TR-Dizin İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.14720/5

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The Complementary Nabla Bennett-Leindler Type Inequalities
(Ankara Univ, Fac Sci, 2022) Kayar, Zeynep; Kaymakcalan, Billur
We aim to find the complements of the Bennett-Leindler type inequalities in nabla time scale calculus by changing the exponent from 0 < zeta < 1 to zeta > 1. Different from the literature, the directions of the new inequalities, where zeta > 1, are the same as that of the previous nabla Bennett-Leindler type inequalities obtained for 0 < zeta < 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.
Implementation of Drbem for the Determination of the Heat Flux in an Inverse Problem
(Ankara Univ, Fac Sci, 2021) Alsoy Akgun, Nagehan
A numerical investigation of inverse unsteady natural convection flow in a square cavity filled with Cu-water nanofluid is performed. In the direct problem, the enclosure is bounded by one isothermally heated vertical wall at temperature T-m 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 (phi) and percentage of noise (rho), 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)).
Introduction To Temporal Intuitionistic Fuzzy Approximate Reasoning
(Ankara Univ, Fac Sci, 2020) Kutlu, Fatih; Tugrul, Feride; Citil, Mehmet
In this study; temporal intuitionistic fuzzy negation, temporal intuitionistic fuzzy triangular norm and temporal intuitionistic fuzzy triangular conorm have been researched. The aim of this study is to define negator, t-norm and t-conorms, which is the generalization of negation, conjunctions and disconjunctions in the temporal intuitionistic fuzzy sets and to examine the De Morgan relations between these concepts. The thing to note here is that conjunctions generalized with t-norm and t-conorm is changed depending on time. We will carry concept of implication and coimplication to temporal intuitionistic fuzzy sets. With the new implication definitions, a causal structure will be established which will match the variable structure of the systems depending on the position and time variables. It is evident that successful results will be achieved in this type of system, which is being dealt with by this new structure.
A Numerical Method on Bakhvalov Shishkin Mesh for Volterra Integro-Differential Equations With A Boundary Layer
(Ankara Univ, Fac Sci, 2022) Guckir Cakir, Hayriye; Cakir, Firat; Cakir, Musa
We 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 O(N-1) uniformly convergent, where N is the mesh parameter. The numerical results are also provided for a couple of examples.
A Numerical Solution Study on Singularly Perturbed Convection-Diffusion Nonlocal Boundary Problem
(Ankara Univ, Fac Sci, 2019) Arslan, Derya; Cakir, Musa
This important numerical method is given for the numerical solution of singularly perturbed convection-diffusion nonlocal boundary value problem. First, the behavior of the exact solution is analyzed, which is needed for analysis of the numerical solution in later sections. Next, uniformly convergent finite difference scheme on a Shishkin mesh is established, which is based on the method of integral identities with the use exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. It is shown that the method is first order accurate expect for a logarithmic factor, in the discrete maximum norm. Finally, the numerical results are presented in table and graphs, and these results reveal the validity of the theoretical results of our method.
Parameter Uniform Second-Order Numerical Approximation for the Integro-Differential Equations Involving Boundary Layers
(Ankara Univ, Fac Sci, 2022) Durmaz, Muhammet Enes; Cakir, Musa; Amirali, Gabil
The work handles a Fredholm integro-differential equation involv-ing boundary layers. A fitted second-order difference scheme has been created on a uniform mesh utilizing interpolating quadrature rules and exponential basis functions. The stability and convergence of the proposed discretization technique are analyzed and one example is solved to display the advantages of the presented technique.
A Second-Order Numerical Method for Pseudo-Parabolic Equations Having Both Layer Behavior and Delay Parameter
(Ankara Univ, Fac Sci, 2024) Gunes, Baransel; Duru, Hakki
In this paper, singularly perturbed pseudo-parabolic initial-boundary value problems with time-delay parameter are considered by numerically. Initially, the asymptotic properties of the analytical solution are investigated. Then, a discretization with exponential coefficient is suggested on a uniform mesh. The error approximations and uniform convergence of the presented method are estimated in the discrete energy norm. Finally, some numerical experiments are given to clarify the theory.
Statistical Inference for Geometric Process With the Rayleigh Distribution
(Ankara Univ, Fac Sci, 2019) Bicer, Cenker; Bicer, Hayrinisa Demirci; Kara, Mahmut; Aydogdu, Halil
The aim of this study is to investigate the solution of the statistical inference problem for the geometric process (GP) when the distribution of first occurrence time is assumed to be Rayleigh. Maximum likelihood (ML) estimators for the parameters of GP, where a and lambda are the ratio parameter of GP and scale parameter of Rayleigh distribution, respectively, are obtained. In addition, we derive some important asymptotic properties of these estimators such as normality and consistency. Then we run some simulation studies by different parameter values to compare the estimation performances of the obtained ML estimators with the non-parametric modified moment (MM) estimators. The results of the simulation studies show that the obtained estimators are more efficient than the MM estimators.
A Study on Comparisons of Bayesian and Classical Parameter Estimation Methods for the Two-Parameter Weibull Distribution
(Ankara Univ, Fac Sci, 2020) Yilmaz, Asuman; Kara, Mahmut; Aydogdu, Halil
The main objective of this paper is to determine the best estimators of the shape and scale parameters of the two parameter Weibull distribution. Therefore, both classical and Bayesian approximation methods are considered. For parameter estimation of classical approximation methods maximum likelihood estimators (MLEs), modified maximum likelihood estimators-I (MMLEs-I), modified maximum likelihood estimators-II (MMLEs-II), least square estimators (LSEs), weighted least square estimators (WLSEs), percentile estimators (PEs), moment estimators (MEs), L-moment estimators (LMEs) and TL-moment estimators (TLMEs) are used. Since the Bayesian estimators don't have the explicit form. There are Bayes estimators are obtained by using Lindley's and Tierney Kadane's approximation methods in this study. In Bayesian approximation, the choice of loss function and prior distribution is very important. Hence, Bayes estimators are given based on both the non-informative and informative prior distribution. Moreover, these estimators have been calculated under different symmetric and asymmetric loss functions. The performance of classical and Bayesian estimators are compared with respect to their biases and MSEs through a simulation study. Finally, a real data set taken from Turkish State Meteorological Service is analysed for better understanding of methods presented in this paper.
Upper Bounds for the Blow Up Time for the Kirchhoff-Type Equation
(Ankara Univ, Fac Sci, 2023) Dinc, Yavuz; Piskin, Erhan; Tunc, Cemil
. In this research, we take into account the Kirchhoff type equation with variable exponent. The Kirchhoff type equation is known as a kind of evolution equations,namely, PDEs, where t is an independent variable. This type problem can be extensively used in many mathematical models of various applied sciences such as flows of electrorheological fluids, thin liquid films, and so on. This research, we investigate the upper bound for blow up time under suitable conditions.

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