Cilt:70 Sayı:01 (2021)

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

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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; Other
A 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)).
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.
Set operators and associated functions
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Modak, Shyamapada; Selim, Sk; Other; Other
The 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.
Medical model estimation with particle swarm optimization
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Sarı, Murat; Ahmad, Arshed; Uslu, Hande; Other; Other
In 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.
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.
Univalence criteria of the certain integral operators
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Mustafa, Nizami; Korkmaz, Semra; Other; Other
In this paper, we give some sufficient conditions for the univalence of some integral operators. For this, we use the Becker's and generalized version of the well known Ahlfor's and Becker's univalence criteria.
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.
On the Lipschitz stability of inverse nodal problem for Dirac system
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Yılmaz, Emrah; Kemaloğlu, Hikmet; Other; Other
Inverse 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.
On exponential type P-functions
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Numan, Selim; İşcan, İmdat; Other; Other
In 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.
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.
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.
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.
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; Other
In 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.
On almost Hurewicz property in bitopological spaces
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) CHAUHAN, Harsh Vardhan; SİNGH, Beenu; Other; Other
The purpose of this paper is to investigate properties and results of the almost Hurewicz property in bitopological spaces. We characterize this property using ( i , j ) - regular open sets and almost continuous surjective map.
Some properties of a new class of analytic functions defined via Rodrigues formula
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Gezer, Halil; Kaanoğlu, Cem; Other; Other
In this paper, we introduce and study the new family of analytic functions via Rodrigues formula. Some main properties, the generating function, various recurrence relations and differential properties of these functions are obtained. Furthermore, the differential equations are given for the subclasses of this family of analytic functions.
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.
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 .
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.
The uniform convergence of Fourier series expansions of a Sturm-Liouville problem with boundary condition which contains the eigenparameter
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Göktaş, Sertaç; Maris, Emir Ali; Other; Other
This paper is devoted to investigating the uniform convergence conditions of Fourier series expansions of continuous functions in terms of eigenfunctions of a Sturm-Liouville problem with eigenparameter in one of the boundary conditions on a closed interval. Such problems are quite common in mathematical physics problems.
New fuzzy differential subordinations
(Ankara Üniversitesi Fen Fakültesi, 2021-06-30) Oros, Georgia İ.; Other; Other
In this paper, some new fuzzy differential subordinations obtained by using the integral operator Im γ : An →An introduced in [13] are obtained.

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