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Öğe A fractional-order mathematical model based on vaccinated and infected compartments of SARS-CoV-2 with a real case study during the last stages of the epidemiological event(PMC, 2023) Bilgil, Halis; Yousef, Ali; Erciyes, Ayhan; Erdinç, Ümmügülsüm; Öztürk, ZaferIn 2020 the world faced with a pandemic spread that affected almost everything of humans' social and health life. Regulations to decrease the epidemiological spread and studies to produce the vaccine of SARS-CoV-2 were on one side a hope to return back to the regular life, but on the other side there were also notable criticism about the vaccines itself. In this study, we established a fractional order differential equations system incorporating the vaccinated and re-infected compartments to a S I R frame to consider the expanded and detailed form as an S V I I v R model. We considered in the model some essential parameters, such as the protection rate of the vaccines, the vaccination rate, and the vaccine's lost efficacy after a certain period. We obtained the local stability of the disease-free and co-existing equilibrium points under specific conditions using the Routh-Hurwitz Criterion and the global stability in using a suitable Lyapunov function. For the numerical solutions we applied the Euler's method. The data for the simulations were taken from the World Health Organization (WHO) to illustrate numerically some scenarios that happenedÖğe Actions of internal groupoids in the category of leibniz algebras(Ankara Üniversitesi, 2019) Şahan, TunÇar; Erciyes, AyhanThe aim of this paper is to characterize the notion of internal category (groupoid) in the category of Leibniz algebras and investigate some properties of well-known notions such as covering groupoids and groupoid operations (actions) in this category. Further, for a fixed internal groupoid G in the category of Leibniz algebras, we prove that the category of covering groupoids of G and the category of internal groupoid actions of G on Leibniz algebras are equivalent. Finally, we interpret the corresponding notion of covering groupoids in the category of crossed modules of Leibniz algebras.Öğe Local T3 constant filter convergence spaces(Gazi University, 2020) Baran, Tesnim Meryem; Erciyes, AyhanIn this paper, we characterize each of local T3(resp. T3?, ST?3, ST3?) constant filter convergence spaces and investigate the relationships among these various forms. We show that the full subcategories T?3ConFCO and ST?3ConFCO (resp. T3?ConFCO and ST3?ConFCO) of ConFCO are isomorphic categories. Moreover, we show that if a constant filter convergence space (B,K) is T?3 (resp. T3?, ST?3 or ST3?) at p and M?B with p?M, then M is T?3 (resp. T3? ) at p.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 T-0 and T-1 semiuniform convergence spaces(UNIV NIS, FAC SCI MATH, 2013) Baran, Mehmet; Kula, Sümeyye; Erciyes, AyhanIn previous papers, various notions of T-0 and T-1 objects in a topological category were introduced and compared. In this paper, we characterize each of these classes of objects in categories of various types of uniform convergence spaces and compare them with the usual ones as well as examine how these generalizations are related.Öğe T4 , Urysohn’s lemma, and Tietze extension theorem for constant filter convergence spaces(TÜBİTAK, 2021) Baran, Tesnim Meryem; Erciyes, AyhanIn 1978, Schwarz [14] introduced the category ConF CO whose objects are constant filter convergence spaces and morphisms are continuous maps, and he showed that ConF CO is isomorphic to the category FILTER whose objects are filter spaces and morphisms are continuous maps. He also showed that it is a bireflective subcategory of F CO whose objects are filter convergence spaces and morphisms are continuous maps. Hence, Schwarz proved that ConF CO is the natural link between FILTER and the category F CO. In 1991, Baran [3] introduced the local T1 separation property that is used to define the notion of strongly closed subobject of an object of a topological category, which are used in the notions of compactness [8], connectedness [10], and normal objects [3]. In general topology, one of the most important uses of separation properties is theorems such as the Urysohn?s lemma and the Tietze extension theorem. In this regard, it is useful to be able to extend these In this paper, we characterize various local forms of T4 constant filter convergence spaces and investigate the relationships among them as well as showing that the full subcategories of the category of constant filter convergence spaces consisting of local T4 constant filter convergence spaces that are hereditary. Furthermore, we examine the relationship between local T4 and general T4 constant filter convergence spaces. Finally, we present Urysohn?s lemma and Tietze extension theorem for constant filter convergence spaces.
