Cilt:70 Sayı:02 (2021)

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

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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.
A graph associated to a commutative semiring
(Ankara Üniversitesi, 2021) Khoramdel, Mehdi; Other; Other
Let R be a commutative finite semiring with nonzero identity and H be an arbitrary multiplicatively closed subset R. The generalized identity-summand graph of R is the (simple) graph GH(R) with all elements of R as the vertices, and two distinct vertices x and y are adjacent if and only if x+y∈H. In this paper, we study some basic properties of GH(R). Moreover, we characterize the planarity, chromatic number, clique number and independence number of GH(R).
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.
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 revised generalized F-test for testing the equality of group means under non-normality caused by skewness
(Ankara Üniversitesi, 2021) Çavuş, Mustafa; Other; Other
The non-normality may occur in the data due to several reasons such as the presence of the outlier or skewness. It leads to lose the power and fail to control Type I error probability of the tests which are used to test the equality of the group means under heteroscedasticity. To overcome this problem, a revised generalized F-test (RGF) is proposed to test the equality of group means under heteroscedasticity in which non-normality caused by skewness in this study. An extensive Monte-Carlo simulation study is conducted to investigate the performance of the proposed test under several values of skewness for different number of groups. The proposed RGF is the best choice in the high level of skewness for k = 3, 4, 5. The Kruskal-Wallis test shows better performance than the others in small and moderate sample sizes for k = 6, and 7. It is shown that the proposed RGF test is superior than the non-parametric alternatives in the most of the conditions.
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].
An efficient variant of dual to product and ratio estimators in sample surveys
(Ankara Üniversitesi, 2021) VİSHWAKARMA, Gajendra K.; Other; Other
This manuscript considers a dual to product and ratio estimator for estimating the finite population mean of study variable on applying a simple transformation to the auxiliary variable by using its average values in the population that is generally available in practice. The mean square error (MSE) of the proposed estimator has been obtained to the first degree of approximation. The optimum values and range of suitably chosen scalar, under which the proposed estimator perform better, have been determined. A method to lower the MSE of the proposed estimator relative to that of the MSE of the linear regression estimator is developed for small sample sizes. Theoretical and empirical studies have been done to demonstrate the superiority of the proposed estimator over the other estimators.
An exceedance model based on bivariate order statistics
(Ankara Üniversitesi, 2021) Erem, Ayşegül; Other; Other
In hydrologic risk analysis, the use of exceedance statistics are very important. In this sense, we construct a random threshold model based on bivariate order statistics. The exact distribution of exceedance statistics is calculated under some well-known copulas such as independent and Farlie-Gumbel-Morgenstern (FGM) copulas. Furthermore, numerical results are provided for expected value and variance of exceedance statistics under independent and Farlie-Gumbel-Morgenstern copulas. The application of the model in hydrology is also discussed.
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.
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].
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.
Cotton tensor on Sasakian 3-manifolds admitting eta-Ricci solitons
(Ankara Üniversitesi, 2021) Kar, Debabrata; Other; Other
The object of the present paper is to characterize Cotton tensor on a 3-dimensional Sasakian manifold admitting η -Ricci solitons. After introduction, we study 3-dimensional Sasakian manifolds and introduce a new notion, namely, Cotton pseudo-symmetric manifolds. Next we deal with the study Cotton tensor on a Sasakian 3-manifold admitting η -Ricci solitons. Among others we prove that such a manifold is a manifold of constant scalar curvature and Einstein manifold with some appropriate conditions. Also, we classify the nature of the soliton metric. Finally, we give an important remark.
Discretization and chaos control in a fractional order predator-prey harvesting model
(Ankara Üniversitesi, 2021) Selwam, Maria G.; Other; Other
The study of interaction between predator and prey species is one of the important subjects in mathematical biology. Optimal strategy control plays a vital role in preserving animals from extinction. Harvesting of species is a vital issue for the conservation biologists. In this work, we investigate the bifurcation and chaos control of the two species interaction model of fractional order in discrete time with harvesting of both prey and predator species. Existence results and the stability conditions of the system are analyzed using the fixed points and jacobian matrix. The chaotic behavior of the system is discussed with bifurcation diagrams. Linear control and hybrid control methods are used in controlling the chaos of the system. Numerical experiments with different phase portraits are simulated for the better understanding of the qualitative behavior of the considered model.
Embeddings between weighted Tandori and Cesàro function spaces
(Ankara Üniversitesi, 2021) Yıldız, Tugçe Ünver; Other; Other
We characterize the weights for which the two-operator inequality ∥∥∥(∫x0f(t)pv(t)pdt)1p∥∥∥q,u,(0,∞)≤c∥∥∥esssupt∈(x,∞)f(t)∥∥∥r,w,(0,∞) holds for all non-negative measurable functions on (0,∞), where 0
Finite Blaschke products and the golden ratio
(Ankara Üniversitesi, 2021) Özgür, Nihal; Other; Other
Geometric properties of finite Blaschke products have been intensively studied by many different aspects. In this paper, our aim is to study geometric properties of finite Blaschke products related to the golden ratio α = 1 + √ 5 2 . Mainly, we focus on the relationships between the zeros of canonical finite Blaschke products of lower degree and the golden ratio. We show that the geometric notions such as "golden triangle, "golden ellipse" and "golden rectangle" are closely related to the geometry of finite Blaschke products.
Fixed point theorems to generalize FR- contraction mappings with application to nonlinear matrix equations
(Ankara Üniversitesi, 2021) Khantwal, Deepak; Other; Other
In the present paper, we introduce the notion of generalize FR-contraction and establish some fixed point results for such mappings, which extend and generalize the result of Alam and Imdad (J. Fixed Point Theory & Appl., 17(4) (2015), 693-702), Sawangsup et al. (J. Fixed Point Theory, 2016 (2016), 1-15) and many others. Our results reveal that the assumption of M-closedness of underlying binary relation is not necessary condition for existence of fixed point in relational metric spaces. We also derive some N-order fixed point theorems from our main results. As an application of our main result, we find a solution of a certain class of nonlinear matrix equations.
Fractional variational problems on conformable calculus
(Ankara Üniversitesi, 2021) Öğrekçi, Süleyman; Other; Other
In this paper, we deal with the variational problems defined by an integral that include fractional conformable derivative. We obtained the optimality results for variational problems with fixed end-point boundary conditions and variable end-point boundary conditions. Then, we studied on the variational problems with integral constraints and holonomic constraints, respectively.
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.
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.

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