Matematik Bölümü Koleksiyonu

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https://hdl.handle.net/20.500.12428/2241

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On ∗-(σ, τ)-Lie ideals of ∗-prime rings with derivation
(Hacettepe Üniversitesi, 2018) Aydın, Neşet; Koç, Emine; Gölbaşı, Öznur
Let R be a ∗−prime ring with characteristic not 2, U be a nonzero ∗ − (σ, τ )−Lie ideal of R and d be a nonzero derivation of R. Suppose σ, τ be two automorphisms of R such that σd = dσ, τ d = dτ and ∗ commutes with σ, τ, d. In the present paper it is shown that if d2(U) = (0), then U ⊆ Z.
Statistical Convergence in L-Fuzzy Metric Spaces
(Naim ÇAĞMAN, 2024) Çakı, Ahmet; Or, Aykut
Statistical convergence, defined in terms of the natural density of positive integers, has been studied in many different spaces, such as intuitionistic fuzzy metric spaces, partial metric spaces, and L-fuzzy normed spaces. The main goal of this study is to define statistical convergence in L-fuzzy metric spaces (L-FMSs), one of the essential tools for modeling uncertainty in everyday life. Furthermore, this paper introduces the concept of statistical Cauchy sequences and investigates its relation with statistical convergence. Then, it defines statistically complete L-FMSs and analyzes some of their basic properties. Finally, the paper inquires the need for further research.
IDEAL CONVERGENCE IN FUZZY METRIC SPACES
(Turkic World Mathematical Soc, 2025) Or, Aykut; Karabacak, G.
In this paper, the concepts of K-convergence, K-Cauchy sequences, K-& lowast;- convergence, and K-& lowast;-Cauchy sequences in fuzzy metric spaces is proposed. Also, a few fundamental properties of these concepts are investigated. Then, the concepts of K-limit and /C-cluster points of a sequence in these spaces is defined. Afterwards, some of their basic properties is examined. Finally, the need for further research is discussed.
Testing for random interaction: The symmetry assumption
(Taylor & Francis Inc, 2025) Güven, Bilgehan
The F-test for the hypothesis of no interaction effects in any mixed model is valid under the assumption of normality, symmetry, and variance homogeneity of the error terms. We consider the balanced two-way mixed model in which the usual assumptions do not hold. The model allows for dependence of the random main and interaction effects, variance heterogeneity in the random interaction effects and error terms and also do not require normality. We propose the test for testing the hypothesis of no interaction effect in this model. The asymptotic null distribution of the test statistic is the normal distribution and studied under the condition that the number of levels of random effect tends to be large.
Behaviors of dark energy candidates in the Ruban universe
(World Scientific Publ Co Pte Ltd, 2025) Engin, Melike; Aktaş, Can
In this study, we investigated quintessence and tachyon field dark energy (DE) models for the inhomogeneous and anisotropic Ruban universe in f(R,T) gravitation theory. We utilized the Hubble parameter in the field equations as beta root t+alpha for the solutions. Since DE candidates are classified according to the p/rho values of the EoS parameter omega, we obtained the p and rho solutions for each DE candidate and analyzed the scalar field (SF) and scalar potential solution. We also talked about the model's physical characteristics and parameters with the help of a various of graphics for redshift z and cosmic time t. Additionally, the statefinder parameters, which are essential tools for distinguishing various dark energy models, have been explored.
Applications of Equivalent Curves to Ruled Surfaces
(Int Electronic Journal Geometry, 2025) Bataray, Büşra; Camcı, Çetin
In this paper, the characterization of equivalent curves in E3 is used to define ruled surfaces whose base curves are equivalent curves and to examine the relationships between them. At the same time, an equivalence relation for ruled surfaces is obtained. The equivalence classes resulting from this relation are studied. It is concluded that all ruled surfaces in the equivalence class of a developable surface are developable. Thus, a method is established to obtain an infinite ruled surface from a ruled surface. Finally, a new method is given to obtain a developable surface.
Soft Decision-Making Methods Employing Multiple ifpifs-Matrices and Their Application
(Soc Paranaense Matematica, 2025) Arslan, Burak; Aydın, Tuğçe; Memiş, Samet; Enginoğlu, Serdar
The present study generalizes 36 soft decision-making (SDM) methods employing multiple fuzzy parameterized fuzzy soft matrices (fpfs-matrices) to operable in the intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) space and obtains 44 SDM methods containing several variants of the aforesaid methods. It then compares all the SDM methods herein using three ifpifs-matrices for each test case proposed by the authors' previous study. The comparison shows that 23 of 44 passed all the test cases. Moreover, this study applies the 23 SDM methods to a performance-based value assignment (PVA) problem in which seven well-known salt-and-pepper noise removal filters used in digital images are considered. The results manifest that 10 of 23 produce the same ranking order at the high noise density, just as 8 of 23 do at the low noise density. Finally, this study discusses SDM methods' applications and the need for further research.
Magnetized strange quark matter in reconstructed f(R, T) gravity for Bianchi I and V universes with cosmological constant
(Tubitak Scientific & Technological Research Council Turkey, 2017) Aktaş, Can
In this article, we have investigated the behaviors of magnetized strange quark matter distributions for Bianchi I and V universes in reconstructed f (R, T) = α1R+α2f3(T) gravity (here α1 and α2 are constants; f3(T) is an arbitrary function of T). To get solutions of the field equations we have used a deceleration parameter and the equation of state for strange quark matter. The new represented f(R,T) model includes two models of Harko et al. and transforms to general relativity. When t → ∞, we get the dark energy model (p = −ρ) in reconstructed f (R, T) = α1R + α2f3(T) gravity. However, we obtain zero magnetic field in all f(R, T) gravitation models.
Quark and strange quark matter in f(R) gravity for Bianchi type I and V space-times
(Springer/Plenum Publishers, 2012) Yılmaz, İhsan; Baysal, Hüsnü; Aktaş, Can
Behaviors of quark matter and strange quark matter which exist in the first seconds of the early Universe in f(R) gravity are studied for Bianchi I and V universes. In this respect, we obtain exact solutions of the modified Einstein field equations by using anisotropy feature of Bianchi I and V space-times. In particular, we investigate exact f(R) functions for Bianchi I as the contribution of strange quark and quark matter. Also, we have concluded that quark matter may contribute to the early acceleration of the universe since quark matter behaves like phantom-type dark energy. Furthermore, obtained f(R) solutions represents early eras of the Universe since f(R) solutions for quark matter coincide with f(R) equations for inflation. From this point, we can reach the conclusion that quarks may be source of the early dark energy of the universe or source of little inflation due to their repulsive force.
Domain wall solutions with quark matter in higher dimensional space-times
(Amer Inst Physics, 2007) Aktaş, Can; Yılmaz, İhsan; Baysal, Hüsnü; Aygün, Melis; Demirel, Canan
In this paper, we have examined quark matter in the perfect form attached to domain walls in the higher dimensional spherical symmetric space-time admitting one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for higher dimensional spherical symmetric space-time via conformal motions. Also, we have discussed the features of the obtained solutions.
An investigation of separation near corner points in transonic flow
(Cambridge Univ Press, 2004) Türkyılmaz, İbrahim
The incipient separation from a corner in steady two-dimensional transonic flow is studied based on viscous-inviscid interaction at high Reynolds number. Of particular interest is the investigation of the dependence of the critical deflection angle (when a well-attached flow turns into a separated flow) on the Karman-Guderley parameter which characterizes the local flow field. In accordance with the procedure adopted, the analysis of the flow starts with the analysis of the boundary layer and then the solution of the Karman-Guderley equation describing the inviscid part of the flow near the corner point is investigated. The analysis of the inviscid transonic flow is performed based on the hodograph method and new solutions are obtained corresponding to the present flow topologies. In these solutions, the transonic flow appears to be subsonic everywhere except at the sonic corner point. Then, the interaction problem is formulated using the triple-deck model. Lastly, a procedure based on a semi-direct solution of the governing equations using Newton iterations is developed to obtain the numerical solution of the interaction problem.
Strange quark matter solutions for Marder's universe in f (R, T) gravity with Λ
(Springer, 2016) Aygün, Sezgin; Aktaş, Can; Yılmaz, İhsan
In this paper, we investigate homogeneous cylindrically symmetric Marder's universe in the presence of strange quark matter (SQM) source in f (R, T) gravity with cosmological constant Lambda. For this aim we have used the anisotropy feature (sigma(x)(x)/theta) of Marder type universe and equation of state (EoS) strange quark matter to obtain solutions in two classes f (R, T) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011). Finally, some physical and kinematical properties are discussed.
Quark and strange quark matter solutions for higher dimensional FRW universe in Lyra geometry
(Springer Heidelberg, 2015) Aygün, Sezgin; Çağlar, Halife; Taşer, Doğukan; Aktaş, Can
In this study, we have investigated the higher dimensional flat Friedmann-Robertson-Walker (FRW) universe for a cloud of string with perfect fluid attached quark and strange quark matter (SQM) in Lyra geometry. Generalized (n + 2) dimensional flat FRW universe solutions have been achieved with the aid of equation of states (EOS) and deceleration parameter (q). From the field equations, we have obtained that the cloud of string with perfect fluid does not survive. Since the string tension density vanishes (lambda = 0) for this model, as a result, the cloud of string with perfect-fluid-attached quark and strange quark matter energy-momentum tensor is automatically transformed into a perfect-fluid-attached quark and strange quark matter energy-momentum tensor. Also, our solutions agree with Halford's study. beta(2) behaves like a cosmological constant. When t -> infinity the pressure of quark matter and the density go to zero, then, the quark matter transforms into another matter with time. Also our quark matter solutions are in agreement with the present idea.
Magnetized strange quark matter solutions in f(R, T) gravity with cosmological constant
(Elsevier Science Bv, 2017) Aktaş, Can; Aygün, Sezgin
In this research, we have studied magnetized strange quark matter (SQM) solutions for Friedmann-Robertson-Walker (FRW) universe in f(R, T) gravity. To obtain exact solutions of modified field equations we have used f(R, T) = R + 2 f(T) and f(R, T) = f(1)(R) + f(2)(T) models given by Harko et al. (Harko et al. in Phys. Rev. D 84: 024020, 2011) and f(R, T) = R + f(3)(T) model (here f(3) is an arbitrary function) with cosmological constant Lambda. For t -> 8 we obtain p = -rho dark energy situation with small constant values of cosmological constant in three different f (R, T) gravitation models. In our solutions magnetic field does not observe also we have transformed our solutions from FRW universe to Static Einstein Universe (SEU) and we get f(R, T) gravity results for SEU universe. Finally we discussed our physical solutions. (C) 2016 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.
Relationship between magnetic field and anisotropy parameter in gravitation theories
(World Scientific Publ Co Pte Ltd, 2018) Aktaş, Can; Aygün, Sezgin; Sahoo, Pradyumn Kumar
The magnetized strange quark matter (MSQM) solutions are obtained for a Marder type universe using constant deceleration parameter. The exact solutions of field equations are obtained for f(R,T) = R 2f(T) model given by [T. Harko et al., Phys. Rev. D 84, 024020 (2011)] with cosmological term. Also, we have obtained General Relativity (GR) solutions for MSQM distributions. For t -> infinity, we get the dark energy model, i.e. p -> -B-c, rho -> B-c and omega = -1. However, for t -> infinity, we find the cosmological constant A as negative in f (R, T) theory and GR. These results agree with [S. Aygun et al., Astrophys. Space Sci. 361, 380 (2016); C. Aktas and S. Aygun, Chinese T. Phys. 55, 71 (2017); P. K. Sahoo et al., Mod. Phys. Lett. A 32, 1750105 (2017)] in f(R,T) theory. The physical consequences of our obtained models are discussed at the end.
Magnetized quark and strange quark matter in the spherical symmetric space-time admitting conformal motion
(Springer/Plenum Publishers, 2007) Aktaş, Can; Yılmaz, İhsan
In this paper, we have examined magnetized quark and strange quark matter in the spherical symmetric space-time admitting one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for spherical symmetric space-time via conformal motions. Also, we have discussed the features of the obtained solutions.
A Source of Semiprimeness on Inverse and Completely Regular Semigroups
(Springer, 2025) Mekera, Rasie; Yeşil, Didem
We define |SS|-inverse semigroup and |SS|-completely regular semigroup structures that are not encountered in the literature. They are studied in our work for the first time. The properties of these new semigroup types and their relations with the other semigroup types, such as |SS|-idempotent, |SS|-regular, |SS|-nonzero, and |SS|-reduced semigroups, are discussed. Furthermore, the relationship between the source of semiprimeness and the semiprime ideal is analyzed. It is also shown that the intersection of all semiprime ideals is equal to the source of semiprimeness. Moreover, if a function is surjective, then it can be shown that the analyzed two structures are preserved under homomorphism.
Does magnetized strange quark matter exist in the early universe?
(World Scientific Publ Co Pte Ltd, 2022) Kalkan, Sinem; Aktaş, Can; Aygün, Sezgin
In this paper, we have examined the magnetized strange quark matter (MSQM) distribution in the inhomogeneous anisotropic Einstein-Rosen universe model within the framework of f(R,T) theory and General Relativity (GR) in order to investigate whether there was a magnetic field in the first moments of the universe. With the help of the arbitrary F(r) function, we researched for solutions in both theories for various cases. We have seen that the cubic function F(r) = r(3) gives meaningful results in both theories. We have obtained magnetic field-free strange quark matter solutions for the quadratic and constant states of the arbitrary function F(r). It is seen that the choice of geometry (selection of the F(r) function) has an effect on the presence of the magnetic field. Finally, the physical results are examined on 3D graph.
Non-existence of a massive scalar field for the Marder universe in Lyra and Riemannian geometries
(Elsevier, 2012) Aygün, Sezgin; Aktaş, Can; Yılmaz, İhsan
In this paper, we have studied a massive scalar field for a Marder type universe in the context of Lyra and Riemannian geometries. From the exact solutions obtained we show that the massive scalar field does not survive in Lyra and Riemannian geometries for an anisotropic Marder type universe. Therefore we have solved the massless scalar field problem in Lyra and Riemann geometries for two cases. Also we have obtained vacuum solutions for homogeneous and anisotropic Marder space time in Lyra geometry and the solutions obtained are compared by considering Lyra and Riemann geometries. Finally, some physical and kinematical properties are discussed by using graphics. (C) 2011 Elsevier B.V. All rights reserved.
Behaviors of dark energy and mesonic scalar field for anisotropic universe in f (R) gravity
(Elsevier, 2012) Aktaş, Can; Aygün, Sezgin; Yılmaz, İhsan
In this Letter, we study behaviors of dark energy in the form of perfect fluid and mesonic scalar field for Marder space-time which is anisotropic and homogeneous in f (R) gravity. Exact solutions of the modified Einstein field equations in f (R) gravity are obtained by using anisotropic features, of Marder space-time. We do not make any assumptions about f (R) function while we are solving f (R I equations. We have investigated dark energy behaviors in f (R) gravity. We have concluded that dark energy in our model behaves like phantom type. Also we have concluded that mesonic scalar field transforms to another matters into time. In our solutions, obtained f (R) functions existed by dark energy and mesonic scalar field are same like general one accepted in the literature. Furthermore, physical and kinematical quantities are examined for two matters, separately. Finally obtained solutions are discussed. (C) 2011 Elsevier B.V. All rights reserved.

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