadets, Vladimir; Katkova, Olga; Martín, Miguel; Vishnyakova, Anna<br/><br/>Abstract: We estimate the (midpoint) modulus of convexity at the unit 1 of a Banach algebra Ashowing that inf {max±||1 ± x|| − 1 : x ∈ A, ||x||=ε} ≥ (π/4e)ε²+o(ε²) as ε → 0. We also give a characterization of two-dimensional subspaces of Banach algebras containing the identity in terms of polynomial inequalities.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary: 46B20. Secondary: 46H99, 47A12.First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints
http://hdl.handle.net/10525/2618
Title: First-Order Conditions for Optimization Problems with Quasiconvex Inequality Constraints<br/><br/>Authors: Ginchev, Ivan; Ivanov, Vsevolod I.<br/><br/>Abstract: The constrained optimization problem min f(x), gj(x) ≤ 0 (j = 1,…p) is considered, where f : X → R and gj : X → R are nonsmooth functions with domain X ⊂ Rn. First-order necessary and first-order sufficient optimality conditions are obtained when gj are quasiconvex functions. Two are the main features of the paper: to treat nonsmooth problems it makes use of Dini derivatives; to obtain more sensitive conditions, it admits directionally dependent multipliers. The two cases, where the Lagrange function satisfies a non-strict and a strict inequality, are considered. In the case of a non-strict inequality pseudoconvex functions are involved and in their terms some properties of the convex programming problems are generalized. The efficiency of the obtained conditions is illustrated on examples.<br/><br/>Description: 2000 Mathematics Subject Classification: 90C46, 90C26, 26B25, 49J52.Warped Product Semi-Slant Submanifolds of a Sasakian Manifold
http://hdl.handle.net/10525/2615
Title: Warped Product Semi-Slant Submanifolds of a Sasakian Manifold<br/><br/>Authors: Al-Solamy, Falleh R.; Khan, Viqar Azam<br/><br/>Abstract: In the present note, it is proved that there donot exist warped product semi-slant submanifolds in a Sasakian manifold other than contact CR-warped product submanifolds and thus the results obtained in [8] are generalized.<br/><br/>Description: 2000 Mathematics Subject Classification: 53C40, 53C25.Predegree Polynomials of Plane Configurations in Projective Space
http://hdl.handle.net/10525/2612
Title: Predegree Polynomials of Plane Configurations in Projective Space<br/><br/>Authors: Tzigantchev, Dimitre<br/><br/>Abstract: We work over an algebraically closed field of characteristic zero. The group PGL(4) acts naturally on PN which parameterizes surfaces of a given degree in P3. The orbit of a surface under this action is the image of a rational map PGL(4) ⊂ P15→PN. The closure of the orbit is a natural and interesting object to study. Its predegree is defined as the degree of the orbit closure multiplied by the degree of the above map restricted to a general Pj, j being the dimension of the orbit. We find the predegrees and other invariants for all surfaces supported on unions of planes. The information is encoded in the so-called predegree polynomials , which possess nice multiplicative properties allowing us to compute the predegree (polynomials) of various special plane configurations. The predegree has both combinatorial and geometric significance. The results obtained in this paper would be a necessary step in the solution of the problem of computing predegrees for all surfaces.<br/><br/>Description: 2000 Mathematics Subject Classification: 14N10, 14C17.Generalized D-Symmetric Operators I
http://hdl.handle.net/10525/2608
Title: Generalized D-Symmetric Operators I<br/><br/>Authors: Bouali, S.; Ech-chad, M.<br/><br/>Abstract: Let H be an infinite-dimensional complex Hilbert space and let A, B ∈ L(H), where L(H) is the algebra of operators on H into itself. Let δAB: L(H) → L(H) denote the generalized derivation δAB(X) = AX − XB. This note will initiate a study on the class of pairs (A,B) such that [‾(R(δAB))] = [‾(R(δB*A*))]; i.e. [‾(R(δAB))] is self-adjoint.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary: 47B47, 47B10; secondary 47A30.Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions
http://hdl.handle.net/10525/2605
Title: Taylor Spectrum and Characteristic Functions of Commuting 2-Contractions<br/><br/>Authors: Bendoukha, Berrabah<br/><br/>Abstract: In this paper, we give a description of Taylor spectrum of commuting 2-contractions in terms of characteritic functions of such contractions. The case of a single contraction obtained by B. Sz. Nagy and C. Foias is generalied in this work.<br/><br/>Description: 2000 Mathematics Subject Classification: 47A10, 47A13.Oscillation of Nonlinear Neutral Delay Differential Equations
http://hdl.handle.net/10525/2604
Title: Oscillation of Nonlinear Neutral Delay Differential Equations<br/><br/>Authors: Elabbasy, E. M.; Hassan, T. S.<br/><br/>Abstract: In this paper, we study the oscillatory behavior of first order nonlinear neutral delay differential equation(x(t) − q(t) x(t − σ(t))) ′ +f(t,x( t − τ(t))) = 0,where σ, τ ∈ C([t0,∞),(0,∞)), q О C([t0,∞), [0,∞)) and f ∈ C([t0,∞) ×R,R). The obtained results extended and improve several of the well known previously results in the literature. Our results are illustrated with an example.<br/><br/>Description: 2000 Mathematics Subject Classification: 34K15, 34C10.