Cilt:71 Sayı:01 (2022)
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Item Associated curves of a Frenet curve in the dual Lorentzian space(Ankara Üniversitesi, 2022) Yücesan, Ahmet; Other; OtherIn this work, we firstly introduce notions of principal directed curves and principal donor curves which are associated curves of a Frenet curve in the dual Lorentzian space D 3 1 . We give some relations between the curvature and the torsion of a dual principal directed curve and the curvature and the torsion of a dual principal donor curve. We show that the dual principal directed curve of a dual general helix is a plane curve and obtain the equation of dual general helix by using position vector of plane curve. Then we show that the principal donor curve of a circle in D 2 or a hyperbola in D 2 1 and the principal directed curve of a slant helix in D 3 1 are a helix and general helix, respectively. We explain with an example for the second case. Finally, according to causal character of the principal donor curve of principal directed rectifying curve in D 3 1 , we show this curve to correspond to any timelike or spacelike ruled surface in Minkowski 3−space R 3 1 .Item Some group actions and Fibonacci numbers(Ankara Üniversitesi, 2022) Şanlı, Zeynep; Other; OtherThe Fibonacci sequence has many interesting properties and studied by many mathematicians. The terms of this sequence appear in nature and is connected with combinatorics and other branches of mathematics. In this paper, we investigate the orbit of a special subgroup of the modular group. Taking T c := ( c 2 + c + 1 − c c 2 1 − c ) ∈ Γ 0 ( c 2 ) , c ∈ Z , c ≠ 0 , we determined the orbit { T r c ( ∞ ) : r ∈ N } . Each rational number of this set is the form P r ( c ) / Q r ( c ) , where P r ( c ) and Q r ( c ) are the polynomials in Z [ c ] . It is shown that P r ( 1 ) and Q r ( 1 ) the sum of the coefficients of the polynomials P r ( c ) and Q r ( c ) respectively, are the Fibonacci numbers, where P r ( c ) = r ∑ s = 0 ( 2 r − s s ) c 2 r − 2 s + r ∑ s = 1 ( 2 r − s s − 1 ) c 2 r − 2 s + 1 and Q r ( c ) = r ∑ s = 1 ( 2 r − s s − 1 ) c 2 r − 2 s + 2Item Modified-Lindley distribution and its applications to the real data(Ankara Üniversitesi, 2022) Karakaya, Kadir; Other; OtherIn this paper, a new three-parameter lifetime distribution is proposed by mixing modified Weibull and generalized gamma distributions. The point estimation on the distribution parameters are discussed through several estimators. The interval estimation is also studied with two methods based on asymptotic normality and likelihood ratio. A Monte Carlo simulation study is performed to evaluate the biases and mean square errors behaviors of point estimates for a different sample of size. A simulation study is also conducted to investigate the coverage probabilities of confidence intervals. The distribution modeling analyses are provided based on several real data sets to demonstrate the fitting ability of the introduced distribution.Item k-Free numbers and integer parts of αp(Ankara Üniversitesi, 2022) Çelik, Şermin Çam; Other; OtherIn this note, we obtain asymptotic results on integer parts of αp that are free of kth powers of primes, where p is a prime number and α is a positive real number.Item Generalized relative Nevanlinna order (α,β) and generalized relative Nevanlinna type (α,β) based some growth properties of composite analytic functions in the unit disc(Ankara Üniversitesi, 2022) Tanmay, Biswas; Other; OtherOur aim in this paper is to introduce some idea about generalized relative Nevanlinna order (α,β) and generalized relative Nevanlinna type (α,β) of an analytic function with respect to another analytic function in the unit disc where α and β are continuous non-negative functions on (-∞,+∞). So we discuss about some growth properties relating to the composition of two analytic functions in the unit disc on the basis of generalized relative Nevanlinna order (α,β) and generalized relative Nevanlinna type (α,β) as compared to the growth of their corresponding left and right factors.Item Generalized osculating curves of type (n-3) in the n-dimensional Euclidean space(Ankara Üniversitesi, 2022) Bekiryazıcı, Zafer; Other; OtherIn this paper, we give a generalization of the osculating curves to the n -dimensional Euclidean space. Based on the definition of an osculating curve in the 3 and 4 dimensional Euclidean spaces, a new type of osculating curve has been defined such that the curve is independent of the ( n − 3 ) th binormal vector in the n-dimensional Euclidean space, which has been called ”a generalized osculating curve of type ( n − 3 ) ”. We find the relationship between the curvatures for any unit speed curve to be congruent to this osculating curve in E n . In particular, we characterize the osculating curves in E n in terms of their curvature functions. Finally, we show that the ratio of the ( n − 1 ) th and ( n − 2 ) th curvatures of the osculating curve is the solution of an ( n − 2 ) th order linear nonhomogeneous differential equation.Item Operator inequalities in reproducing kernel Hilbert spaces(Ankara Üniversitesi, 2022) Yamancı, Ulaş; Other; OtherIn this paper, by using some classical Mulholland type inequality, Berezin symbols and reproducing kernel technique, we prove the power inequalities for the Berezin number b e r ( A ) for some self-adjoint operators A on H ( Ω ) . Namely, some Mulholland type inequality for reproducing kernel Hilbert space operators are established. By applying this inequality, we prove that ( b e r ( A ) ) n ≤ C 1 b e r ( A n ) for any positive operator A on H ( Ω ) .Item Nonoscillation and oscillation criteria for class of higher - order difference equations involving generalized difference operator(Ankara Üniversitesi, 2022) Gevgeşoğlu, Murat; Other; OtherIn this paper, sufficient conditions are obtained for nonoscillation/oscillation of all solutions of a class of higher-order difference equations involving the generalized difference operator of the form Δ k a ( p n Δ 2 a y n ) = f ( n , y n , Δ a y n , Δ 2 a y n , . . . , Δ k + 1 a y n ) , where Δ a is generalized difference operator which is defined as Δ a y n = y n + 1 − a y n , a ≠ 0 .Item Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters(Ankara Üniversitesi, 2022) Öner, Tahsin; Other; OtherIn this paper, some types of fuzzy filters of a strong Sheffer stroke non-associative MV-algebra (for short, strong Sheffer stroke NMV-algebra) are introduced. By presenting new properties of filters, we define a prime filter in this algebraic structure. Then (prime) fuzzy filters of a strong Sheffer stroke NMV-algebra are determined and some features are proved. Finally, we built quotient strong Sheffer stroke NMV-algebra by a fuzzy filter.Item Study strong Sheffer stroke non-associative MV-algebras by fuzzy filters(Ankara Üniversitesi, 2022) Öner, Tahsin; Other; OtherIn this paper, some types of fuzzy filters of a strong Sheffer stroke non-associative MV-algebra (for short, strong Sheffer stroke NMV-algebra) are introduced. By presenting new properties of filters, we define a prime filter in this algebraic structure. Then (prime) fuzzy filters of a strong Sheffer stroke NMV-algebra are determined and some features are proved. Finally, we built quotient strong Sheffer stroke NMV-algebra by a fuzzy filter.Item Split complex bi-periodic Fibonacci and Lucas numbers(Ankara Üniversitesi, 2022) Yılmaz, Nazmiye; Other; OtherThe initial idea of this paper is to investigate the split complex bi-periodic Fibonacci and Lucas numbers by using SCFLN now on. We try to show some properties of SCFLN by taking into account the properties of the split complex numbers. Then, we present interesting relationships between SCFLN.Item On the matrix representation of 5th order Bezier curve and derivatives in E 3(Ankara Üniversitesi, 2022) Kılıçoğlu, Şeyda; Other; OtherUsing the matrix representation form, the first, second, third, fourth, and fifth derivatives of 5th order Bezier curves are examined based on the control points in E 3 . In addition to this, each derivative of 5th order Bezier curves is given by their control points. Further, a simple way has been given to find the control points of a Bezier curves and its derivatives by using matrix notations. An example has also been provided and the corresponding figures which are drawn by Geogebra v5 have been presented in the end.Item Application of the rational (G' /G)-expansion method for solving some coupled and combined wave equations(Ankara Üniversitesi, 2022) Ekici, Mustafa; Other; OtherIn this paper, we explore the travelling wave solutions for some nonlinear partial differential equations by using the recently established rational (G' /G)-expansion method. We apply this method to the combined KdV-mKdV equation, the reaction-diffusion equation and the coupled Hirota-Satsuma KdV equations. The travelling wave solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values, the solitary waves are also derived from the travelling waves. We have also given some figures for the solutions.Item Exponential stability of a Timoshenko type thermoelastic system with Gurtin-Pipkin thermal law and frictional damping(Ankara Üniversitesi, 2022) Fareh, Abdalfeteh; Other; OtherIn this paper we consider a linear thermoelastic system of Timoshenko type where the heat conduction is given by the linearized law of Gurtin-Pipkin. An existence and uniqueness result is proved by the use of a semigroup approach. We establish an exponential stability result without any assumption on the wave speeds once here we have a fully damped system.Item Similar and self-similar null Cartan curves in Minkowski-Lorentzian spaces(Ankara Üniversitesi, 2022) Şimşek, Hakan; Other; OtherIn this paper, differential invariants of null Cartan curves are studied in (n+2) dimensional Lorentzian similarity geometry. The fundamental theorem for a null Cartan curve in similarity geometry is investigated and the characterization of all self-similar null Cartan curves parameterized by de Sitter parameter in Minkowski space-time is given.Item On a nonlinear fuzzy difference equation(Ankara Üniversitesi, 2022) Yalçınkaya, İbrahim; Other; OtherIn this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation z n + 1 = A z n − 1 1 + z p n − 2 , n ∈ N 0 z n+1 = 1+z n−2 p Az n−1 , n∈N 0 where ( z n ) is a sequence of positive fuzzy numbers, A and the initial conditions z − j ( j = 0 , 1 , 2 ) are positive fuzzy numbers and p is a positive integer.Item A numerical method on Bakhvalov-Shishkin mesh for Volterra integro-differential equations with a boundary layer(Ankara Üniversitesi, 2022) Çakır, Hayriye Guckir; Other; OtherWe construct a finite difference scheme for a first-order linear singularly perturbed Volterra integro-differential equation(SPVIDE) on Bakhvalov-Shishkin mesh. For the discretization of the problem, we use the integral identities and deal with the emerging integrals terms with interpolating quadrature rules which also yields remaining terms. The stability bound and the error estimates of the approximate solution are established. Further, we demonstrate that the scheme on Bakhvalov-Shishkin mesh is N(O−1)uniformly convergent, where N is the mesh parameter. The numerical results are also provided for a couple of examples.Item Motions on curves and surfaces using geometric algebra(Ankara Üniversitesi, 2022) Arslan, Selahattin; Matematik; Fen FakültesiGeometric algebra is a useful tool to overcome some problems in kinematics. Thus, the geometric algebra has attracted the attention of many researchers. In this paper, quaternion operators on curves and surfaces in Euclidean 3-space are defined by using geometric algebra. These operators generate the curves or the surfaces from the points, curves or surfaces. Using quaternion operators, we obtain motions that have orbits along the generated curve or surface. Also, these motions are expressed as 1-parameter or 2-parameter homothetic motions.Item q-Meromorphic closed-to-convex functions related with Janowski function(Ankara Üniversitesi, 2022) Sakar, Müge; Other; OtherIn the present paper, we introduce and explore certain new classes of meromorphic functions related with closed-to-convexity and q-calculus. Such results as coefficient estimates, grow the property and partial sums are derived. It is important to mentioned that our results are generalization of number of existing results in literature.Item An investigation on the triple ideal convergent sequences in fuzzy metric spaces(Ankara Üniversitesi, 2022) Gürdal, Mehmet; Other; OtherThe notion of ideal convergence is a process of generalizing of statistical convergence which is dependent on the idea of the ideal I of subsets of the set positive integer numbers. In this study we also present the concept of ideal convergence for triple sequences in fuzzy metric spaces (FMS) in the manner of George and Veeramani and the terms of ideal Cauchy sequence and I ∗ -Cauchy sequence in FMS and study their certain properties.