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Article Citation - WoS: 72Citation - Scopus: 75On the Lupas q-analogue of the Bernstein Operator(Rocky Mt Math Consortium, 2006) Ostrovska, SofiyaLet R-n(f,q;x) : C[0, 1] -> C[0, 1] be q-analogues of the Bernstein operators defined by Lupas in 1987. If q = 1, then R-n (f, 1; x) are classical Bernstein polynomials. For q not equal 1, the operators R-n (f, q; x) are rational functions rather than polynomials. The paper deals with convergence properties of the sequence {R-n (f, q; x)}. It is proved that {R-n (f, q(n); x)} converges uniformly to f(x) for any f(x) is an element of C[0, 1] if and only if q(n) -> 1. In the case q > 0, q not equal 1 being fixed the sequence I R. (f, q; x) I converges uniformly to f(x) is an element of C[0, 1] if and only if f(x) is linear.Article G-7 Ülkelerinin Borsalarının İstanbul Menkul Kıymetler Borsası Üzerindeki Etkileri(2006) Ceylan, Nildağ BaşakBu çalışmada, DAX (Almanya), CAC 40 (Fransa), FTSE (İngiltere), S&P TSX Composite (Kanada), NIKKEI 225 (Japonya), S&P500 (Amerika), DOW JONES (Amerika), NASDAQ (Amerika) ve MIBTEL (İtalya)’den oluşan G-7 ülkeleri borsa endekslerinin, İstanbul Menkul Kıymetler Borsası (İMKB-100) üzerindeki etkileri, blok üçlemsel VAR modeli kullanılarak incelenmiştir. Elde edilen bulgular, NIKKEI 225 haricindeki diğer tüm endekslerin, İMKB-100 endeksi üzerinde pozitif ve istatistiki olarak önemli etkileri olduğunu göstermektedir. Analizlerin sonucunda, Türkiye’nin krizsiz gecen 01.01.1995-31.10.2000 dönemi için diğer borsalardan etkileşiminin azaldığı, ancak 11 Eylül saldırıları sonrası globalleşmenin arttığı dönemde ise borsa endekslerinin İMKB-100 üzerindeki etkilerinin daha da arttığı görülmüştür.Article Citation - WoS: 20Citation - Scopus: 22Electrochemical and Optical Properties of an Azo Dye Based Conducting Copolymer(Tubitak Scientific & Technological Research Council Turkey, 2009) Cihaner, Atilla; Algi, FatihThe electrochemical and optical properties of a novel conducting copolymer called poly(2,5'-dimethyl-[4-(2,5-di-thiophen-2-yl-pyrrol-1-yl)-phenyl]azobenzene-co-(3,4-ethylenedioxythiophene)) (poly(1-co-EDOT)) are reported. Electrochemically synthesized poly(1-co-EDOT) based on the azo dye has a well-defined and reversible redox couple (0.37 V vs. Ag/AgCl) with good cycle stability. The copolymer film exhibits high conductivity (13 S/cm) as well as electrochromic behavior (magenta when neutralized and transmissive sky blue when oxidized). Furthermore, electro-optically active copolymer film has a low band gap of 1.79 eV with a pi-pi* transition at 555 nm.Article Citation - WoS: 16Citation - Scopus: 15Dynamical Systems and Poisson Structures(Amer inst Physics, 2009) Guerses, Metin; Guseinov, Gusein Sh; Zheltukhin, KostyantynWe first consider the Hamiltonian formulation of n=3 systems, in general, and show that all dynamical systems in R-3 are locally bi-Hamiltonian. An algorithm is introduced to obtain Poisson structures of a given dynamical system. The construction of the Poisson structures is based on solving an associated first order linear partial differential equations. We find the Poisson structures of a dynamical system recently given by Bender et al. [J. Phys. A: Math. Theor. 40, F793 (2007)]. Secondly, we show that all dynamical systems in R-n are locally (n-1)-Hamiltonian. We give also an algorithm, similar to the case in R-3, to construct a rank two Poisson structure of dynamical systems in R-n. We give a classification of the dynamical systems with respect to the invariant functions of the vector field (X) over right arrow and show that all autonomous dynamical systems in R-n are super-integrable. (C) 2009 American Institute of Physics. [doi:10.1063/1.3257919]Conference Object Citation - Scopus: 7Normalizing relational database schemas using mathematica(Springer Verlag, 2006) Yazici,A.; Karakaya,Z.In this paper, basic relational database (DB) normalization algorithms are implemented efficiently as Mathematica modules. It was observed that, Mathematica provided a straightforward platform as opposed to previous ones, mainly Prolog based tools which required complex data structures such as linked list representations with pointers. A Java user interface called JMath-Norm was designed to execute the Mathematica modules in a systematic way. For this purpose, Mathematical Java link facility (JLink) is utilized to drive the Mathematica kernel. JMath-Norm provides an effective interactive tool in an educational setting for teaching DB normalization theory. © Springer-Verlag Berlin Heidelberg 2006.Article Citation - Scopus: 2The Approximation of Power Function by the Q-Bernstein Polynomials in the Case Q > 1(Element D.O.O., 2008) Ostrovska,S.Since for q > 1, q-Bernstein polynomials are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. It is known that, in the case q > 1, the q-Bernstein polynomials approximate the entire functions and, in particular, polynomials uniformly on any compact set in ℂ. In this paper, the possibility of the approximation for the function (z + a)α, a ≥ 0, with a non-integer α > -1 is studied. It is proved that for a > 0, the function is uniformly approximated on any compact set in {z: \z| < a}, while on any Jordan arc in {z: \z\ > a}, the uniform approximation is impossible. In the case a = 0, the results of the paper reveal the following interesting phenomenon: the power function zα, α > 0, is approximated by its q-Bernstein polynomials either on any (when α ∈ ℕ) or no (when α ∉ ℕ) Jordan arc in ℂ.Article Araç Dinamiğinin Tek İzli Araç Modeli Yardımıyla Tanılanması(2004) Arıkan, Kutluk Bilge; Ünlüsoy, Y. SamimTek izli araç modeli yapısı kullanılarak, aracın dönüş dinamiğini anlatan matematiksel modeller tanılanmıştır. ARMAX ve durum uzayı modelleri parametre kestirimlerinde kullanılmıştır. Öngörü hatası kestir imi yöntemi uygulanmıştır. Kestirilen modellerden tek izli araç modelini oluşturan fiziksel parametreler de hesaplanmıştır.Article Citation - WoS: 5Citation - Scopus: 5Concentration Dependent Different Action of Progesterone on the Order, Dynamics and Hydration States of the Head Group of Dipalmitoyl-Phosphatidylcholine Membrane(Hindawi Ltd, 2005) Korkmaz, F; Kirbiyik, H; Severcan, FInteractions of progesterone with zwitterionic dipalmitoyl phosphatidylcholine (DPPC) multilamellar liposomes (MLVs) were investigated as a function of progesterone concentration at selected temperatures monitoring both the gel and liquid crystalline phase, by using Fourier Transform Infrared spectroscopy (FTIR). It has been show that the effect of progesterone on membrane dynamics is dependent on progesterone concentration. At 1 mol%, which is close to physiological level, progesterone behaves differently. At this concentration the decrease in dynamics is more noticeable. Additionally a dramatic decrease in the strength of hydrogen bonding in the interfacial region of the bilayer is also observed. When concentration increases up to 12 mol% opposite behaviour is observed at all interactions. Above 12 mol%, progesterone-DPPC interactions shows almost linear plot.Article Citation - WoS: 32Citation - Scopus: 34Semileptonic Λb,c To Nucleon Transitions in Full Qcd at Light Cone(Amer Physical Soc, 2009) Azizi, K.; Bayar, M.; Sarac, Y.; Sundu, H.The tree-level semileptonic Lambda(b)-> pl nu and Lambda(c)-> nl nu transitions are investigated using the light cone QCD sum rules approach in full theory. The spin 1/2, Lambda(Q) baryon with Q=b or c, is considered by the most general form of its interpolating current. The time ordering product of the initial and transition currents is expanded in terms of the nucleon distribution amplitudes with different twists. Considering two sets of independent input parameters entering to the nucleon wave functions, namely, QCD sum rules and lattice QCD parameters, the related form factors and their heavy quark effective theory limits are calculated and compared with the existing predictions of other approaches. It is shown that our results satisfy the heavy quark symmetry relations for lattice input parameters and b case exactly and the maximum violation is for charm case and QCD sum rules input parameters. The obtained form factors are used to compute the transition rates both in full theory and heavy quark effective theory. A comparison of the results on decay rate of Lambda(b)-> pl nu with those predicted by other phenomenological methods or the same method in heavy quark effective theory with different interpolating current and distribution amplitudes of the Lambda(b) is also presented.Article Citation - WoS: 18Oscillation of Second-Order Neutral Delay and Mixed-Type Dynamic Equations on Time Scales(Hindawi Publishing Corporation, 2006) Sahiner, Y.We consider the equation (r(t)(y(Delta)(t))(gamma))(Delta) + f (t, x(delta(t))) = 0, t is an element of T, where y(t) = x(t) + p(t) x(t(t)) and. is a quotient of positive odd integers. We present some sufficient conditions for neutral delay and mixed-type dynamic equations to be oscillatory, depending on deviating arguments tau(t) and delta(t), t is an element of T. Copyright (c) 2006 Y. Sahiner.
