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Article Citation - WoS: 9Citation - Scopus: 9The Approximation of Logarithmic Function by q-bernstein Polynomials in the Case q > 1(Springer, 2007) Ostrovska, SofiyaSince in the case q > 1, q-Bernstein polynomials are not positive linear operators on C[ 0, 1], the study of their approximation properties is essentially more difficult than that for 0 < q < 1. Despite the intensive research conducted in the area lately, the problem of describing the class of functions in C[ 0, 1] uniformly approximated by their q-Bernstein polynomials ( q > 1) remains open. It is known that the approximation occurs for functions admitting an analytic continuation into a disc {z : | z| < R}, R > 1. For functions without such an assumption, no general results on approximation are available. In this paper, it is shown that the function f ( x) = ln( x + a), a > 0, is uniformly approximated by its q-Bernstein polynomials ( q > 1) on the interval [ 0, 1] if and only if a >= 1.Article Citation - WoS: 8Citation - Scopus: 11Proposing a novel mixed-reality framework for basic design and its hybrid evaluation using linkography and interviews(Springer, 2022) Cindioglu, Hasane Ceren; Gursel Dino, Ipek; Surer, ElifImmersive Virtual Environments (IVEs), particularly Mixed-Reality (MR) technologies, continue to have an increasing impact on design processes and design education. This study focuses on MR's potentials in Basic Design (BD) education and its influence on novice designers' design thinking abilities. In this study, through a newly developed MR-based design framework, DesignMR, a comparative analysis between design processes in MR and the physical environment is presented. A hybrid evaluation methodology is used in the context of three-dimensional (3D) BD tasks through two sets of protocol studies: Linkography and exit interviews. Linkography is a method to analyze the design process based on detecting design moves and their links with each other. In this study, linkographic analyses point to an increase in critical moves and link index values in MR as compared to the physical environment for all participants. This indicates that MR can trigger improved creativity, design productivity, and design exploration by idea generation. Exit interviews highlighted the positive impact of DesignMR on the motivation, work efficiency, and 3D perception of the participants. Further research will be pursued for improved hand gestures to increase the effectiveness of object interaction.Article Citation - WoS: 20Citation - Scopus: 32What foresees college students' tendency to use facebook for diverse educational purposes?(Springer, 2019) Toker, Sacip; Baturay, Meltem HuriThe present study investigates some factors affecting college students' tendency to use Facebook for different educational purposes. We reached 120 participants who were college students. Our sample comprised of 63 (52.5%) females and 57 (47.5%) males. We applied convenience sampling technique and an online questionnaire to collect data. Descriptive statistics, multiple regression analysis, and Structural Equation Modelling using IBM SPSS AMOS were utilized. The findings provide that GPA, Personal Use of Facebook for Studying and Socialization, Autonomy Psychological Need, and Academic Procrastination foresee college students' willingness to use Facebook in their courses. GPA and Personal Use of Facebook for studying are the most influential factors while Autonomy Psychological Need is the least impactful. We also examined the impact of these factors on different educational use types of Facebook: communication, collaboration, resources and material sharing. The results are discussed, and further recommendations for future research and implications are presented in the current study.Article Citation - WoS: 1Citation - Scopus: 2Predictors of E-Democracy Applicability in Turkish K-12 Schools(Springer, 2022) Sendag, Serkan; Toker, Sacip; Uredi, Lutfi; Islim, Omer FarukToday, the COVID-19 pandemic has paved the way for a more democratic climate in K-12 schools. Administrators and teachers have had to seek out new ways through which to interact. This raises two questions; "What about the quality of interaction and participation in decision-making?" and "Which factors affect the level of participation in decision-making?" The aim of the current research is to determine the factors that predict the applicability level of e-democracy (i.e., "reporting and declaring opinions" and "decision-making") in K-12 schools. An associational research design was used in order to attain the main goal of the study, with Discriminant Function Analysis (DFA) technique used to analyze the factors predicting the applicability level of e-democracy. Data were collected from a total of 765 inservice K-12 teachers through a questionnaire developed by the researchers. DFA results showed "motivation to participate," "the level of participatory democracy in the country," and higher levels of the "use of Twitter" as the significant determinants of different levels of e-democracy application. Moreover, the results also indicated that those participants with the belief of e-democracy's applicability at the decision-making level found the "motivation level of stakeholders" to be the most critical. Their level of Twitter use was higher. They also believed that the level of participatory democracy in the country was at a higher level. Another result of the DFA pointed to "security and ethical issues," and lower levels of the "use of Twitter" as factors differentiating the group believing that e-democracy can be applicable with reporting and the declaration of opinions to administrators from the other groups. The discussions highlighted the critical role of participation level in e-democracy within K-12 schools.Article Citation - WoS: 1Citation - Scopus: 2Functions Whose Smoothness Is Not Improved Under the Limit q-bernstein Operator(Springer, 2012) Ostrovska, SofiyaThe limit q-Bernstein operator B-q emerges naturally as a modification of the Szasz-Mirakyan operator related to the Euler probability distribution. At the same time, this operator serves as the limit for a sequence of the q-Bernstein polynomials with 0 < q < 1. Over the past years, the limit q-Bernstein operator has been studied widely from different perspectives. Its approximation, spectral, and functional-analytic properties, probabilistic interpretation, the behavior of iterates, and the impact on the analytic characteristics of functions have been examined. It has been proved that under a certain regularity condition, B-q improves the smoothness of a function which does not satisfy the Holder condition. The purpose of this paper is to exhibit 'exceptional' functions whose smoothness is not improved under the limit q-Bernstein operator. MSC: 26A15; 26A16; 41A36Article Citation - WoS: 14Citation - Scopus: 16Determination of Sediment Deposition of Hasanlar Dam Using Bathymetric and Remote Sensing Studies(Springer, 2019) Darama, Yakup; Selek, Zeliha; Selek, Bulent; Akgul, Mehmet Ali; Dagdeviren, MuratHasanlar Dam and Hydroelectric Power Plant are located on Kucuk Melen Creek in the Western Black Sea Basin of Turkey. The dam was constructed in 1974 to provide domestic water needs of the Duzce Province, to supply irrigation water need, to control and mitigate floods and to produce hydroelectric power. This dam has been subjected to severe sedimentation since its construction in 1974. Therefore, bathymetric field survey studies were conducted to determine storage loss in the Hasanlar Dam reservoir by sedimentation. Bathymetric survey data from the reservoir site of the Hasanlar Dam were obtained in 1979, 1999 and 2014. Analysis of the bathymetric data, GIS and remotes sensing techniques showed that storage loss in reservoir active volume between 1974 and 1999 was 24% and between 1974 and 2014 storage loss was 26%. Analysis of the bathymetric maps also showed that sediment accumulation is severe near and around the dam body and the spillway whose discharge capacity was decreased by sediment accumulation. This is extremely critical because the flood of May 1998 caused the high risk of collapse of dam due to reduced capacity of the spillway. Remote sensing technique was used to determine the future deposition of sediment in the reservoir. For this purpose, 35 points in the reservoir area were determined by comparing the relative water depths and actual water depths using satellite image of the bathymetry in July 2017 and Lake Observation Station. High correlation (R-2=0.833) was calculated by using logarithmic nonlinear regression analysis between actual and relative water depths for those 35 control points. The average of absolute values of differences between the estimated and actual water depths was found as 1.06m, and RMSE was calculated as 1.25m. This analysis shows that in the future, remote sensing data can be used in the studies of determining the depth of water and the total sediment thickness. In addition, the volume of the entire reservoir can be predicted by measuring the actual water depth only at those 35 control points without making a bathymetric map of the whole dam reservoir.Article Citation - WoS: 31Citation - Scopus: 35Fractional Unit-Root Tests Allowing for a Fractional Frequency Flexible Fourier Form Trend: Predictability of Covid-19(Springer, 2021) Omay, Tolga; Baleanu, DumitruIn this study we propose a fractional frequency flexible Fourier form fractionally integrated ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of the Fourier function. We provide the asymptotics of the newly proposed test and investigate its small-sample properties. Moreover, we show the best estimators for both fractional frequency and fractional difference operator for our newly proposed test. Finally, an empirical study demonstrates that not considering the structural break and fractional integration simultaneously in the testing process may lead to misleading results about the stochastic behavior of the Covid-19 pandemic.Article Citation - WoS: 2Citation - Scopus: 1Age replacement policies for discrete and continuous heterogeneous k-out-of-n systems(Springer, 2024) Eryilmaz, Serkan; Bulanik, IremThis paper studies age replacement policy for the k-out-of-n system that consists of independent but nonidentical components. Both continuously and discretely distributed components' lifetimes are considered. The failed components are replaced by new components and non-failed components are rejuvenated. Because the components are non-identical, the acquisition and rejuvenation costs of the components are chosen differently. The policy and the associated optimization problem are presented for general k and n, and 2-out-of-3 systems are studied in detail. The findings of the present paper extend the results in the literature from parallel systems to k-out-of-n systems.Article Citation - WoS: 8Citation - Scopus: 8Thermoluminescence Properties of Zno Nanoparticles in the Temperature Range 10-300 K(Springer, 2016) Isik, M.; Yildirim, T.; Gasanly, N. M.Low-temperature thermoluminescence (TL) properties of ZnO nanoparticles grown by sol-gel method were investigated in the 10-300 K temperature range. TL glow curve obtained at 0.2 K/s constant heating rate exhibited one broad peak around 83 K. The observed peak was analyzed using curve fitting method to determine the activation energies of trapping center(s) responsible for glow curve. Analyses resulted in the presence of three peaks at 55, 85 and 118 K temperatures with activation energies of 12, 30 and 45 meV, respectively. Thermal cleaning process was applied to separate overlapped peaks and get an opportunity to increase the reliability of results obtained from curve fitting method. Heating rate dependence of glow curve was also studied for rates between 0.2 and 0.7 K/s. The shift of the peak maximum temperatures to higher values and decrease in peak height with heating rate were observed. Moreover, X-ray diffraction and scanning electron microscopy were used for structural characterization.Article Citation - WoS: 76Citation - Scopus: 73Measuring the Efficiency of Hospitals: a Fully-Ranking Dea-Fahp Approach(Springer, 2019) Rouyendegh, Babak Daneshvar; Oztekin, Asil; Ekong, Joseph; Dag, AliThe goal of this study is to present a DEA-based fuzzy multi-criteria decision making model for firms in the health care industry in order to enhance their business performance. The study demonstrates a real-life use of the proposed model, mainly designed for hospitals. Data envelopment analysis enhanced with fuzzy analytic hierarchy process are collectively utilized to quantify the data and structure the model in decision-making. The juxtaposition of the two methods is used to compile a ranked list of multiple proxies containing diverse input and output variables which occur in two stages. This hybrid model provides several benefits, one of which is the ability to make the most appropriate decision considering the value of the weights determined by the data from the hybrid model.
