Cilt:70 Sayı:02 (2021)

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https://dspace.ankara.edu.tr/handle/20.500.12575/86251

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The Lomax-Lindley distribution: properties and applications to lifetime data
(Ankara Üniversitesi, 2021) Tarvirdizade, Bahman; Other; Other
This paper introduces a new three-parameter distribution which is obtained by combining the Lomax and Lindley distributions in a serial system and is called the Lomax-Lindley distribution. The new distribution is quite flexible to model lifetime data. This distribution provides a simple form for hazard rate function which can be increasing, decreasing, bathtub-shaped and unimodal for different choices of the parameter values. Some statistical properties of the Lomax-Lindley distribution such as quantiles, moments, order statistics, Renyi entropy and mean deviations are discussed. The maximum likelihood estimators of its unknown parameters are obtained and the approximate confidence intervals of the parameters are provided. A Monte Carlo simulation study is conducted to investigate the performance of the maximum likelihood estimators and their corresponding confidence intervals. Finally, two real data sets having bathtub-shaped and unimodal hazard rate functions are analyzed and it is shown that the proposed distribution can provide a better fit than other distributions for both lifetime data.
A note on the generating sets for the mapping class groups
(Ankara Üniversitesi, 2021) Dalyan, Elif; Other; Other
In this short note, we obtain generating sets with two elements for the mapping class group of closed, oriented surfaces of genus three and four, containing elements of the lowest order known so far.
A variant of the proof of Van der Waerden's theorem by Furstenberg
(Ankara Universitesi, 2021) Özkurt, Ali Aslan; Other; Other
Let R be a commutative ring with identity. In this paper, for a given monotone decreasing positive sequence and an increasing sequence of subsets of R, we will define a metric on R using them. Then, we will use this kind of metric to obtain a variant of the proof of Van der Waerden's theorem by Furstenberg [3].
A generalization of purely extending modules relative to a torsion theory
(Ankara Universitesi, 2021) Doğruöz, Semra; Other; Other
In this work we introduce a new concept, namely, τ s -extending modules (rings) which is torsion-theoretic analogues of extending modules and then we extend many results from extending modules to this new concept. For instance we show that for any ring R with unit, if R R is purely τ s -extending if and only if every cyclic τ -nonsingular R -module is flat. Also, we make a classification for the direct sums of the rings to be purely τ s -extending.
Some properties of convolution in symmetric spaces and approximate identity
(Ankara Üniversitesi, 2021) Hashimov, Chingiz; Other; Other
This paper deals with the symmetric space of functions and its subspace where continuous functions are dense is considered. Main properties of convolution which plays a vital role in harmonic analysis, as in other areas of mathematics are established in this space. Following the classical case, it is proved that the convolution can be approximated by linear combinations of shifts in a subspace of the considered space. An approximate identity for the convolution is also considered in that subspace.
On certain subclass of univalent functions of complex order associated with Pascal distribution series
(Ankara Üniversitesi, 2021) Şeker, Bilal; Other; Other
In this study, by establishing a connection between normalized univalent functions in the unit disc and Pascal distribution series, we have obtained the necessary and sufficient conditions for these functions to belong to some subclasses of univalent functions of complex-order. We also determined some conditions by considering the integral operator for these functions.
Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations
(Ankara Üniversitesi, 2021) Yılmaz, Abdullah; Other; Other
The inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce a circular distribution based on an existing linear model. By the genesis of the ISP method, many important circular models have been provided by many researchers. In this study, we propose a new symmetric unimodal/bimodal circular distribution by the rotated ISP method considering the hyperbolic secant distribution as a baseline distribution. Rotation means that fixing the origin and rotating all other points the same amount counterclockwise. Considering the effect of rotation on the circular distribution to be obtained with the bilinear transformation, it is seen that it actually induces a location parameter in the obtained circular probability distribution. We analyze some of the stochastic properties of the proposed distribution. The methods for the parameter estimation of the new circular model and the simulation-based compare results of these estimators are extensively provided by the paper. Furthermore, we compare the fitting performance of the new model according to its well-known symmetric alternatives, such as Von-Misses, and wrapped Cauchy distributions, on a real data set. From the information obtained by the analysis on the real data, we say that the fitting performance of the new distribution is better than its alternatives according to the criteria frequently used in the literature.
The triple zero graph of a commutative ring
(Ankara Üniversitesi, 2021) Çelikel, Ece Yetkin; Other; Other
Let R be a commutative ring with non-zero identity. We define the set of triple zero elements of R by T Z ( R ) = { a ∈ Z ( R ) ∗ : there exists b , c ∈ R ∖ { 0 } such that a b c = 0 , a b ≠ 0 , a c ≠ 0 , b c ≠ 0 } . In this paper, we introduce and study some properties of the triple zero graph of R which is an undirected graph T Z Γ ( R ) with vertices T Z ( R ) , and two vertices a and b are adjacent if and only if a b ≠ 0 and there exists a non-zero element c of R such that a c ≠ 0 , b c ≠ 0 , and a b c = 0 . We investigate some properties of the triple zero graph of a general ZPI-ring R , we prove that d i a m ( T Z Γ ( R ) ) ∈ { 0 , 1 , 2 } and g r ( G ) ∈ { 3 , ∞ } .
S - δ -connectedness in S -proximity spaces
(Ankara Üniversitesi, 2021) Sing, Beenu; Other; Other
New types of connectedness in S -proximity spaces, named as an S - δ -connectedness, local S - δ -connectedness are introduced. Also, their inter-relationships are studied. In an S -proximity space ( X , δ X ) , the S - δ -connectedness of a subset U of X with respect to δ X may not be same as the S - δ -connectedness of U with respect to its subspace proximity δ U . Further, S - δ -component and S - δ -treelike spaces are also defined and a number of results are given.
An extension of trapezoid inequality to the complex integral
(Ankara Universitesi, 2021) Dragomir, Sever; Other; Other
In this paper we extend the trapezoid inequality to the complex integral by providing upper bounds for the quantity | ( v − u ) f ( u ) + ( w − v ) f ( w ) − ∫ γ f ( z ) d z | under the assumptions that γ is a smooth path parametrized by z ( t ) , t ∈ [ a , b ] , u = z ( a ) , v = z ( x ) with x ∈ ( a , b ) and w = z ( b ) while f is holomorphic in G , an open domain and γ ∈ G . An application for circular paths is also given.
Logarithmic coefficients of starlike functions connected with k-Fibonacci numbers
(Ankara Üniversitesi, 2021) Bulut, Serap; Other; Other
Let A denote the class of analytic functions in the open unit disc U normalized by f ( 0 ) = f ′ ( 0 ) − 1 = 0 , and let S be the class of all functions f ∈ A which are univalent in U . For a function f ∈ S , the logarithmic coefficients δ n ( n = 1 , 2 , 3 , … ) are defined by log f ( z ) z = 2 ∑ ∞ n = 1 δ n z n ( z ∈ U ) . and it is known that | δ 1 | ≤ 1 and | δ 2 | ≤ 1 2 ( 1 + 2 e − 2 ) = 0 , 635 ⋯ . The problem of the best upper bounds for | δ n | of univalent functions for n ≥ 3 is still open. Let S L k denote the class of functions f ∈ A such that z f ′ ( z ) f ( z ) ≺ 1 + τ 2 k z 2 1 − k τ k z − τ 2 k z 2 , τ k = k − √ k 2 + 4 2 ( z ∈ U ) . In the present paper, we determine the sharp upper bound for | δ 1 | , | δ 2 | and | δ 3 | for functions f belong to the class S L k which is a subclass of S . Furthermore, a general formula is given for | δ n | ( n ∈ N ) as a conjecture.
The existence of the bounded solutions of a second order nonhomogeneous nonlinear differential equation
(Ankara Üniversitesi, 2021) Büyükkahraman, Mehtap Falcı; Other; Other
In this paper, we consider a second order nonlinear differential equation and establish two new theorems about the existence of the bounded solutions of a second order nonlinear differential equation. In these theorems, we use different Lyapunov functions with different conditions but we get the same result. In addition, two examples are given to support our results with some figures.
Some fixed point theorems on complex valued modular metric spaces with an application
(Ankara Üniversitesi, 2021) Özkan, Kübra; Other; Other
In this article, we introduce the notion of complex valued modular metric spaces. We also a prove generalization of Banach Fixed Point Theorem, which is one of the most simple and significant tests for existence and uniqueness of solution of problems arising in mathematics and engineering for complex valued modular metric spaces. In addition, we express some results related to these spaces. Finally, we give an application of our results to digital programming.
Comparison of different estimation methods for the inverse weighted Lindley distribution
(Ankara Universitesi, 2021) Balav, İklim Gedik; Other; Other
In this paper, different estimation methods are considered for the parameters of the inverse weighted Lindley (IWL) distribution introduced by Ramos et al.(2019). Parameters of the IWL are estimated by the method of maximum likelihood (ML), least squares (LS), weighted least squares (WLS), Cram´er-von Mises (CVM) and Anderson Darling (AD). The performances of the estimators are compared using Monte Carlo simulation study via bias, mean square error and deficiency (Def) criteria. Finally, a real data set is analyzed for illustrative purposes.
hesitant fuzzy sets, hesitant fuzzy topology, hesitant fuzzy interior, hesitant fuzzy closure, hesitant fuzzy subspaces
(Ankara Üniversitesi, 2021) Kızılsu, Aysun Selçuk; Matematik; Fen Fakültesi
Integral inequalities are very important in applied sciences. Chebyshev's integral inequality is widely used in applied mathematics. First of all, some necessary definitions and results regarding conformable derivative are given in this article. Then we give Chebyshev inequality for simultaneously positive (or negative) functions using the conformable fractional derivative. We used the Gronwall inequality to prove our results, unlike other studies in the literature.
A new approach to the bi-univalent analytic functions connected with q-analogue of Noor integral operator
(Ankara Üniversitesi, 2021) Akgül, Arzu; Other; Other
Recently, q-analogue of Noor integral operator and other special operators became importance in the field of Geometric Function Theory. In this study, by connecting this operators and the principle of subordination we introduced an interesting class of bi-univalent functions and obtained coefficient estimates for this new class.
A new subclass of meromorphic functions defined by Rapid operator
(Ankara Üniversitesi, 2021) Wankatesvarlu, B.; Other; Other
We present and investigate a new subclass of meromorphic univalent functions described by the Rapid operator in this study. Coefficient inequalities is discussed, as well as distortion properties, closure theorems, Hadamard product. After this, integral transforms for the class ∑ ∗ ( ϑ , ϱ , ℘ , θ , μ ) are obtained.
Approximation by truncated Lupaş operators of max-product kind
(Ankara Üniversitesi, 2021) Örkçü, Mediha; Other; Other
The goals of the present paper are to introduce truncated Lupaş type operators of max-product kind and give an estimation for the degree of approximation with respect to first modulus of continuity function. We prove that this estimate can not be improved; on the other hand, for some subclasses of functions, better degree of approximation is obtained. We also showed the piecewise convexity of the constructed operators on the interval [0,1].
Hypersurface families with Smarandache curves in Galilean 4-space
(Ankara Üniversitesi, 2021) Aydın, Mustafa; Other; Other
In this paper, we study the hypersurface families with Smarandache curves in 4-dimensional Galilean space G4 and give the conditions for different Smarandache curves to be parameter and the curve which generates the Smarandache curves is geodesic on a hypersurface in G4. Also, we investigate three types of marching-scale functions for one of these hypersurfaces and construct an example for it.
On the reliability characteristics of the standard two-sided power distribution
(Ankara Üniversitesi, 2021) Çetinkaya, Çağatay; Other; Other
In this study, the standard two-sided power (STSP) distribution is considered with regard to statistical reliability analysis in detail. For this purpose, along with the reliability and hazard functions of the distribution, particular reliability indices that are useful in maintenance and replacement policies are obtained and they are evaluated with their plots. The STSP distribution is classified based on aging according to various cases of its parameters. Then, we studied the classical and Bayesian estimations of the reliability and hazard functions. In Bayesian estimation, symmetric and different asymmetric loss functions are considered. For obtaining the Bayes estimates, Monte Carlo Markov Chain simulation using the Gibbs algorithm is performed. Various simulation schemes are performed for comparing the performances of the estimators. Further, the Bayesian predictions of the future observations based on the observed samples are obtained. A real data example is used to illustrate the theoretical outcomes.

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