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Article Citation - WoS: 29Citation - Scopus: 30Boundary Value Problems for Second Order Nonlinear Differential Equations on Infinite Intervals(Academic Press inc Elsevier Science, 2004) Guseinov, GS; Yaslan, IIn this paper, we consider boundary value problems for nonlinear differential equations on the semi-axis (0, infinity) and also on the whole axis (-infinity, infinity), under the assumption that the left-hand side being a second order linear differential expression belongs to the Weyl limit-circle case. The boundary value problems are considered in the Hilbert spaces L-2(0, infinity) and L-2(-infinity, infinity), and include boundary conditions at infinity. The existence and uniqueness results for solutions of the considered boundary value problems are established. (C) 2003 Elsevier Inc. All rights reserved.Article Citation - WoS: 36Citation - Scopus: 40On the Improvement of Analytic Properties Under the Limit Q-Bernstein Operator(Academic Press inc Elsevier Science, 2006) Ostrovska, SLet B-n(f, q; x), n = 1, 2,... be the q-Bernstein polynomials of a function f is an element of C[0, 1]. In the case 0 < q < 1, a sequence {B-n(f, q; x)} generates a positive linear operator B-infinity = B-infinity,B-q on C[0, 1], which is called the limit q-Bernstein operator In this paper, a connection between the smoothness of a function f and the analytic properties of its image under Boo is studied. (c) 2005 Elsevier Inc. All rights reserved.Article Citation - WoS: 49Citation - Scopus: 54Elimination of Overflow Oscillations in Digital Filters Employing Saturation Arithmetic(Academic Press inc Elsevier Science, 2005) Kar, H; Singh, VA criterion for the nonexistence of overflow oscillations in a class of digital filters employing saturation arithmetic is presented. The criterion is based on a novel characterization of the saturation nonlinearity (namely, the 'reduced sector' characterization) and, hence, is quite distinct from previously reported criteria. (c) 2005 Elsevier Inc. All rights reserved.Article Citation - WoS: 43Citation - Scopus: 43Stability Criteria for Linear Periodic Impulsive Hamiltonian Systems(Academic Press inc Elsevier Science, 2007) Guseinov, G. Sh.; Zafer, A.In this paper we obtain stability criteria for linear periodic impulsive Hamiltonian systems. A Lyapunov type inequality is established. Our results improve also the ones previously obtained for systems without impulse effect. (c) 2007 Elsevier Inc. All rights reserved.Article Citation - WoS: 170Citation - Scopus: 188q-bernstein Polynomials and Their Iterates(Academic Press inc Elsevier Science, 2003) Ostrovska, SLet B-n (f,q;x), n = 1,2,... be q-Bernstein polynomials of a function f: [0, 1] --> C. The polynomials B-n(f, 1; x) are classical Bernstein polynomials. For q not equal 1 the properties of q-Bernstein polynomials differ essentially from those in the classical case. This paper deals with approximating properties of q-Bernstein polynomials in the case q>1 with respect to both n and q. Some estimates on the rate of convergence are given. In particular, it is proved that for a function f analytic in {z: \z\ < q + ε} the rate of convergence of {B-n(f, q; x)} to f (x) in the norm of C[0, 1] has the order q(-n) (versus 1/n for the classical Bernstein polynomials). Also iterates of q-Bernstein polynomials {B-n(jn) (f, q; x)}, where both n --> infinity and j(n) --> infinity, are studied. It is shown that for q is an element of (0, 1) the asymptotic behavior of such iterates is quite different from the classical case. In particular, the limit does not depend on the rate of j(n) --> infinity. (C) 2003 Elsevier Science (USA). All rights reserved.Article Citation - WoS: 5Citation - Scopus: 5The Euler-Lagrange Theory for Schur's Algorithm: Algebraic Exposed Points(Academic Press inc Elsevier Science, 2006) Khrushchev, SIn this paper the ideas of Algebraic Number Theory are applied to the Theory of Orthogonal polynomials for algebraic measures. The transferring tool are Wall continued fractions. It is shown that any set of closed arcs on the circle supports a quadratic measure and that any algebraic measure is either a Szego measure or a measure supported by a proper subset of the unit circle consisting of a finite number of closed arcs. Singular parts of algebraic measures are finite sums of point masses. (C) 2005 Elsevier Inc. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 3The Euler-Lagrange Theory for Schur's Algorithm: Wall Pairs(Academic Press inc Elsevier Science, 2006) Khrushchev, SThis paper develops a techniques of Wall pairs for the study of periodic exposed quadratic irrationalities in the unit ball of the Hardy algebra. (C) 2005 Elsevier Inc. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 2Turan measures(Academic Press inc Elsevier Science, 2003) Khrushchev, SA probability measure a on the unit circle T is called a Turan measure if any point of the open unit disc D is a limit point of zeros of the orthogonal polynomials associated to a. We show that many classes of measures, including Szego measures, measures with absolutely convergent series of their parameters, absolutely continuous measures with smooth densities, contain Turan measures. (C) 2003 Elsevier Science (USA). All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1Uncorrelatedness Sets of Bounded Random Variables(Academic Press inc Elsevier Science, 2004) Ostrovska, SAn uncorrelatedness set of two random variables shows which powers of random variables are uncorrelated. These sets provide a measure of independence: the wider an uncorrelatedness set is, the more independent random variables are. Conditions for a subset of N-2 to be an uncorrelatedness set of bounded random variables are studied. Applications to the theory of copulas are given. (C) 2004 Elsevier Inc. All rights reserved.Article Citation - WoS: 21Citation - Scopus: 20Cartan-Slodkowski Spectra, Splitting Elements and Noncommutative Spectral Mapping Theorems(Academic Press inc Elsevier Science, 2006) Dosiev, AIn this paper, we prove Slodkowski version of the infinite-dimensional spectral mapping theorem and Cartan-Slodkowski version of the finite-dimensional spectral mapping theorem for nilpotent operator Lie subalgebras with respect to the various noncommutative functional calculi. (C) 2005 Elsevier Inc. All rights reserved.
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