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Article Citation - WoS: 56Citation - Scopus: 68The 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.Article Citation - WoS: 19Citation - Scopus: 22Improved 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, VimalAn 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.Article Citation - WoS: 55Citation - Scopus: 61Encoding 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.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: 2Citation - Scopus: 1The 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; MathematicsThe 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.Article Citation - WoS: 14Citation - Scopus: 14On Relations Between Transportation Cost Spaces and l1<(Academic Press inc Elsevier Science, 2020) Ostrovska, Sofiya; Ostrovskii, Mikhail I.The present paper deals with some structural properties of transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces and Wasserstein spaces. The main results of this work are: (1) A necessary and sufficient condition on an infinite metric space M, under which the transportation cost space on M contains an isometric copy of l(1). The obtained condition is applied to answer the open questions asked by Cuth and Johanis (2017) concerning several specific metric spaces. (2) The description of the transportation cost space of a weighted finite graph G as the quotient l(1) (E(G))/Z(G), where E(G) is the edge set and Z(G) is the cycle space of G. (C) 2020 Elsevier Inc. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 9Cesaro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures(Academic Press inc Elsevier Science, 2002) Golinskii, L; Khrushchev, SThe 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).Article Citation - WoS: 12Citation - Scopus: 11Oscillation Criterion for Half-Linear Differential Equations With Periodic Coefficients(Academic Press inc Elsevier Science, 2012) Dosly, O.; Ozbekler, A.; Simon Hilscher, R.In this paper, we present an oscillation criterion for second order half-linear differential equations with periodic coefficients. The method is based on the nonexistence of a proper solution of the related modified Riccati equation. Our result can be regarded as an oscillatory counterpart to the nonoscillation criterion by Sugie and Matsumura (2008). These two theorems provide a complete half-linear extension of the oscillation criterion of Kwong and Wong (2003) dealing with the Hill's equation. (C) 2012 Elsevier Inc. All rights reserved.Article Citation - WoS: 26Citation - Scopus: 31New Lmi Condition for the Nonexistence of Overflow Oscillations in 2-D State-Space Digital Filters Using Saturation Arithmetic(Academic Press inc Elsevier Science, 2007) Singh, VimalA new criterion for the nonexistence of overflow oscillations in 2-D state-space digital filters described by Roesser model using saturation arithmetic is presented. The criterion is in the form of a linear matrix inequality (LMI) and hence computationally tractable. The criterion is compared with an earlier LMI-based criterion due to Xiao and Hill. It turns out that the present criterion may uncover some new A (i.e., other than those arrived at via Xiao-Hill's criterion) for which the absence of overflow oscillations is assured. (c) 2006 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.
