Cilt:70 Sayı:01 (2021)
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Item An approach for designing a surface pencil through a given geodesic curve(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Atalay, Günnur Şaffak; Güler, Fatma; Bayram, Ergin; Kasap, Emin; Other; OtherIn the present paper, we propose a new method to construct a surface interpolating a given curve as the geodesic curve of it. Also, we analyze the conditions when the resulting surface is a ruled surface. In addition, developablity along the common geodesic of the members of surface family are discussed. Finally, we illustrate this method by presenting some examples.Item Bivariate Bernstein polynomials that reproduce exponential functions(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Bozkurt, Kenan; Özsaraç, Fırat; Aral, Ali; Other; OtherIn this paper, we construct Bernstein type operators that reproduce exponential functions on simplex with one moved curved side. The operator interpolates the function at the corner points of the simplex. Used function sequence with parameters α and β not only are gained more modeling flexibility to operator but also satisfied to preserve some exponential functions. We examine the convergence properties of the new approximation processes. Later, we also state its shape preserving properties by considering classical convexity. Finally, a Voronovskaya-type theorem is given and our results are supported by graphics.Item Natural and conjugate mates of Frenet curves in three-dimensional Lie group(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Mak, Mahmut; Other; OtherIn this study, we introduce the natural mate and conjugate mate of a Frenet curve in a three dimensional Lie group G with bi-invariant metric. Also, we give some relationships between a Frenet curve and its natural mate or its conjugate mate in G . Especially, we obtain some results for the natural mate and the conjugate mate of a Frenet curve in G when the Frenet curve is a general helix, a slant helix, a spherical curve, a rectifying curve, a Salkowski (constant curvature and non-constant torsion), anti-Salkowski (non-constant curvature and constant torsion), Bertrand curve. Finally, we give nice graphics with numeric solution in Euclidean 3-space as a commutative Lie group.Item Differential geometric aspects of nonlinear Schrödinger equation(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Erdoğdu, Melek; Yavuz, Ayşe; Other; OtherThe main scope of this paper is to examine the smoke ring (or vortex filament) equation which can be viewed as a dynamical system on the space curve in E³. The differential geometric properties the soliton surface accociated with Nonlinear Schrödinger (NLS) equation, which is called NLS surface or Hasimoto surface, are investigated by using Darboux frame. Moreover, Gaussian and mean curvature of Hasimoto surface are found in terms of Darboux curvatures k_{n}, k_{g} and τ_{g.}. Then, we give a different proof of that the s- parameter curves of NLS surface are the geodesics of the soliton surface. As applications we examine two NLS surfaces with Darboux Frame.Item On exponential type P-functions(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Numan, Selim; İşcan, İmdat; Other; OtherIn this paper, we introduce and study the concept of exponential type P-function and establish Hermite-Hadamard's inequalities for this type of functions. In addition, we obtain some new Hermite-Hadamard type inequalities for functions whose first derivative in absolute value is exponential type P-function by using Hölder and power-mean integral inequalities. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula and for some inequalities related to special means of real numbers.Item Best proximity point theorems for proximal b-cyclic contractions on b-metric spaces(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Aslantaş, Mustafa; Other; OtherIn this paper, we first introduce a new notion of the property (M_{C}) to improve and generalize the property (G_{C}). After that, we present two new concepts, proximal b-cyclic contraction of first type and second type, on b-metric spaces. Then, we obtain two best proximity point results for such mappings in the frameworks of best proximally complete b-metric spaces by using the property (M_{C}). Hence, we generalize some results existing in the literature. Finally, we present some illustrative and interesting examples.Item Medical model estimation with particle swarm optimization(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Sarı, Murat; Ahmad, Arshed; Uslu, Hande; Other; OtherIn this paper, a nonlinear medical model based on observational variables has been produced and the particle swarm optimization (PSO) technique, which is an effective technique to predict optimum parameters of the biomedical model, has been used. This study has been conducted on a dataset consisting of 539 subjects. For comparison purposes, nonlinear regression analysis, nonlinear deep learning, and nonlinear regression neural network methods are also considered and the PSO results appear to be slightly better than that of other methods. Built on observational variables and findings, the model is expected to be a good guide for healthcare professionals in diagnosing pathologies and planning treatment programs for their patients. It is therefore strongly believed that the article will be particularly useful for those interested in emerging biomedical models in various medical modelling areas such as infectious and hematological diseases such as anemia.Item Set operators and associated functions(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Modak, Shyamapada; Selim, Sk; Other; OtherThe study of two operators local function and the set operator ψ on the ideal topological spaces are likely to be same to the study of closure and interior operator of the topological spaces. However, they are not exactly equal with the interior and closure operator of the topological spaces. In this context, we introduce two new set operators on the ideal topological spaces. Detail properties of these two operators are the part of this article. Furthermore, the operators interior (resp. ψ ) and closure (local function) obey the relation I n t ( A ) = X \ C l (X \ A) (resp. ψ (A) = X \(X \A) ∗ ) . We search the general method of these relations, through this manuscript.Item Intuitionistic fuzzy hypersoft sets(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Yolcu, Adem; SMARANDACHE, Florentin; Öztürk, Taha Yasin; Other; OtherIn this paper, a new environment namely, intuitionistic fuzzy hypersoft set (IFHSS) is defined. We introduce some fundamental operators of intuitionistic fuzzy hypersoft sets such as subset, null set, absolute set, complement, union, intersection, equal set etc. Validity and application are presented with appropriate examples. For greater precision and accuracy, in the future, proposed operations in decision making processes such as personal selection, management issues and others will play a vital role.Item Implementation of computation formulas for certain classes of Apostol-type polynomials and some properties associated with these polynomials(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Küçükoğlu, İrem; Other; OtherThe main purpose of this paper is to present various identities and computation formulas for certain classes of Apostol-type numbers and polynomials. The results of this paper contain not only the λ -Apostol-Daehee numbers and polynomials, but also Simsek numbers and polynomials, the Stirling numbers of the first kind, the Daehee numbers, and the Chu-Vandermonde identity. Furthermore, we derive an infinite series representation for the λ -Apostol-Daehee polynomials. By using functional equations containing the generating functions for the Cauchy numbers and the Riemann integrals of the generating functions for the λ -Apostol-Daehee numbers and polynomials, we also derive some identities and formulas for these numbers and polynomials. Moreover, we give implementation of a computation formula for the λ -Apostol-Daehee polynomials in Mathematica by Wolfram language. By this implementation, we also present some plots of these polynomials in order to investigate their behaviour some randomly selected special cases of their parameters. Finally, we conclude the paper with some comments and observations on our results.Item Implementation of DRBEM for the determination of the heat flux in an inverse problem(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Alsoy-Akgün, Negehan; Other; OtherA numerical investigation of inverse unsteady natural convection flow in a square cavity filled with C u − water nanofluid is performed. In the direct problem, the enclosure is bounded by one isothermally heated vertical wall at temperature Tm and by three adiabatic walls. In the inverse problem, the enclosure is bounded by right hostile wall on which no boundary condition can be prescribed or measured and by left accessible wall on which both the boundary temperature and heat flux data are overspecified. The dual reciprocity boundary element method (DRBEM) with the fundamental solutions of Laplace and modified Helmholtz equations is used for the solutions of direct and inverse problems. Inhomogeneities are approximated with radial basis functions. Computations are performed for several values of Rayleigh number (Ra), solid volume fraction (φ) and percentage of noise (ρ), and accurate and stable results are given for three forms of heat flux namely, steady heat flux (q=q(y)), time dependent uniform heat flux (q=q(t)) and non-uniform time dependent heat flux (q=q(y,t)).Item Lump-type solutions of a new extended (3+1)-dimensional nonlinear evolution equation(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Yıldırım, Yakup; Yaşar, Emrullah; Other; OtherIn this paper, we study lump-type solutions to a new extended (3+1)-dimensional nonlinear evolution equation which appears in the field of wave propagation in the nonlinear systems. We generate these types of solutions by considering the prime number p = 3 of the generalized Hirota bilinear operators. With the help of Maple symbolic computations, we retrieve twenty-two classes of lump-type solutions which are a special kind of rational function solutions, localized in all directions in the space and describe various dispersive wave phenomena. These lump-type solutions are derived from positive quadratic function solutions by using the generalized Hirota bilinear form of the considered model. The lump solutions are recovered along with the existence conditions: Analyticity, positivity and localization in all directions. The required conditions of the analyticity and positivity of the solutions can be easily achieved by taking special choices of the involved parameters. The main ingredients for this scheme are to recover the Hirota bilinear forms and their generalized equivalences. Lastly, the graphical simulations of the exact solutions are depicted.Item On the lifts of F_{a}(5,1)-structure on tangent and cotangent bundle(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) JABRAİLZADE, Fidan; Other; OtherThis paper consist of three main sections. In the first part, we obtain the complete lifts of the F_{a}(5,1)-structure on tangent bundle. We have also obtained the integrability conditions by calculating the Nijenhuis tensors of the complete lifts of F_{a}(5,1)-structure. Later we get the conditions of to be the almost holomorfic vector field with respect to the complete lifts of F_{a}(5,1)- structure. Finally, we obtained the results of the Tachibana operator applied to the vector fields with respect to the complete lifts of F_{a}(5,1)-structure on tangent bundle. In the second part, all results obtained in the first section investigated according to the horizontal lifts of F_{a}(5,1)-structure in tangent bundle T(Mⁿ). In finally section, all results obtained in the first and second section were investigated according to the horizontal lifts of the F_{a}(5,1)- structure in cotangent bundle T^{∗}(Mⁿ).Item Chebyshev type inequalities with fractional delta and nabla h-sum operators(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Aslıyüce, Serkan; Güvenilir, Ayşe Feyza; Matematik; Fen FakültesiThe aim of this study is to establish new discrete inequalities for synchronous functions using fractional order delta and nabla h-sum operators. We give examples to illustrate our results.Item On the Lipschitz stability of inverse nodal problem for Dirac system(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Yılmaz, Emrah; Kemaloğlu, Hikmet; Other; OtherInverse nodal problem on Dirac operator is determination problem of the parameters in the boundary conditions, number m and potential function V by using a set of nodal points of a component of two component vector eigenfunctions as the given spectral data. In this study, we solve a stability problem using nodal set of vector eigenfunctions and show that the space of all V functions is homeomorphic to the partition set of all space of asymptotically equivalent nodal sequences induced by an equivalence relation. Moreover, we give a reconstruction formula for the potential function as a limit of a sequence of functions and associated nodal data of one component of vector eigenfunction. Our technique depends on the explicit asymptotic expressions of the nodal parameters and, it is basically similar to [1, 2] which is given for Sturm-Liouville and Hill's operators, respectively.Item Determination of a time-dependent potential in a Rayleigh-Love equation with non-classical boundary condition(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Tekin, İbrahim; Other; OtherMathematical model of the longitudinal vibration of bars includes higher-order derivatives in the equation of motion under considering the effect of the lateral motion of a relatively thick bar. This paper considers such an inverse coefficient problem of determining time-dependent potential of a linear source together with the unknown longitudinal displacement from a Rayleigh-Love equation (containing the fourth-order space derivative) by using an additional measurement. Existence and uniqueness theorem of the considered inverse coefficient problem is proved for small times by using contraction principle.Item A metric formula on a quotient space which is related to the sequence space Σ 2(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Saltan, Mustafa; Aslan, Nisa; Other; OtherIn this paper, we first define an equivalence relation on the sequence space Σ 2 . Then we equip the quotient set Σ 2 / ∼ with a metric d 1 . We also determine an isometry map between the metric spaces ( Σ 2 / ∼ , d 1 ) and ( [ 0 , 1 ] , d e u c l ) . Finally, we investigate the symmetry conditions with respect to some points on the metric space ( Σ 2 / ∼ , d 1 ) and we compare truncation errors for the computations which is obtained by the metrics d e u c l and d 1 .Item Existence and decay of solutions for a higher-order viscoelastic wave equation with logarithmic nonlinearity(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Pişkin, Erhan; Irkıl, Nazlı; Other; OtherThe main goal of this paper is to study for the local existence and decay estimates results for a high-order viscoelastic wave equation with logarithmic nonlinerity. We obtain several results: Firstly, by using Feado-Galerkin method and a logaritmic Sobolev inequality, we proved local existence of solutions. Later, we proved general decay results of solutions.Item A study on the modeling and simulation for the motor unit action potential(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Özbek, Levent; Temuçin, Çağrı; Cengiz, Bülent; İstatistik; Fen FakültesiElectromyography (EMG) is a technique that gives information about the neuromuscular pattern and function which is commonly-used in the practice of neurology. With this method, the signals obtained from the muscle cells using an amplificatore are enhanced to an amount enough to study on. The potentials monitored are called Motor Unit Action Potentials (MUAPs). In this study, the findings gathered by the simulation using the dipole model for the motor unit action potential (MUAP) have been evaluated. With the motor unit modeling and simulation, the effect of different anatomic characteristics of nerves and muscles on MUAP and EMG signals may be examined. It is not possible to perform such an action empirically. The modeling and simulation for MUAP and EMG also provides a good opportunity of practicing and studying for those who started recently and wish to learn EMG. In the simulation made using the dipole model, the variables such as the diameter and distribution of muscle fibers and the location of motor end-plate area have been studied; and the effect of these variables on the formation of MUAP has been analyzed. The result of the study has suggested that the MUAP simulation with the dipole and line source model was a proper tool to understand the physiology of MUAP and the pathological processes. Reliability and efficiency on diagnosing muscle and nerve disorders using electromyography (EMG) are essential points. We analyze the dipole and line-source model for modeling muscular action potential (AP).Item Deferred Nörlund statistical relative uniform convergence and Korovkin-type approximation theorem(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Demirci, Kamil; Dirik, Fadime; Yıldız, Sevda; Other; OtherIn this paper, we define the concept of statistical relative uniform convergence of the deferred Nörlund mean and we prove a general Korovkin-type approximation theorem by using this convergence method. As an application, we use classical Bernstein polynomials for defining an operator that satisfies our new approximation theorem but does not satisfy the theorem given before. Additionally, we estimate the rate of convergence of approximating positive linear operators by means of the modulus of continuity.