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Öğe Lorentz-Sasakian space forms on w0 ?curvature tensor(Palestine Polytechnic University, 2024) Mert, T.; Atçeken, M.In this article, Lorentz-Sasakian space forms on W0-curvature tensor are investigated. Riemann, Ricci, concircular, and projective curvature tensors are discussed for (2m + 1)dimensional Lorentz-Sasakian space forms, and with the help of these curvature tensors, some special curvature conditions established on the W0-curvature tensor are examined. Also, with the help of these curvature conditions, some properties of Lorentz-Sasakian space forms such as Einstein manifold, ?-Einstein manifold, and real space form have been obtained.Öğe Certain Results for Invariant Submanifolds of an Almost ?-Cosymplectic (k, µ, ?)-Space(Murat TOSUN, 2024) Uygun, Pakize; Atçeken, Mehmet; Mert, TuğbaIn this paper we present invariant submanifolds of an almost ?-cosymplectic (k, µ, ?)-space. Then, we gave some results for an invariant submanifold of an almost ?-cosymplectic (k, µ, ?)-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic (k, µ, ?)-space.Öğe Invariant and Anti-Invariant Submanifolds of Generalized Sasakian Space Forms(Pleiades Publishing, 2024) Mert, T.; Pandey, S.; Atçeken, M.; De, U.C.In this article, invariant and anti-invariant submanifolds of generalized Sasakian space forms are investigated. The important properties of such submanifolds are determined according to both Levi-Civita connection and semisymmetric metric connection. Characterizations of Ricci solitons have researched according to Levi-Civita connection and semisymmetric metric connection on invariant and anti-invariant submanifolds of generalized Sasakian space form.Öğe From cssc-crossed modules to categorical groups(Tbilisi Centre for Mathematical Sciences, 2024) Datuashvili, Tamar; Mucuk, Osman; Alemdar, Nazmiye; Şahan, TunçarFor any cssc-crossed module a category is constructed, equipped with a structure and proved that this is a coherent categorical group. Together with a result of the previous paper, where to any categorical group the cssc-crossed module is associated, this construction will enable us to prove an equivalence between the categories of categorical groups and of cssc-crossed modules in the sequel to this paper.Öğe Non-Newtonian Pell and Pell-Lucas numbers(Tokat Gaziosmanpaşa Üniversitesi, 2024) Yağmur, TülayIn the present paper, we introduce a new type of Pell and Pell-Lucas numbers in terms of non-Newtonian calculus, which we call non-Newtonian Pell and non-Newtonian Pell-Lucas numbers, respectively. In non-Newtonian calculus, we study some significant identities and formulas for classical Pell and Pell-Lucas numbers. Therefore, we derive some relations with non-Newtonian Pell and Pell-Lucas numbers. Furthermore, we investigate some properties of non-Newtonian Pell and Pell-Lucas numbers, including Catalan-like identities, Cassini-like identities, Binet-like formulas, and generating functions.Öğe Hyper-Dual Leonardo Quaternions(Naim Çağman, 2024) Yağmur, TülayIn this paper, hyper-dual Leonardo quaternions are defined and studied. Some basic properties of the hyper-dual Leonardo quaternions, including their relationships with the hyper-dual Fibonacci quaternions and hyper-dual Lucas quaternions, are analyzed. In addition, some formulae and identities, such as the recurrence relations, Binet's formula, generating functions, Vajda's identity, certain sum formulae, and some binomial-sum formulae, are investigated for hyper-dual Leonardo quaternions.Öğe (?, ?)-TYPE ALMOST ?-RICCI–YAMABE SOLITONS IN PERFECT FLUID SPACETIME(Comenius University in Bratislava, 2024) Pandey, Shashikant; Mert, Tuğba; Atçeken, MehmetIn this paper, we consider perfect fluid spacetime admitting (?, ?)-type almost ?-Ricci–Yamabe solitons by means of some curvature tensors. Ricci pseudosymmetry concepts of perfect fluid spacetime admitting (?, ?)-type almost ?-Ricci–Yamabe soliton are introduced according to the choice of some special curvature tensors such as Riemann, concircular and projective curvature tensor. After then, according to choosing of the curvature tensors, necessary conditions are given for perfect fluid spacetime admitting (?, ?)-type almost ?-Ricci–Yamabe soliton to be Ricci semisymmetric. Then, some important characterizations are given for Ricci, Yamabe, Einstein and ?-Einstein solitons on perfect fluid spacetime.Öğe New approach for investigating a class of multi-cost interval-valued extremization problems(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Trean??, Savin; Özgül, EmineThis study concentrates on a new approach for solving a class of multi-cost convex interval-valued extremization problems. Namely, we apply the weighting technique to find efficient solutions to these problems, defined in terms of (Formula presented.) -efficiency and weak (Formula presented.) -efficiency. Thus, an auxiliary weighting extremization problem related to the considered multi-cost interval-valued extremization problem is introduced. Under appropriate convexity hypotheses, an equivalence is established between the (weakly) (Formula presented.) -efficient solution of the multi-cost interval-valued extremization problem and the optimal solution of the auxiliary weighting extremization problem. Also, a numerical example is formulated to support the theoretical developments derived in the paper.Öğe A note on P-Sasakian manifolds satisfying certain conditions(Universidad Catolica del Norte, 2024) Uygun, Pakize; Atçeken, MehmetIn the present paper, we have studied the curvature tensors of P-Sasakian manifold. For a P-Sasakian manifold, (Formula presented) and W9 · W1 = 0 cases are considered. According these cases, P-Sasakian manifolds have been characterized such as ?-Einstein and Einstein. In addition, we research W1-flat and W9-flat for a P-Sasakian manifold. The results are interesting and give an idea about the geometry of P-Sasakian manifold.Öğe A novel fractional forecasting model for time dependent real world cases(National Statistical Institute, 2024) Erdinç, Ümmügülsüm; Bilgil, Halis; Öztürk, ZaferThe grey modelling in the prediction of time series has been one of the interesting study fields recently due to its efficiency and convenience. Fractional grey models, on the other hand, have become preferable, despite the difficulty in calculations, since they give more effective results than standard models. Difficulties in fractional accumulation and difference calculations have begun to be overcome thanks to new definitions and theorems made in recent years. The new trend in grey modelling is to compose models that are more useful than the previous ones and give results with less error. In this paper, a new grey model derived from the conformable fractional order is defined and it is shown that more effective estimates are made compared to the models created in recent years. The verification of the method is shown with real data set. The results show that the proposed conformable fractional grey model is more effective than the existing models.Öğe Novel algorithms based on forward-backward splitting technique: effective methods for regression and classification(Springer, 2024) Atalan, Yunus; Hacıoğlu, Emirhan; Ertürk, Müzeyyen; Gürsoy, Faik; Milovanovi?, Gradimir V.In this paper, we introduce two novel forward-backward splitting algorithms (FBSAs) for nonsmooth convex minimization. We provide a thorough convergence analysis, emphasizing the new algorithms and contrasting them with existing ones. Our findings are validated through a numerical example. The practical utility of these algorithms in real-world applications, including machine learning for tasks such as classification, regression, and image deblurring reveal that these algorithms consistently approach optimal solutions with fewer iterations, highlighting their efficiency in real-world scenarios.Öğe Separation, compactness, and sobriety in the category of constant limit spaces(Ankara Üniv. Fen Fakültesi, 2024) Erciyes, Ayhan; Qasim, Muhammad; Alper, Güvey İsmailThe objective of this article is to characterize each of compact, sober, and Ti for i=0,1,2 constant limit spaces as well as to investigate the relationships between them. Finally, we compare our results in some topological categories.Öğe Certain Results for Invariant Submanifolds of an Almost ?-Cosymplectic (k, µ, ?)-Space(Murat TOSUN, 2024) Uygun, Pakize; Atçeken, Mehmet; Mert, TuğbaIn this paper we present invariant submanifolds of an almost alpha-cosymplectic (k,mu,nu)-space. Then, we gave some results for an invariant submanifold of an almost alpha-cosymplectic (k,mu,nu)-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic (k,mu,nu)-space.Öğe On some important characterizations of Lorentz para-Kenmotsu manifolds on some special curvature tensors(World Scientific, 2024) Mert, Tuğba; Atçeken, MehmetIn this paper, some properties of Lorentz para-Kenmotsu manifolds are studied using specified curvature tensors. The Lorentz para-Kenmotsu manifold is investigated in terms of the curvature tensors W8 and W9. Initially, the tensor-based characterization of semisymmetric Lorentz para-Kenmotsu manifolds is studied. Subsequently, we consider the Lorentzian para-Kenmotsu manifold, which admits almost ?-Ricci solitons via these curvature tensors. According to the W8 and W9 curvature tensors, Ricci pseudosymmetry notions of Lorentzian para-Kenmotsu manifolds accepting ?-Ricci soliton have been developed. Following that, required conditions for the Lorentzian para-Kenmotsu manifold, admitting ?-Ricci soliton to be Ricci semisymmetric, are presented based on the curvature tensors chosen. Further, various characterizations are provided, and classifications are made under certain conditions. Finally, the characterizations of the invariant submanifolds of Lorentz para-Kenmotsu manifold on the W8 and W9 curvature tensors are investigated. We obtained the necessary and sufficient conditions for an invariant submanifold of a para-Kenmotsu to be W8 and W9 pseudoparallel.Öğe On invariant submanifolds of normal paracontact metric manifolds on generalized B?curvature tensor(University of Nis, 2024) Mert, Tuğba; Atçeken, MehmetSciVal Topics Abstract In this article, pseudoparallel submanifolds for normal paracontact metric manifolds are stud-ied. B-curvature tensor in a normal paracontact metric manifold has been considered. For an invariant submanifold of a paracontact metric manifold, B?pseudoparallel, B 2-pseudoparallel, B?Ricci generalized pseudoparallel, and B 2? Ricci generalized pseudoparallel has been searched. Also, characterizations of invariant submanifold types are given by means of quasi-conformal, Weyl-conformal, concircular, conhar-monic curvature tensors for special cases of generalized B?curvature tensor.Öğe Invariant pseudoparallel submanifold of an SQ-Sasakian manifolds(Walter de Gruyter GmbH, 2024) Atçeken, Mehmet; Mert, Tu?ba; Uygun, PakizeThe aim of the present paper is to study invariant pseudoparallel submanifolds in an SQ-Sasakian manifold with respect to semisymmetric metric connection. We search the necessary and sufficient conditions for an invariant submanifold to be totally geodesic under the some hypotheses.Öğe Some characterizations for a (k, µ)-paracontact metric manifold to be an ?-Einstein manifold(Palestine Polytechnic University, 2024) Uygun, P.; Atçeken, M.In this paper we introduce the curvature tensors of (k,µ)-paracontact manifold satisfying the conditions (formula presented) According these cases, (k, µ)-paracontact manifolds have been characterized such as ?-Einstein.Öğe A new application of fractional glucose-insulin model and numerical solutions(Yildiz Technical University, 2024) Öztürk, Zafer; Halis, Bi?lgi?l; Sorgun, SezerAlong with the developing technology, obesity and diabetes are increasing rapidly among people. The identification of diabetes diseases, modeling, predicting their behavior, conducting simulations, studying control and treatment methods using mathematical methods has become of great importance. In this paper, we have obtained numerical solutions by considering the glucose-insulin fractional model. This model consists of three compartments: the blood glucose concentration (G), the blood insulin concentration (I) and the ready-to-absorb glucose concentration (D) in the small intestine. The fractional derivative is used in the sense of Caputo. By performing mathematical analyzes for the Glucose-Insulin fractional mathematical model, numerical results were obtained with the help of the Euler method and graphs were drawn.Öğe Elliptic inversions in taxicab geometry(2024) Can, ZeynepThe goal of this research is to introduce inversion with respect to an ellipse which is a generalization of the classical circular inversion in taxicab plane and to investigate general properties and basic concepts of this transformation in taxicab geometry. The cross ratio is preserved under the elliptic inversion in taxicab plane though this transformation is not an isometry. Thus some properties such as cross ratio and harmonic conjugates of the elliptic inversions in R_T^2 are also studied.Öğe Pseudoparallel invariant submanifolds of a Para-Sasakian manifold(Matematikçiler Derneği, 2023) Mert, Tuğba; Atçeken, MehmetIn this paper, invariant submanifolds of a para-Sasakian manifold have been studied. Some special submanifolds such as pseudoparallel, 2-pseudoparallel, Ricci generalized pseudoparallel, and 2-Ricci generalized pseudoparallel submanifolds of a para-Sasakian manifold have been considered. The necessary and sufficient conditions for an invariant submanifold to be totally geodesic under some conditions have been given.
