Cilt:70 Sayı:02 (2021)
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Item An extension of trapezoid inequality to the complex integral(Ankara Universitesi, 2021) Dragomir, Sever; Other; OtherIn this paper we extend the trapezoid inequality to the complex integral by providing upper bounds for the quantity | ( v − u ) f ( u ) + ( w − v ) f ( w ) − ∫ γ f ( z ) d z | under the assumptions that γ is a smooth path parametrized by z ( t ) , t ∈ [ a , b ] , u = z ( a ) , v = z ( x ) with x ∈ ( a , b ) and w = z ( b ) while f is holomorphic in G , an open domain and γ ∈ G . An application for circular paths is also given.Item A generalization of purely extending modules relative to a torsion theory(Ankara Universitesi, 2021) Doğruöz, Semra; Other; OtherIn this work we introduce a new concept, namely, τ s -extending modules (rings) which is torsion-theoretic analogues of extending modules and then we extend many results from extending modules to this new concept. For instance we show that for any ring R with unit, if R R is purely τ s -extending if and only if every cyclic τ -nonsingular R -module is flat. Also, we make a classification for the direct sums of the rings to be purely τ s -extending.Item Comparison of different estimation methods for the inverse weighted Lindley distribution(Ankara Universitesi, 2021) Balav, İklim Gedik; Other; OtherIn this paper, different estimation methods are considered for the parameters of the inverse weighted Lindley (IWL) distribution introduced by Ramos et al.(2019). Parameters of the IWL are estimated by the method of maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cram´er-von Mises (CVM) and Anderson Darling (AD). The performances of the estimators are compared using Monte Carlo simulation study via bias, mean square error and deficiency (Def) criteria. Finally, a real data set is analyzed for illustrative purposes.Item The effect of semi perforated duct on ring sourced acoustic diffraction(Ankara Universitesi, 2021) Tiryakioğlu, Burhan; Other; OtherAn analytical solution is obtained for the diffraction problem. In an infinite cylindrical duct, the sound waves are emanating by a ring source. The duct is rigid for z < l and perforated for z > l. The mixed boundary value problem is defined by a Wiener Hopf equation, by using the Fourier transform technique. Then the numerical solution is obtained. The influence of the parameters of the problem on the diffraction phenomenon is displayed graphically. The present study can be used as a model for different applications. Reducing noise in exhaust systems, ventilation systems are some of these applications.Item A variant of the proof of Van der Waerden's theorem by Furstenberg(Ankara Universitesi, 2021) Özkurt, Ali Aslan; Other; OtherLet R be a commutative ring with identity. In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of R, we will define a metric on R using them. Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].Item On bivariate extension of the univariate transmuted distribution family(Ankara Universitesi, 2021) Yılmaz, Mehmet; İstatistik; Fen FakültesiThe aim of this study is to examine the bivariate transmuted distributions in the literature and to propose alternative distribution. The method is based on mixing distributions of pairs of order statistics of a sample of size two. Some of proposed distributions allow both negative and positive Pearson correlations with admissible range between pairs of random variates. The results of the study gain importance in terms of eliminating or completing the missing aspects of the bivariate transmuted distributions existing in the literature.Item A revised generalized F-test for testing the equality of group means under non-normality caused by skewness(Ankara Üniversitesi, 2021) Çavuş, Mustafa; Other; OtherThe non-normality may occur in the data due to several reasons such as the presence of the outlier or skewness. It leads to lose the power and fail to control Type I error probability of the tests which are used to test the equality of the group means under heteroscedasticity. To overcome this problem, a revised generalized F-test (RGF) is proposed to test the equality of group means under heteroscedasticity in which non-normality caused by skewness in this study. An extensive Monte-Carlo simulation study is conducted to investigate the performance of the proposed test under several values of skewness for different number of groups. The proposed RGF is the best choice in the high level of skewness for k = 3, 4, 5. The Kruskal-Wallis test shows better performance than the others in small and moderate sample sizes for k = 6, and 7. It is shown that the proposed RGF test is superior than the non-parametric alternatives in the most of the conditions.Item New integral type inequalities via Raina-convex functions and its applications(Ankara Üniversitesi, 2021) Butt, Saad İhsan; Other; OtherIn this work, we discuss and introduce the novel literature about Raina-convex function and its algebraic properties. In addition, We elaborate and investigate Hermite-Hadamard and Fejer-type inequalities for newly discussed definition. Finally, using newly introduced definition, we find and prove amazing new integral type inequalities and applications for mean to positive real numbers. The amazing techniques and wonderful ideas of this paper may inspire and motivate for further activities and research in this direction furthermore.Item An efficient variant of dual to product and ratio estimators in sample surveys(Ankara Üniversitesi, 2021) VİSHWAKARMA, Gajendra K.; Other; OtherThis manuscript considers a dual to product and ratio estimator for estimating the finite population mean of study variable on applying a simple transformation to the auxiliary variable by using its average values in the population that is generally available in practice. The mean square error (MSE) of the proposed estimator has been obtained to the first degree of approximation. The optimum values and range of suitably chosen scalar, under which the proposed estimator perform better, have been determined. A method to lower the MSE of the proposed estimator relative to that of the MSE of the linear regression estimator is developed for small sample sizes. Theoretical and empirical studies have been done to demonstrate the superiority of the proposed estimator over the other estimators.Item A graph associated to a commutative semiring(Ankara Üniversitesi, 2021) Khoramdel, Mehdi; Other; OtherLet R be a commutative finite semiring with nonzero identity and H be an arbitrary multiplicatively closed subset R. The generalized identity-summand graph of R is the (simple) graph GH(R) with all elements of R as the vertices, and two distinct vertices x and y are adjacent if and only if x+y∈H. In this paper, we study some basic properties of GH(R). Moreover, we characterize the planarity, chromatic number, clique number and independence number of GH(R).Item The Lomax-Lindley distribution: properties and applications to lifetime data(Ankara Üniversitesi, 2021) Tarvirdizade, Bahman; Other; OtherThis paper introduces a new three-parameter distribution which is obtained by combining the Lomax and Lindley distributions in a serial system and is called the Lomax-Lindley distribution. The new distribution is quite flexible to model lifetime data. This distribution provides a simple form for hazard rate function which can be increasing, decreasing, bathtub-shaped and unimodal for different choices of the parameter values. Some statistical properties of the Lomax-Lindley distribution such as quantiles, moments, order statistics, Renyi entropy and mean deviations are discussed. The maximum likelihood estimators of its unknown parameters are obtained and the approximate confidence intervals of the parameters are provided. A Monte Carlo simulation study is conducted to investigate the performance of the maximum likelihood estimators and their corresponding confidence intervals. Finally, two real data sets having bathtub-shaped and unimodal hazard rate functions are analyzed and it is shown that the proposed distribution can provide a better fit than other distributions for both lifetime data.Item Discretization and chaos control in a fractional order predator-prey harvesting model(Ankara Üniversitesi, 2021) Selwam, Maria G.; Other; OtherThe study of interaction between predator and prey species is one of the important subjects in mathematical biology. Optimal strategy control plays a vital role in preserving animals from extinction. Harvesting of species is a vital issue for the conservation biologists. In this work, we investigate the bifurcation and chaos control of the two species interaction model of fractional order in discrete time with harvesting of both prey and predator species. Existence results and the stability conditions of the system are analyzed using the fixed points and jacobian matrix. The chaotic behavior of the system is discussed with bifurcation diagrams. Linear control and hybrid control methods are used in controlling the chaos of the system. Numerical experiments with different phase portraits are simulated for the better understanding of the qualitative behavior of the considered model.Item A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator(Ankara Üniversitesi, 2021) Akgül, Arzu; Other; OtherRecently, q-analogue of Noor integral operator and other special operators became importance in the field of Geometric Function Theory. In this study, by connecting this operators and the principle of subordination we introduced an interesting class of bi-univalent functions and obtained coefficient estimates for this new class.Item Approximation by truncated Lupaş operators of max-product kind(Ankara Üniversitesi, 2021) Örkçü, Mediha; Other; OtherThe goals of the present paper are to introduce truncated Lupaş type operators of max-product kind and give an estimation for the degree of approximation with respect to first modulus of continuity function. We prove that this estimate can not be improved; on the other hand, for some subclasses of functions, better degree of approximation is obtained. We also showed the piecewise convexity of the constructed operators on the interval [0,1].Item Logarithmic coefficients of starlike functions connected with k-Fibonacci numbers(Ankara Üniversitesi, 2021) Bulut, Serap; Other; OtherLet A denote the class of analytic functions in the open unit disc U normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 , and let S be the class of all functions f ∈ A which are univalent in U . For a function f ∈ S , the logarithmic coefficients δ n ( n = 1 , 2 , 3 , … ) are defined by log f ( z ) z = 2 ∑ ∞ n = 1 δ n z n ( z ∈ U ) . and it is known that | δ 1 | ≤ 1 and | δ 2 | ≤ 1 2 ( 1 + 2 e − 2 ) = 0 , 635 ⋯ . The problem of the best upper bounds for | δ n | of univalent functions for n ≥ 3 is still open. Let S L k denote the class of functions f ∈ A such that z f ′ ( z ) f ( z ) ≺ 1 + τ 2 k z 2 1 − k τ k z − τ 2 k z 2 , τ k = k − √ k 2 + 4 2 ( z ∈ U ) . In the present paper, we determine the sharp upper bound for | δ 1 | , | δ 2 | and | δ 3 | for functions f belong to the class S L k which is a subclass of S . Furthermore, a general formula is given for | δ n | ( n ∈ N ) as a conjecture.Item hesitant fuzzy sets, hesitant fuzzy topology, hesitant fuzzy interior, hesitant fuzzy closure, hesitant fuzzy subspaces(Ankara Üniversitesi, 2021) Kızılsu, Aysun Selçuk; Matematik; Fen FakültesiIntegral inequalities are very important in applied sciences. Chebyshev's integral inequality is widely used in applied mathematics. First of all, some necessary definitions and results regarding conformable derivative are given in this article. Then we give Chebyshev inequality for simultaneously positive (or negative) functions using the conformable fractional derivative. We used the Gronwall inequality to prove our results, unlike other studies in the literature.Item On some weaker hesitant fuzzy open sets(Ankara Üniversitesi, 2021) Hariwan, İbrahim; Other; OtherThe purpose of this paper is to define and study some new types of hesitant fuzzy open sets namely, hesitant fuzzy α-open, hesitant fuzzy preopen, hesitant fuzzy semiopen, hesitant fuzzy b-open and hesitant fuzzy β-open in hesitant fuzzy topological space. Some properties and the relationships between these hesitant fuzzy sets are investigated. Furthermore, some relationships between them in hesitant fuzzy subspace are introduced.Item Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations(Ankara Üniversitesi, 2021) Yılmaz, Abdullah; Other; OtherThe inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce a circular distribution based on an existing linear model. By the genesis of the ISP method, many important circular models have been provided by many researchers. In this study, we propose a new symmetric unimodal/bimodal circular distribution by the rotated ISP method considering the hyperbolic secant distribution as a baseline distribution. Rotation means that fixing the origin and rotating all other points the same amount counterclockwise. Considering the effect of rotation on the circular distribution to be obtained with the bilinear transformation, it is seen that it actually induces a location parameter in the obtained circular probability distribution. We analyze some of the stochastic properties of the proposed distribution. The methods for the parameter estimation of the new circular model and the simulation-based compare results of these estimators are extensively provided by the paper. Furthermore, we compare the fitting performance of the new model according to its well-known symmetric alternatives, such as Von-Misses, and wrapped Cauchy distributions, on a real data set. From the information obtained by the analysis on the real data, we say that the fitting performance of the new distribution is better than its alternatives according to the criteria frequently used in the literature.Item A new subclass of meromorphic functions defined by Rapid operator(Ankara Üniversitesi, 2021) Wankatesvarlu, B.; Other; OtherWe present and investigate a new subclass of meromorphic univalent functions described by the Rapid operator in this study. Coefficient inequalities is discussed, as well as distortion properties, closure theorems, Hadamard product. After this, integral transforms for the class ∑ ∗ ( ϑ , ϱ , ℘ , θ , μ ) are obtained.Item On certain subclass of univalent functions of complex order associated with Pascal distribution series(Ankara Üniversitesi, 2021) Şeker, Bilal; Other; OtherIn this study, by establishing a connection between normalized univalent functions in the unit disc and Pascal distribution series, we have obtained the necessary and sufficient conditions for these functions to belong to some subclasses of univalent functions of complex-order. We also determined some conditions by considering the integral operator for these functions.