Cilt:70 Sayı:01 (2021)

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https://dspace.ankara.edu.tr/handle/20.500.12575/76441

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A classification of ( k , μ ) ′ -almost Kenmotsu manifolds admitting Cotton tensor
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) DEY, Dibakar; MAJHİ, Pradip; Other; Other
The object of the present paper is to classify ( k , μ ) ′ -almost Kenmotsu manifolds admitting Cotton tensors. We characterize ( k , μ ) ′ -almost Kenmotsu manifolds with vanishing and parallel Cotton tensors. Beside this, ( k , μ ) ′ -almost Kenmotsu manifolds satisfying Cotton semisymmetry and Q ( g , C ) = 0 are studied. Further, Cotton pseudo-symmetric ( k , μ ) ′ -almost Kenmotsu manifolds are classified.
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; Other
In 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 .
A new lifetime distribution: transmuted exponential power distribution
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Saraçoğlu, Buğra; Tanış, Caner; Other; Other
In this study, a new statistical distribution called as Transmuted Exponential Power distribution using the quadratic rank transmutation map introduced by Shaw and Buckley [23,24] is suggested. The various mathematical and statistical properties of this distribution are examined. The method of maximum likelihood estimation has been used to estimate the unknown parameters of this distribution. Moreover, real data analysis is used to compare this new distribution with other some distributions using some goodness of fit measures.
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 Fakültesi
Electromyography (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).
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; Other
In 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.
Best proximity point theorems for proximal b-cyclic contractions on b-metric spaces
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Aslantaş, Mustafa; Other; Other
In 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.
Best proximity point theory on vector metric spaces
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Şahin, Hakan; Other; Other
In this paper, we first give a new definition of Ω-Dedekind complete Riesz space (E,≤) in the frame of vector metric space (Ω,ρ,E) and we investigate the relation between Dedekind complete Riesz space and our new concept. Moreover, we introduce a new contraction so called α-vector proximal contraction mapping. Then, we prove certain best proximity point theorems for such mappings in vector metric spaces (Ω,ρ,E) where (E,≤) is Ω-Dedekind complete Riesz space. Thus, for the first time, we acquire best proximity point results on vector metric spaces. As a result, we generalize some fixed point results proved in both vector metric spaces and partially ordered vector metric spaces such as main results of V4. Further, we provide nontrivial and comparative examples to show the effectiveness of our main results.
Bipolar fuzzy soft D-metric spaces
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Dalkılıç, Orhan; Demirtaş, Naime; Other; Other
The first aim to this paper is to introduce the notions of bipolar fuzzy soft metric space and bipolar fuzzy soft (D-)metric space. In order to define these concepts, the concept of bipolar fuzzy soft points has been brought to the literature and bipolar fuzzy soft points have been examined in detail. Moreover, the bipolar fuzzy soft sequences and bipolar fuzzy soft cauchy sequences were defined and some of their properties were examined. In addition to all this, many examples are given in order to better understand the concepts and features studied and contribute to a better understanding of the paper.
Bivariate Bernstein polynomials that reproduce exponential functions
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Bozkurt, Kenan; Özsaraç, Fırat; Aral, Ali; Other; Other
In 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.
Bootstrap based multi-step ahead joint forecast densities for financial interval-valued time series
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Beyaztaş, Beste Hamiye; Other; Other
This study presents two interval-valued time series approaches to construct multivariate multi-step ahead joint forecast regions based on two bootstrap algorithms. The first approach is based on fitting a dynamic bivariate system via a VAR process for minimum and maximum of the interval while the second approach applies for mid-points and half-ranges of interval-valued time series. As a novel perspective, we adopt two bootstrap techniques into the proposed interval-valued time series approaches to obtain joint forecast regions of the lower/upper bounds of the intervals. The forecasting performances of the proposed approaches are evaluated by extensive Monte Carlo simulations and two real-world examples: (i) monthly S&P 500 stock indices; (ii) monthly USD/SEK exchange rates. Our results demonstrate that the proposed approaches are capable of producing valid multivariate forecast regions for interval-valued time series.
Change-constrained stochastic programming problem with normal, t and skew normal, skew t distributions
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) İnan, Gültaç Eroğlu; İstatistik; Fen Fakültesi
In this paper, a change constrained optimization programming problem is studied under the assumption that the model coe¢ cients in the inequalities defned as random variables are independent and assumed to be Normal, t; Non Normal Skew distributions; Skew Normal and Skew t distributions. The Hulkursar method transform the stochastic programming problem into a non-linear deterministic problem is used in the study. The most common distribution in CCSP is the Normal Distribution; but the real world problems always may not include normality. Therefore; in the practice stage, an application that the aij technologic coefficient and the bi right side values in the inequalities have both Normal, t; Skew Normal and Skew t distributions is given. Finally the obtained results have been compared.
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 Fakültesi
The 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.
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; Other
In 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.
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; Other
Mathematical 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.
Differential geometric aspects of nonlinear Schrödinger equation
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Erdoğdu, Melek; Yavuz, Ayşe; Other; Other
The 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.
Dual-complex generalized k-Horadam numbers
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Köme, Sure; Köme, Cahit; Yazlık, Yasin; Other; Other
The purpose of this paper is to provide a broad overview of the generalization of the various dual-complex number sequences, especially in the disciplines of mathematics and physics. By the help of dual numbers and dual-complex numbers, in this paper, we define the dual-complex generalized k-Horadam numbers. Furthermore, we investigate the Binet formula, generating function, some conjugation identities, summation formula and a theorem which is generalization of the Catalan's identity, Cassini's identity and d'Ocagne's identity.
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; Other
The 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.
Green's function for impulsive periodic solutions in alternately advanced and delayed differential systems and applications
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) CHİU, Kuo-shou; Other; Other
In this paper we investigate the existence of the periodic solutions of a nonlinear impulsive differential system with piecewise alternately advanced and retarded arguments, in short IDEPCAG, that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such system are obtained. In the process we use the Green's function for impulsive periodic solutions and convert the given the IDEPCAG into an equivalent integral equation system. Then we construct appropriate mappings and employ Krasnoselskii's fixed point theorem to show the existence of a periodic solution of this type of nonlinear impulsive differential systems. We also use the contraction mapping principle to show the existence of a unique impulsive periodic solution. Appropriate examples are given to show the feasibility of our results.
Hermite-Hadamard-Fejér inequalities for double integrals
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Other; Other
In this paper, we first obtain Hermite-Hadamard-Fejer inequalities for co-ordinated convex functions in a rectangle from the plane R2. Moreover, we give the some refinement of these obtained Hermite-Hadamard-Fejer inequalities utilizing two mapping. The inequalities obtained in this study provide generalizations of some result given in earlier works.
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; Other
The 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.

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