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Öğe Reconstructing f(T) gravity and exploring the torsion driven warm inflationary cosmology(Springer, 2025) Ghosh, Moli; Aktaş, Can; Chattopadhyay, SurajitThe current paper reports an investigation of a warm inflationary scenario in the context of f (T ) gravity for a spatially flat FLRW universe. In our model, inflation is driven purely by the torsional sector of f (T ) gravity, without introducing any additional scalar fields.We focus on the high dissipative regime (R >> 1), reconstruct the Hubble parameter as a function of the e-folding number N, and derive the slow-roll parameters ε1(N) and ε2(N). The study has encapsulated the dynamics of inflation and its duration under strong dissipation. The dissipative coefficient Γ is modeled with a temperature-dependent power-law form, linking the inflationary dynamics to thermal corrections and the particle content of the early universe. The analysis has affirmed that the torsion-induced energy density ρT successfully transitions to radiation energy density ρrad, facilitating a graceful exit from inflation. Finally, we have validated our model by comparing the scalar spectral index and tensor-to-scalar ratio with Planck 2018 results, demonstrating consistency within observational bounds. Additionally, it is verified that the thermal domination condition T∗/H > 1 and the torsion dominance condition ρT /ρrad > 1 are satisfied.Öğe Investigating Concepts in Soft Topological Structures through Subspaces(World Scientific Publ Co Pte Ltd, 2025) Arslan, Burak; Aydın, TuğçeFollowing the study of Molodtsov on soft topological structures in 2015, this study discusses the concepts in soft topological structures through subspaces, investigates some of their crucial properties, and provides their characterizations. To ensure consistency with Molodtsov's framework, this paper defines the tau-neighborhood in a subspace S⊆X of any x∈S as ˜τ(x)∩S, noting that his definition of the τ-neighborhood in X of any x∈X is ˜τ(x), which equals τ(x)∩X. Moreover, this study researches some of the relations between concepts in a space and their correspondences in subspaces. Besides, it explores whether τ -C-, ˜τ-T-, ˜τ-B-, and ˜τ-I-soft discrete and indiscrete topologies is hereditary or not. Finally, this study handles if further research concerning these aspects is needed.Öğe Kaluza-Klein model in f(R,T) theory with Λ(T): Implications from data-constrained analysis(World Scientific Publ Co Pte Ltd, 2025) Baysal, Hüsnü; Sofuoğlu, D.In this study, we investigate a class of five-dimensional Kaluza-Klein cosmological models within the framework of f(R,T) gravity, where the functional form is chosen as f(R,T) = f(R) + f(T) with f(R) = λR and f(T) = λT. This formulation leads to a dynamically evolving effective cosmological constant Λ(T), which depends on the trace of the energy-momentum tensor. Exact solutions to the field equations are derived by assuming a varying deceleration parameter. The resulting cosmological model exhibits a transition from a decelerating to an accelerating expansion phase, in agreement with observational evidence. To constrain the model parameters, we employ recent observational datasets such as Hubble parameter measurements and Type Ia supernovae from the Union 2.1 compilation. A statistical analysis using chi-square minimization provides optimal parameter values. The kinematical and dynamical properties of the model are analyzed. We determine some important cosmological quantities such as the transition redshift, the present-day deceleration and equation of state parameters, and the age of the universe, which align well with observational estimates. Furthermore, the jerk parameter and statefinder parameters are employed to compare the behavior of the model with standard and alternative dark energy scenarios. The findings indicate that our model closely follows the ΛCDM evolution at late times while allowing for deviations in earlier epochs, resembling quintessence-like behavior at the late phase of the universe.Öğe Soft Limit and Soft Continuity(Mdpi, 2025) Sapan, Kenan; Arslan, Burak; Enginoğlu, SerdarThis study presents the soft limit and upper (lower) soft limit proposed by Molodtsov, with several theoretical contributions. It investigates some of their basic properties, such as some fundamental soft limit rules, the relation between soft limit and boundedness, and the sandwich/squeeze theorem. Moreover, the paper proposes left and right soft limits and studies some of their main properties. Furthermore, it defines the soft limit at infinity and explores some of its basic properties. Additionally, the present study exemplifies these concepts and their properties to better understand them. The paper then compares the aforesaid concepts with their classical forms. Afterward, this paper presents soft continuity and upper (lower) soft continuity, proposed by Molodtsov, theoretically contributes to these concepts, and investigates some of their key properties, such as some fundamental soft continuity rules, the relation between soft continuity and boundedness, Bolzano's theorem, and the intermediate value theorem. Moreover, it defines left and right soft continuity and studies some of their basic properties. The present study exemplifies soft continuity types and their properties. In addition, it compares them with their classical forms. Finally, this study discusses whether the aspects should be further analyzed.Öğe Refining and extending the theoretical foundations of r-near topology(Amer Inst Mathematical Sciences-Aims, 2025) Aydın, TuğçeThe present paper aims to refine and extend the theoretical foundations of r-near topology. For this reason, it first redefines the concept of r-near neighborhoods to address inconsistencies in previous studies and clarifies the relationship between r-near open neighborhoods and r-near closure. This study then elaborates on the fundamental properties of r-near closed sets, r-near interior, rnear closure, and r-near neighborhoods. Subsequently, it introduces four novel concepts within rnear topology: r-near accumulation points, r-near isolated points, r-near exterior points, and rnear boundary points. Furthermore, this study explores some of their basic properties and provides illustrative examples regarding the aforesaid concepts. Additionally, it researches the relationships between r-near interior, r-near closure, and r-near exterior in the r-near topological spaces and their classical topological counterparts. Lastly, the study highlights the theoretical significance of r-near topology and suggests potential directions for further research.Öğe Equivalent curves in En(Amer Inst Mathematical Sciences-Aims, 2025) Mollaoğulları, Ahmet; Gümüş, Mehmet; Karalarlıoğlu Camcı, Didem; İlarslan, Kazım; Camcı, ÇetinIn this paper, we first define an equivalence relation for curves in En. Based on this equivalence relation, we investigate the relationships between the Frenet frame and curvatures of equivalent curves. Next, we introduce the concept of linearly dependent curvatures in Enand examine its implications for equivalent curves. Building on this concept and the proposed equivalence relation, we present a method to construct (1,3)-Bertrand curves in E4. Additionally, we derive the relationships between the harmonic curvatures of equivalent curves and use these relationships to establish several properties of equivalent helical curves. These results enable systematic construction of curves with prescribed geometric properties.Öğe Soft Derivative(Soc Paranaense Matematica, 2025) Arslan, Burak; Enginoğlu, SerdarThis study presents a comprehensive investigation of soft and upper (lower) soft derivatives within the framework of Molodtsov's soft set theory, extending it through the introduction of novel and complementary notions: left and right soft derivatives. It rigorously develops the fundamental properties of these concepts, including algebraic and order-theoretic rules, and establishes their relationships with boundedness and soft continuity types. The paper offers insightful geometric interpretations that significantly enhance conceptual understanding. Furthermore, it introduces absolute epsilon-extrema, investigates their fundamental properties, and characterizes the local (tau, epsilon)-extrema defined by Molodtsov. This study presents analogs of Rolle's Theorem for upper and lower soft derivatives and interprets them geometrically with supporting visual illustrations. Moreover, it establishes and geometrically interprets analogs of the Mean Value Theorem for upper and lower soft derivatives. By systematically investigating fundamental concepts in soft analysis and presenting detailed results, the present paper constructs a comprehensive foundation that strengthens the mathematical structure of soft analysis and paves the way for advanced developments, such as soft integrals, soft directional derivatives, and soft gradients.Öğe Weak Forms of ΨΓ − C Sets(Univ Punjab, Dept Mathematics, 2025) Tunç, Ayşe Nur; Özen Yıldırım, SenaIn this study, we introduce Γ−ΨΓ−sets and pre−Γ−ΨΓ−sets in ideal topological spaces. We investigate various properties of these sets and we obtain new results. Moreover, we analyze the relationships between these sets and some special sets such as ΨΓ−C set and σ-open set in the literature. Additionally, we observe that the families of Γ−ΨΓ−sets and pre−Γ−ΨΓ− sets form a supratopology on W in the case cl(υ)∩I = {∅}.Öğe On ∗-(σ, τ)-Lie ideals of ∗-prime rings with derivation(Hacettepe Üniversitesi, 2018) Aydın, Neşet; Koç, Emine; Gölbaşı, ÖznurLet 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.Öğe Statistical Convergence in L-Fuzzy Metric Spaces(Naim ÇAĞMAN, 2024) Çakı, Ahmet; Or, AykutStatistical 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.Öğe 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.Öğe Testing for random interaction: The symmetry assumption(Taylor & Francis Inc, 2025) Güven, BilgehanThe 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.Öğe Behaviors of dark energy candidates in the Ruban universe(World Scientific Publ Co Pte Ltd, 2025) Engin, Melike; Aktaş, CanIn 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.Öğe Applications of Equivalent Curves to Ruled Surfaces(Int Electronic Journal Geometry, 2025) Bataray, Büşra; Camcı, ÇetinIn 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.Öğe Soft Decision-Making Methods Employing Multiple ifpifs-Matrices and Their Application(Soc Paranaense Matematica, 2025) Arslan, Burak; Aydın, Tuğçe; Memiş, Samet; Enginoğlu, SerdarThe 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.Öğe 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, CanIn 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.Öğe Testing for main fixed effects: The symmetry assumption and monotone incomplete data(Taylor & Francis Inc, 2024) Demircioğlu, Sevgi; Güven, BilgehanWe consider the balanced two-way mixed effects design with some empty cells. A test procedure for the hypothesis of no main fixed effects is developed under violation of the assumption of variance homogeneity and symmetry. The asymptotic null distribution of the test statistics is studied under the condition that the number of levels of the random effects tends to infinity as both the number of complete and incomplete observations tend to infinity. An illustrative example is given.Öğe 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, CanBehaviors 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.Öğe Domain wall solutions with quark matter in higher dimensional space-times(Amer Inst Physics, 2007) Aktaş, Can; Yılmaz, İhsan; Baysal, Hüsnü; Aygün, Melis; Demirel, CananIn 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.Öğe An investigation of separation near corner points in transonic flow(Cambridge Univ Press, 2004) Türkyılmaz, İbrahimThe 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.
