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Article On the Lupas q-transform of Unbounded Functions(Walter de Gruyter Gmbh, 2023) Ostrovska, Sofiya; Turan, MehmetThe Lupa , s q-transform comes out naturally in the study of the Lupa , s q-analogue of the Bernstein operator. It is closely related to the Heine q-distribution which has a numerous application in q-boson operator calculus and to the Valiron method of summation for divergent series. In this paper, the Lupa , s q-transform (lambda(q)f)(z), q is an element of (0, 1), of unbounded functions is considered in distinction to the previous researches, where only the case f is an element of C[0, 1] have been investigated. First, the condition for a function to possess the Lupa , s q-transform is presented. Also, results concerning the connection between growth rate of the function f (t) as t -> 1(-) and the growth of its Lupa , s q-transform (lambda(q)f)(z) as z -> infinity are established. (c) 2023 Mathematical Institute Slovak Academy of SciencesArticle Citation - WoS: 1Talk the Talk, or Walk the Walk? Changing Narratives in Europeanization Research(Walter de Gruyter Gmbh, 2017) Agarin, Timofey; Yilmaz, GozdeOver the past two decades, there has been a growing interest in Europeanization, both within and beyond the European Union (EU). The impact of Eastern enlargement in 2004 on candidate and neighbourhood countries has attracted scholarly attention, and a consensus currently exists on the success of the EU's transformative power through the employment of a conditionality mechanism. However, the limits of EU conditionality upon candidate countries and neighbourhood Europeanization, in addition to the problems experienced by the EU itself, have brought into question whether the end of Europeanization research is in sight. Considering this, we critically evaluate the issues discussed in the scholarship on Europeanization and review several points of interest in relation to EU candidate countries in the Western Balkans as well as Turkey.Article Dublin and Istanbul: the Two Formative Forces in the Fiction of James Joyce and Orhan Pamuk(Walter de Gruyter Gmbh, 2015) Tekin, KuguThis comparative article explores how James Joyce and Orhan Pamuk approach and reflect upon their native cities in their works entitled Dubliners and Istanbul Memories and the City. The article puts particular emphasis on the two authors' parallel as well as different ways of representing Dublin and Istanbul. One of the most noteworthy similarities between Joyce and Pamuk is their preference for contemplating their birthplaces from outside as both authors have gone to a self-imposed exile. To a large extent, the said exile in the case of both authors is occasioned by a strong conviction that a double perspective-that of a native and that of a foreigner-is crucial for drawing an authentic picture of their cities. The article examines this double perspective as a parallactic structure. Parallax serves as a conceptual tool in understanding the two authors' manipulations of space and time in their writings. Where the two authors differ are the particular sentiments they entertain for their native cities. While a strong sense of hatred towards Dublin and Dublin life prevails in Dubliners, Pamuk's relationship with his city is defined by a deep love in Istanbul Memories and the City. And, it is these two contrasting emotional responses, namely hatred and love, that form the respective concepts of cityscape in the fiction of James Joyce and Orhan Pamuk.Article Citation - WoS: 1Citation - Scopus: 2Existence of Solutions for Odd-Order Multi-Point Impulsive Boundary Value Problems on Time Scales(Walter de Gruyter Gmbh, 2022) Georgiev, Svetlin G.; Akgol, Sibel Dogru; Kus, Murat EymenUsing a fixed point theorem due to Schaefer, the existence of solutions for an odd-order m-point impulsive boundary value problem on time scales is obtained. The problem considered is of general form, where both the differential equation and the impulse effects are nonlinear. Illustrative examples are provided.Article Citation - WoS: 9Citation - Scopus: 9Existence and Uniqueness of Best Proximity Points Under Rational Contractivity Conditions(Walter de Gruyter Gmbh, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Sadarangani, KishinThe main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.Article Citation - WoS: 2Citation - Scopus: 2On the q-bernstein Polynomials of the Logarithmic Function in the Case q > 1(Walter de Gruyter Gmbh, 2016) Ostrovska, SofiyaThe q-Bernstein basis used to construct the q-Bernstein polynomials is an extension of the Bernstein basis related to the q-binomial probability distribution. This distribution plays a profound role in the q-boson operator calculus. In the case q > 1, q-Bernstein basic polynomials on [0, 1] combine the fast increase in magnitude with sign oscillations. This seriously complicates the study of q-Bernstein polynomials in the case of q > 1. The aim of this paper is to present new results related to the q-Bernstein polynomials B-n,B- q of discontinuous functions in the case q > 1. The behavior of polynomials B-n,B- q(f; x) for functions f possessing a logarithmic singularity at 0 has been examined. (C) 2016 Mathematical Institute Slovak Academy of SciencesReview Citation - WoS: 22Citation - Scopus: 36Principles of Reverse Electrodialysis and Development of Integrated-Based System for Power Generation and Water Treatment: a Review(Walter de Gruyter Gmbh, 2022) Othman, Nur Hidayati; Kabay, Nalan; Guler, EnverReverse electrodialysis (RED) is among the evolving membrane-based processes available for energy harvesting by mixing water with different salinities. The chemical potential difference causes the movement of cations and anions in opposite directions that can then be transformed into the electrical current at the electrodes by redox reactions. Although several works have shown the possibilities of achieving high power densities through the RED system, the transformation to the industrial-scale stacks remains a challenge particularly in understanding the correlation between ion-exchange membranes (IEMs) and the operating conditions. This work provides an overview of the RED system including its development and modifications of IEM utilized in the RED system. The effects of modified membranes particularly on the psychochemical properties of the membranes and the effects of numerous operating variables are discussed. The prospects of combining the RED system with other technologies such as reverse osmosis, electrodialysis, membrane distillation, heat engine, microbial fuel cell), and flow battery have been summarized based on open-loop and closed-loop configurations. This review attempts to explain the development and prospect of RED technology for salinity gradient power production and further elucidate the integrated RED system as a promising way to harvest energy while reducing the impact of liquid waste disposal on the environment.Article Citation - WoS: 1Citation - Scopus: 1On the Rate of Convergence for the q-durrmeyer Polynomials in Complex Domains(Walter de Gruyter Gmbh, 2024) Gurel, Ovgu; Ostrovska, Sofiya; Turan, MehmetThe q-Durrmeyer polynomials are one of the popular q-versions of the classical operators of approximation theory. They have been studied from different points of view by a number of researchers. The aim of this work is to estimate the rate of convergence for the sequence of the q-Durrmeyer polynomials in the case 0 < q < 1. It is proved that for any compact set D subset of C, the rate of convergence is O(q(n)) as n -> infinity. The sharpness of the obtained result is demonstrated.Article Citation - WoS: 8Effect of Austenitizing Temperatures on the Microstructure and Mechanical Properties of Aisi 9254 Steel(Walter de Gruyter Gmbh, 2021) Murathan, Omer Faruk; Davut, Kemal; Kilicli, VolkanIn this study, the effect of austenitizing temperatures and low-temperature isothermal heat treatment (below martensite start temperature) on the microstructure and mechanical properties of AISI 9254 high silicon spring steel has been investigated. Experimental studies show that ultra-fine carbide-free bainite, tempered martensite and carbon enriched retained austenite could be observed in isothermally heat-treated samples where the as-received sample consisted of fine pearlite. A high tensile strength of similar to 2060 MPa, a total elongation of similar to 8 %, and absorbed energy of 105 J were achieved in a commercial high-Si steel by austempering below the Ms temperature. A good combination of strength and ductility has been obtained in prolonged austempering below the martensite start temperature (225 degrees C) from an austenitizing temperature of 870 degrees C.Article Citation - WoS: 104Citation - Scopus: 109On Generalized Α - Ψ-Geraghty Contractions on b-metric Spaces(Walter de Gruyter Gmbh, 2020) Afshari, Hojjat; Aydi, Hassen; Karapinar, ErdalIn this paper, we consider generalized alpha - psi-Geraghty contractive type mappings and investigate the existence and uniqueness of a fixed point for mappings involving such contractions. In particular, we extend, improve and generalize some earlier results in the literature on this topic. An application concerning the existence of an integral equation is also considered to illustrate the novelty of the main result.
