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Citation - WoS: 5
Citation - Scopus: 5
Analytical Properties of the Lupas q-transform
(Academic Press inc Elsevier Science, 2012) Ostrovska, Sofiya
The Lupas q-transform emerges in the study of the limit q-Lupas operator. The latter comes out naturally as a limit for a sequence of the Lupas q-analogues of the Bernstein operator. Given q is an element of (0, 1), f is an element of C left perpendicular0, 1right perpendicular, the q-Lupas transform off is defined by (Lambda(q)f) (z) := 1/(-z; q)(infinity) . Sigma(infinity)(k=0) f(1 - q(k))q(k(k -1)/2)/(q; q)(k)z(k). The transform is closely related to both the q-deformed Poisson probability distribution, which is used widely in the q-boson operator calculus, and to Valiron's method of summation for divergent series. In general, Lambda(q)f is a meromorphic function whose poles are contained in the set J(q) := {-q(-j)}(j=0)(infinity). In this paper, we study the connection between the behaviour of f on leftperpendicular0, 1right perpendicular and the decay of Lambda(q)f as z -> infinity. (C) 2012 Elsevier Inc. All rights reserved.
Citation - WoS: 23
Citation - Scopus: 23
Anisotropic mechanical properties of Tl₄Ag₁₈Te₁₁ compound with low thermal conductivity
(Academic Press inc Elsevier Science, 2020) Gencer, Aysenur; Surucu, Ozge; Surucu, Gokhan; Deligoz, Engin
The anisotropic mechanical properties of Tl4Ag18Te11 compound was investigated elaborately for the first time by using Density Functional Theory calculations with the Vienna Ab-initio Simulation Package in this work. Tl4Ag18Te11 compound was optimized in the I4mm space group and the formation energy was determined as a negative value that is the indication of the experimental synthesizability of this compound. The optimized crystal structure was employed for the calculations of the elastic constants and the obtained values revealed the mechanical stability of Tl4Ag18Te11 compound. The polycrystalline properties were determined such as shear modulus, Poisson's ratio, etc. In addition, the anisotropic elastic properties were presented. The direction dependent sound waves velocities, polarization of the sound waves, enhancement factor and the power flow angle were determined. The thermal conductivity studies were performed and the minimum thermal conductivity (0.259 W m(-1)K(-1)) and the diffusion thermal conductivity (0.202 W m(-1)K(-1)) were calculated. This study illustrates the capability of this compound for the thermoelectric materials.
Citation - WoS: 29
Citation - Scopus: 30
Boundary Value Problems for Second Order Nonlinear Differential Equations on Infinite Intervals
(Academic Press inc Elsevier Science, 2004) Guseinov, GS; Yaslan, I
In 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.
Citation - WoS: 20
Citation - Scopus: 19
Cartan-Slodkowski Spectra, Splitting Elements and Noncommutative Spectral Mapping Theorems
(Academic Press inc Elsevier Science, 2006) Dosiev, A
In 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.
Citation - WoS: 7
Citation - Scopus: 9
Cesaro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures
(Academic Press inc Elsevier Science, 2002) Golinskii, L; Khrushchev, S
The convergence in L-2(T) of the even approximants of the Wall continued fractions is extended to the Cesaro-Nevai class CN, which is defined as the class of probability measures sigma with lim(n-->infinity) 1/n Sigma(k=0)(n-1) \a(k)\ = 0, (a(n))(ngreater than or equal to0) being the Geronimus parameters of sigma. We show that CN contains universal measures, that is, probability measures for which the sequence (\phi(n)\(2) dsigma)(ngreater than or equal to0) is dense in the set of all probability measures equipped with the weak-* topology. We also consider the "opposite" Szego class which consists of measures with Sigma(n=0)(infinity) (1-\a(n)\(2))(1/2) < infinity and describe it in terms of Hessenberg matrices. (C) 2002 Elsevier Science (USA).
Citation - WoS: 11
Citation - Scopus: 11
Classification of Some Quadrinomials Over Finite Fields of Odd Characteristic
(Academic Press inc Elsevier Science, 2023) Ozbudak, Ferruh; Temur, Burcu Gulmez
In this paper, we completely determine all necessary and sufficient conditions such that the polynomial f(x) = x3 + axq +2 + bx2q +1 + cx3q, where a, b, c is an element of Fq*, is a permutation quadrinomial of Fq2 over any finite field of odd characteristic. This quadrinomial has been studied first in [25] by Tu, Zeng and Helleseth, later in [24] Tu, Liu and Zeng revisited these quadrinomials and they proposed a more comprehensive characterization of the coefficients that results with new permutation quadrinomials, where char(Fq) = 2 and finally, in [16], Li, Qu, Li and Chen proved that the sufficient condition given in [24] is also necessary and thus completed the solution in even characteristic case. In [6] Gupta studied the permutation properties of the polynomial x3 + axq +2 + bx2q +1 + cx3q, where char(Fq) = 3, 5 and a, b, c is an element of Fq* and proposed some new classes of permutation quadrinomials of Fq2 . In particular, in this paper we classify all permutation polynomials of Fq2 of the form f(x) = x3 + axq +2 + bx2q +1 + cx3q, where a, b, c is an element of Fq*, over all finite fields of odd characteristic and obtain several new classes of such permutation quadrinomials. (c) 2022 Elsevier Inc. All rights reserved.
Citation - WoS: 26
Citation - Scopus: 26
Classification Theorems for General Orthogonal Polynomials on the Unit Circle
(Academic Press inc Elsevier Science, 2002) Khrushchev, SV
The set P of all probability measures a on the unit circle T splits into three disjoint subsets depending on properties of the derived set of {\phi(n)\(2) dsigma}(ngreater than or equal to0), denoted by Lim(sigma). Here {phi(n)}(ngreater than or equal to0) are orthogonal polynomials in L-2(dsigma). The first subset is the set of Rakhmanov measures, i.e., of sigma is an element of P with {m} = Lim(sigma), m being the normalized (m(T) = 1) Lebesgue measure on T. The second subset Mar(T) consists of Markoff measures, i.e., of sigma is an element of P with m is not an element of Lim(sigma), and is in fact the subject of study for the present paper. A measure sigma, belongs to Mar(T) iff there are epsilon > 0 and l > 0 such that sup{\a(n+j)\: 0 less than or equal to j less than or equal to l) > epsilon, n = 0, 1, 2,..., {a(n)} is the Geronimus parameters (= reflection coefficients) of sigma. We use this equivalence to describe the asymptotic behavior of the zeros of the corresponding orthogonal polynomials (see Theorem G). The third subset consists of sigma is an element of P with {m} not subset of or equal toLim(sigma). We show that sigma is ratio asymptotic iff either sigma is a Rakhmanov measure or sigma satisfies the Lopez condition (which implies sigma is an element of Mar(T)). Measures sigma satisfying Lim(sigma) = {v} (i.e., weakly asymptotic measures) are also classified. Either v is the sum of equal point masses placed at the roots of z(n) = lambda, lambda is an element of T, n = 1, 2,..., or v is the equilibrium measure (with respect to the logarithmic kernel) for the inverse image under an m-preserving endomorphism z -->z(n), = 1, 2,..., of a closed arc J (including J = T) with removed open concentric are J(0) (including J(0) = empty set). Next, weakly asymptotic measures are completely described in terms of their Geronimus parameters. Finally, we obtain explicit formulae for the parameters of the equilibrium measures v and show that these measures satisfy {v} = Lim(v). (C) 2002 Elsevier Science (USA).
Citation - WoS: 3
Citation - Scopus: 2
Complementability of Isometric Copies of L1 in Transportation Cost Spaces
(Academic Press inc Elsevier Science, 2024) Ostrovska, Sofiya; Ostrovskii, Mikhail I.
This work aims to establish new results pertaining to the structure of transportation cost spaces. Due to the fact that those spaces were studied and applied in various contexts, they have also become known under different names such as Arens-Eells spaces, Lipschitz-free spaces, and Wasserstein spaces. The main outcome of this paper states that if a metric space X is such that the transportation cost space on X contains an isometric copy of L1, then it contains a 1-complemented isometric copy of $1. (c) 2023 Elsevier Inc. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 1
The Continuity in Q of the Lupaş Q-Analogues of the Bernstein Operators
(Academic Press inc Elsevier Science, 2024) Yilmaz, Ovgue Gurel; Turan, Mehmet; Ostrovska, Sofiya; Turan, Mehmet; Ostrovska, Sofiya; Turan, Mehmet; Ostrovska, Sofiya; Mathematics; Mathematics
The Lupas q-analogue Rn,q of the Bernstein operator is the first known q-version of the Bernstein polynomials. It had been proposed by A. Lupas in 1987, but gained the popularity only 20 years later, when q-analogues of classical operators pertinent to the approximation theory became an area of intensive research. In this work, the continuity of operators Rn,q with respect to parameter q in the strong operator topology and in the uniform operator topology has been investigated. The cases when n is fixed and n -> infinity have been considered. (c) 2022 Elsevier Inc. All rights reserved.
Citation - WoS: 125
Citation - Scopus: 135
Convergence of Generalized Bernstein Polynomials
(Academic Press inc Elsevier Science, 2002) Il'inskii, A; Ostrovska, S
Let f is an element of C[0, 1], q is an element of (0, 1), and B-n(f, q; x) be generalized Bernstein polynomials based on the q-integers. These polynomials were introduced by G. M. Phillips in 1997. We study convergence properties of the sequence {B-n(f, q; x)}(n=1)(infinity). It is shown that in general these properties are essentially different from those in the classical case q = 1. (C) 2002 Elsevier Science (USA).
Citation - WoS: 3
Citation - Scopus: 3
Corrigendum and Addendum To My Paper Concerning Kummer Extensions With Few Roots of Unity (vol 41, Pg 322, 1992)
(Academic Press inc Elsevier Science, 2003) Albu, T
[No Abstract Available]
Citation - WoS: 49
Citation - Scopus: 54
Elimination of Overflow Oscillations in Digital Filters Employing Saturation Arithmetic
(Academic Press inc Elsevier Science, 2005) Kar, H; Singh, V
A 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.
Citation - WoS: 18
Citation - Scopus: 19
Elimination of Overflow Oscillations in Fixed-Point State-Space Digital Filters Using Saturation Arithmetic: an Lmi Approach
(Academic Press inc Elsevier Science, 2006) Singh, V
A criterion for the nonexistence of overflow oscillations in fixed-point state-space digital filters employing saturation arithmetic is presented. The criterion possesses the structure of linear matrix inequality and hence is computationally tractable. The criterion is compared with an earlier LMI-based criterion. (c) 2005 Elsevier Inc. All rights reserved.
Citation - WoS: 55
Citation - Scopus: 61
Encoding the Future: Successful Processing of Intentions Engages Predictive Brain Networks
(Academic Press inc Elsevier Science, 2010) Poppenk, J.; Moscovitch, M.; McIntosh, A. R.; Ozcelik, E.; Craik, F. I. M.
Evidence from cognitive, patient and neuroimaging research indicates that "remembering to remember" intentions, i.e., prospective memory (PM) retrieval, requires both general memory systems involving the medial temporal lobes and an executive system involving rostral PFC (BA 10). However, it is not known how prospective memories are initially formed. Using fMRI, we investigated whether brain activity during encoding Of future intentions and present actions differentially predicted later memory for those same intentions (PM) and actions (retrospective memory). We identified two significant patterns of neural activity: a network linked to overall memory and another linked specifically to PM. While overall memory success was predicted by temporal lobe activations that included the hippocampus, PM success was also uniquely predicted by activations in additional regions, including left rostrolateral PFC and the right parahippocampal gyrus. This finding extends the role of these structures to the formation of individual intentions. It also provides the first evidence that PM encoding, like PM retrieval, is supported by both a common episodic memory network and an executive network specifically recruited by future-oriented processing. (C) 2009 Elsevier Inc. All rights reserved.
Citation - WoS: 5
Citation - Scopus: 5
The Euler-Lagrange Theory for Schur's Algorithm: Algebraic Exposed Points
(Academic Press inc Elsevier Science, 2006) Khrushchev, S
In 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.
Citation - WoS: 4
Citation - Scopus: 3
The Euler-Lagrange Theory for Schur's Algorithm: Wall Pairs
(Academic Press inc Elsevier Science, 2006) Khrushchev, S
This 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.
Citation - WoS: 36
Citation - Scopus: 36
A Fixed Point Theorem and the Ulam Stability in Generalized Dq-Metric Spaces
(Academic Press inc Elsevier Science, 2018) Brzdek, Janusz; Karapinar, Erdal; Petrusel, Adrian
We prove a fixed point theorem for function spaces, that is a very efficient and convenient tool for the investigations of various operator inequalities connected to Ulam stability issues, in classes of functions taking values in various spaces (e.g., in ultrametric spaces, dq-metric spaces, quasi-Banach spaces, and p-Banach spaces). The theorem is a natural generalization and extension of the classical Banach Contraction Principle and some other more recent results. (C) 2018 Elsevier Inc. All rights reserved.
Citation - WoS: 55
Citation - Scopus: 68
The h-laplace and q-laplace Transforms
(Academic Press inc Elsevier Science, 2010) Bohner, Martin; Guseinov, Gusein Sh.
Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the particular concepts of the h-Laplace and q-Laplace transforms. The convolution and inversion problems for these transforms are considered in some detail. (c) 2009 Elsevier Inc. All rights reserved.
Citation - WoS: 170
Citation - Scopus: 188
q-bernstein Polynomials and Their Iterates
(Academic Press inc Elsevier Science, 2003) Ostrovska, S
Let 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.
Citation - WoS: 19
Citation - Scopus: 22
Improved Lmi-Based Criterion for Global Asymptotic Stability of 2-D State-Space Digital Filters Described by Roesser Model Using Two's Complement Arithmetic
(Academic Press inc Elsevier Science, 2012) Singh, Vimal
An LMI-based criterion for the global asymptotic stability of 2-D state-space digital filters described by the Roesser model employing two's complement overflow arithmetic is presented. Under a certain assumption, the criterion turns out to be an improvement over a criterion due to El-Agizi and Fahmy pertaining to two's complement arithmetic and has a form similar to a criterion due to Xiao and Hill pertaining to saturation arithmetic. Examples show the effectiveness of the new criterion. (C) 2012 Elsevier Inc. All rights reserved.

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