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Article Citation - WoS: 5Citation - Scopus: 5Dispersive Optical Constants of Tl2ingase4< Single Crystals(Iop Publishing Ltd, 2007) Qasrawi, A. F.; Gasanly, N. M.The structural and optical properties of Bridgman method grown Tl2InGaSe4 crystals have been investigated by means of room temperature x-ray diffraction, and transmittance and reflectance spectral analysis, respectively. The x-ray diffraction technique has shown that Tl2InGaSe4 is a single phase crystal of a monoclinic unit cell that exhibits the lattice parameters of a = 0.77244 nm, b = 0.64945 nm, c = 0.92205 nm and beta = 95.03 degrees . The optical data have revealed an indirect allowed transition band gap of 1.86 eV. The room temperature refractive index, which was calculated from the reflectance and transmittance data, allowed the identification of the dispersion and oscillator energies, static dielectric constant and static refractive index as 28.51 and 3.45 eV, 9.26 and 3.04, respectively.Article Citation - WoS: 7On the Approximation of Analytic Functions by the q-bernstein Polynomials in the Case q > 1(Kent State University, 2010) Ostrovska, SofiyaSince for q > 1, the q-Bernstein polynomials B(n,q) 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. In this paper, new results on the approximation of continuous functions by the q-Bernstein polynomials in the case q > 1 are presented. It is shown that if f is an element of C[0, 1] and admits an analytic continuation f(z) into {z : |z| < a}, then B(n,q) (f; z) -> f (z) as n -> infinity, uniformly on any compact set in {z : |z| < a}.Article Citation - WoS: 1A Class of Shock Models for a System That Is Equipped With a Protection Block With an Application to Wind Turbine Reliability(Wiley, 2025) Eryilmaz, SerkanThis paper studies a class of shock models for a system that is equipped with a protection block that has its own failure rate. Under the considered class, the system exposed to shocks at random times is protected by the protection block, and the probability of the shock damaging the system varies depending on whether the protection block operates or not. The system failure criteria is defined based on the pattern of the critical/damaging shocks. Exact expressions for the reliability and mean time to failure of the system are obtained, and detailed computations are presented for the run shock model, which is included in the class. The application of the extreme shock model, which is included in the relevant class, to wind turbine reliability is also discussed.Article Citation - WoS: 22Citation - Scopus: 23A Coupled Fixed Point Result in Partially Ordered Partial Metric Spaces Through Implicit Function(Hacettepe Univ, Fac Sci, 2013) Gulyaz, Selma; Karapinar, Erdal; MathematicsIn this manuscript, we discuss the existence of coupled fixed points in the context of partially ordered metric spaces through implicit relations for mappings F:X x X -> X such that F has the mixed monotone property. Our main theorem improves and extends various results in the literature. We also state an example to illustrate our work.Article Citation - WoS: 1Citation - Scopus: 1The Number of Irreducible Polynomials Over Finite Fields With Vanishing Trace and Reciprocal Trace(Springer, 2022) Cakiroglu, Yagmur; Yayla, Oguz; Yilmaz, Emrah SercanWe present the formula for the number of monic irreducible polynomials of degree n over the finite field F-q where the coefficients of x(n)(-1) and x vanish for n >= 3. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements a is an element of F-qn for which Trace(a) = 0 and Trace(a(-1)) = 0.Article Synthesis and Characterization of a Luminol Based Chemiluminescent Trimeric System(Springer/plenum Publishers, 2023) Kesimal, Busra; Balci, Burcu; Cakal, Deniz; Onal, Ahmet M.; Cihaner, AtillaA luminol based chemiluminescent trimeric system, namely 2,3-dihydro-5,8-di(thiophen-2-yl)phthalazine-1,4-dione (T2B-Lum), bearing thiophene rings as donor units and 2,3-dihydrophthalazine-1,4-dione as an acceptor unit was synthesized in two steps via donor-acceptor-donor approach using two different methods. It was found that T2B-Lum emits chemiluminescent light when exposed to H2O2 in a basic medium, and the presence of substituents and the type of aromatic ring bearing chemiluminescent active group have a direct effect on the compound's sensitivity. Among the members of a large family of metal ions, fluorescent and chemiluminescent T2B-Lum exhibited high sensitivity to Cu2+ and Fe3+ ions. Except for other metal cations (silver(I), cadmium(II), cobalt(II), iron(III), lithium(I), magnesium(II), manganese(II), nickel(II), zinc(II)), it has been observed that T2B-Lum is mostly sensitive to copper(II) ions with a detection limit value of 2.2 x 10(- 3) M. On the other hand, T2B-Lum was also found to exhibit a high sensitivity to extremely dilute aqueous solutions (e.g., 1:50.000 dilution) of blood samples, making it a promising candidate for use in forensic applications.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 Citation - Scopus: 56Applications of the Extended Fractional Euler-Lagrange Equations Model To Freely Oscillating Dynamical Systems(Publishing House of the Romanian Academy, 2016) Agila,A.; Baleanu,D.; Eid,R.; Irfanoglu,B.The fractional calculus and the calculus of variations are utilized to model and control complex dynamical systems. Those systems are presented more accurately by means of fractional models. In this study, an extended version of the fractional Euler-Lagrange equations is introduced. In these equations the damping force term is extended to be proportional to the fractional derivative of the displacement with variable fractional order. The finite difference methods and the Coimbra fractional derivative are used to approximate the solution of the introduced fractional Euler-Lagrange equations model. The free oscillating single pendulum system is investigated. © 2016, Editura Academiei Romane. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 2On the Lifetime of a Random Binary Sequence(Elsevier Science Bv, 2011) Eryilmaz, SerkanConsider a system with m elements which is used to fulfill tasks. Each task is sent to one element which fulfills a task and the outcome is either fulfillment of the task ("1") or the failure of the element ("0"). Initially, m tasks are sent to the system. At the second step, a complex of length m(1) is formed and sent to the system, where m(1) is the number of tasks fulfilled at the first step, and so on. The process continues until all elements fail and the corresponding waiting time defines the lifetime of the binary sequence which consists of "1" or "0". We obtain a recursive equation for the expected value of this waiting time random variable. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 35Fixed Point Theorem on Partial Metric Spaces Involving Rational Expressions(Univ Miskolc inst Math, 2013) Karapinar, Erdal; Shatanawi, Wasfi; Tas, KenanWe establish a fixed point theorem involving a rational expression in a complete partial metric space. Our result generalizes a well-known result in (usual) metric spaces. Also, we introduce an example to illustrate the usability of our result.
