Cilt:71 Sayı:02 (2022)
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Item Poisson and negative binomial regression models for zero-inflated data: an experimental study(Ankara Üniversitesi, 2022) Yıldırım, Gizem; Other; OtherCount data regression has been widely used in various disciplines, particularly health area. Classical models like Poisson and negative binomial regression may not provide reasonable performance in the presence of excessive zeros and overdispersion problems. Zero-inflated and Hurdle variants of these models can be a remedy for dealing with these problems. As well as zero-inflated and Hurdle models, alternatives based on some biased estimators like ridge and Liu may improve the performance against to multicollinearity problem except excessive zeros and overdispersion. In this study, ten different regression models including classical Poisson and negative binomial regression with their variants based on zero-inflated, Hurdle, ridge and Liu approaches have been compared by using a health data. Some criteria including Akaike information criterion, log-likelihood value, mean squared error and mean absolute error have been used to investigate the performance of models. The results show that the zero-inflated negative binomial regression model provides the best fit for the data. The final model estimations have been obtained via this model and interpreted in detail. Finally, the experimental results suggested that models except the classical models should be considered as powerful alternatives for modelling count and give better insights to the researchers in applying statistics on working similar data structures.Item Orlicz-lacunary convergent triple sequences and ideal convergence(Ankara Üniversitesi, 2022) Kişi, Ömer; Other; OtherIn the present paper we introduce and study Orlicz lacunary convergent triple sequences over n-normed spaces. We make an effort to present the notion of g 3 -ideal convergence in triple sequence spaces. We examine some topological and algebraic features of new formed sequence spaces. Some inclusion relations are obtained in this paper. Finally, we investigate ideal convergence in these spaces.Item A fractional order model of hepatitis B transmission under the effect of vaccination(Ankara Üniversitesi, 2022) Demirci, Elif; Matematik; Fen FakültesiIn this paper we present a fractional order mathematical model to explain the spread of Hepatitis B Virus (HBV) in a non-constant population. The model we propose includes both vertical and horizontal transmission of the infection and also vaccination at birth and vaccination of the susceptible class. We also use a frequency dependent transmission rate in the model. We give results on existence of equilibrium points of the model and analyze the stability of the disease-free equilibrium. Finally, numerical simulations of the model are presented.Item On the spectrum of the upper triangular double band matrix U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c(Ankara Üniversitesi, 2022) Durna, Nuh; Other; OtherThe upper triangular double band matrix U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) is defined on a Banach sequence space by U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) ( x n ) = ( a n x n + b n x n + 1 ) ∞ n = 0 where a x = a y , b x = b y for x ≡ y ( m o d 3 ) . The class of the operator U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) includes, in particular, the operator U ( r , s ) when a k = r and b k = s for all k ∈ N , with r , s ∈ R and s ≠ 0 . Also, it includes the upper difference operator; a k = 1 and b k = − 1 for all k ∈ N . In this paper, we completely determine the spectrum, the fine spectrum, the approximate point spectrum, the defect spectrum, and the compression spectrum of the operator U ( a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c .Item A novel analysis of integral inequalities in the frame of fractional calculus(Ankara Üniversitesi, 2022) Tariq, Muhammed; Other; OtherIn this paper, we define and explore the new family of exponentially convex functions which are called exponentially s–convex functions. We attain the amazing examples and algebraic properties of this newly introduced function. In addition, we find a novel version of Hermite-Hadamard type inequality in the support of this newly introduced concept via the frame of classical and fractional calculus (non-conformable and Riemann-Liouville integrals operator). Furthermore, we investigate refinement of Hermite-Hadamard type inequality by using exponentially s–convex functions via fractional integral operator. Finally, we elaborate some Ostrowski type inequalities in the frame of fractional calculus. These new results yield us some generalizations of the prior results.Item Explicit formulas for exponential of 2×2 split-complex matrices(Ankara Üniversitesi, 2022) Çakır, Hasan; Other; OtherSplit-complex (hyperbolic) numbers are ordered pairs of real numbers, written in the form x + j y with j 2 = − 1 , used to describe the geometry of the Lorentzian plane. Since a null split-complex number does not have an inverse, some methods to calculate the exponential of complex matrices are not valid for split-complex matrices. In this paper, we examined the exponential of a 2 x 2 split-complex matrix in three cases : i : Δ = 0 , i i : Δ ≠ 0 and Δ is not null split-complex number, i i i : Δ ≠ 0 and Δ is a null split-complex number where Δ = ( t r A ) 2 − 4 d e t A .Item Notes on the second-order tangent bundles with the deformed Sasaki metric(Ankara Üniversitesi, 2022) Gezer, Aydın; Other; OtherThe paper deals with the second-order tangent bundle T2M with the deformed Sasaki metric ¯g over an n−dimensional Riemannian manifold (M,g). We calculate all Riemannian curvature tensor fields of the deformed Sasaki metric ¯g and search Einstein property of T2M. Also the weakly symmetry properties of the deformed Sasaki metric are presented.Item On the well-coveredness of square graphs(Ankara Üniversitesi, 2022) Deniz, Zakir; Other; OtherThe square of a graph G is obtained from G by putting an edge between two distinct vertices whenever their distance in G is 2. A graph is well-covered if every maximal independent set in the graph is of the same size. In this paper, we investigate the graphs whose squares are well-covered. We first provide a characterization of the trees whose squares are well-covered. Afterwards, we show that a bipartite graph G and its square are well-covered if and only if every component of G is K 1 or K r , r for some r ≥ 1 . Moreover, we obtain a characterization of the graphs whose squares are well-covered in the case α ( G ) = α ( G 2 ) + k for k ∈ { 0 , 1 } .Item Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions(Ankara Üniversitesi, 2022) Güngör, Nurcan Bilgili; Other; OtherOrthogonal metric space is a considerable generalization of a usual metric space obtained by establishing a perpendicular relation on a set. Very recently, the notions of orthogonality of the set and orthogonality of the metric space are described and notable fixed point theorems are given in orthogonal metric spaces. Some fixed point theorems for the generalizations of contraction principle via altering distance functions on orthogonal metric spaces are presented and proved in this paper. Furthermore, an example is presented to clarify these theorems.Item Quantum analog of some trapezoid and midpoint type inequalities for convex functions(Ankara Üniversitesi, 2022) Kunt, Mehmet; Other; OtherIn this paper a new quantum analog of Hermite-Hadamard inequality is presented, and based on it, two new quantum trapezoid and midpoint identities are obtained. Moreover, the quantum analog of some trapezoid and midpoint type inequalities are established.Item Independence complexes of strongly orderable graphs(Ankara Üniversitesi, 2022) Yetim, Mehmet Akif; Other; OtherWe prove that for any finite strongly orderable (generalized strongly chordal) graph G, the independence complex Ind(G) is either contractible or homotopy equivalent to a wedge of spheres of dimension at least bp(G)−1, where bp(G) is the biclique vertex partition number of G. In particular, we show that if G is a chordal bipartite graph, then Ind(G) is either contractible or homotopy equivalent to a sphere of dimension at least bp(G) − 1.Item Skew ABC energy of digraphs(Ankara Üniversitesi, 2022) Yalçın, N. Feyza; Büyükköse, Şerife; Other; OtherIn this paper, skew ABC matrix and its energy are introduced for digraphs. Firstly, some fundamental spectral features of the skew ABC matrix of digraphs are established. Then some upper and lower bounds are presented for the skew ABC energy of digraphs. Further extremal digraphs are determined attaining these bounds.Item On certain bihypernomials related to Pell and Pell-Lucas numbers(Ankara Üniversitesi, 2022) LIANA, Anetta SZYNAL; Other; OtherThe bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce the concept of Pell and Pell-Lucas bihypernomials as a generalization of bihyperbolic Pell and Pell-Lucas numbers, respectively.Item Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter λ(Ankara Üniversitesi, 2022) Arslan, Reşat; Other; OtherIn this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λ ∈ [ − 1 , 1 ] . Firstly, we obtain some preliminaries results such as moments and central moments. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.Item Quaternionic Bertrand curves according to type 2-quaternionic frame in R 4(Ankara Üniversitesi, 2022) Aksoyak, Ferdağ Karaman; Other; OtherIn this paper, we give some characterization of quaternionic Bertrand curves whose the torsion is non-zero but bitorsion is zero in R 4 according to Type 2-Quaternionic Frame. One of the most important points in working on quaternionic curves is that given a curve in R 4 , the curve in R 3 associated with this curve is determined individually. So, we obtain some relationships between quaternionic Bertrand curve α ( 4 ) in R 4 and its associated spatial quaternionic curve α in R 3 . Also, we support some theorems in the paper by means of an example.Item Weak subgradient method with path based target level algorithm for nonconvex optimization(Ankara Üniversitesi, 2022) Yalçın, Gülçin Dinç; Other; OtherWe study a new version of the weak subgradient method, recently developed by Dinc Yalcin and Kasimbeyli for solving nonsmooth, nonconvex problems. This method is based on the concept of using any weak subgradient of the objective of the problem at the currently generated point with a version of the dynamic stepsize in order to produce a new point at each iteration. The target value needed in the dynamic stepsize is defined using a path based target level (PBTL) algorithm to ensure the optimal value of the problem is reached. We analyze the convergence and give an estimate of the convergence rate of the proposed method. Furthermore, we demonstrate the performance of the proposed method on nonsmooth, nonconvex test problems, and give the computational results by comparing them with the approximately optimal solutions.Item The complementary nabla Bennett-Leindler type inequalities(Ankara Üniversitesi, 2022) Kayar, Zeynep; Other; OtherWe aim to find the complements of the Bennett-Leindler type inequalities in nabla time scale calculus by changing the exponent from 0 < ζ < 1 to ζ > 1. Different from the literature, the directions of the new inequalities, where ζ > 1 , are the same as that of the previous nabla Bennett-Leindler type inequalities obtained for 0 < ζ < 1 . By these settings, we not only complement existing nabla Bennett-Leindler type inequalities but also generalize them by involving more exponents. The dual results for the delta approach and the special cases for the discrete and continuous ones are obtained as well. Some of our results are novel even in the special cases.Item A study on set-cordial labeling of graphs(Ankara Üniversitesi, 2022) Naduvath, Sudev; Other; OtherFor a non-empty ground set X, finite or infinite, the set-valuation or set-labeling of a given graph G is an injective function f:V(G)→P(X), where P(X) is the power set of the set X. In this paper, we introduce a new type of set-labeling, called set-cordial labeling and study the characteristics of graphs which admit the set-cordial labeling.Item Direction curves of generalized Bertrand curves and involute-evolute curves in E 4(Ankara Üniversitesi, 2022) Önder, Mehmet; Other; OtherIn this study, we define (1,3)-Bertrand-direction curve and (1,3)-Bertrand-donor curve in the 4-dimensional Euclidean space E 4 . We introduce necessary and sufficient conditions for a special Frenet curve to have a (1,3)-Bertrand-direction curve. We introduce the relations between Frenet vectors and curvatures of these direction curves. Furthermore, we investigate whether (1,3)-evolute-donor curves in E 4 exist and show that there is no (1,3)-evolute-donor curve in E 4 .Item On GLM type integral equation for singular Sturm-Liouville operator which has discontinuous coefficient(Ankara Üniversitesi, 2022) Topsakal, Nilüfer; Other; OtherIn this study, we derive Gelfand-Levitan-Marchenko type main integral equation of the inverse problem for singular Sturm-Liouville equation which has discontinuous coefficient. Then we prove the unique solvability of the main integral equation.