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Öğe Applications of the Lefschetz Number to Digital Images(Belgian Mathematical Soc Triomphe, 2014) Ege, Ozgur; Karaca, IsmetDaha fazla The goal of this paper is to develop some applications of the Lefschetz fixed point theorem to digital images. We also deal with relative and reduced Lefschetz fixed point theorem for digital complexes. We give some examples related to the topic. We calculate the degree of the antipodal map for sphere-like digital images using fixed point properties.Daha fazla Öğe The Arnon bases in the Steenrod algebra(Walter De Gruyter Gmbh, 2020) Turgay, Neset Deniz; Karaca, IsmetDaha fazla Let A = A(p) be the mod p Steenrod algebra, where p is a fixed prime and let A' denote the Bockstein-free part of A at odd primes. Being a connected graded Hopf algebra, A has the canonical conjugations. Using this map, we introduce a relationship between the X- and Z-bases of A'. We show that these bases restrict to give bases to the well-known sub-Hopf algebras A(n - 1), n >= 1, of A'.Daha fazla Öğe Banach fixed point theorem for digital images(Int Scientific Research Publications, 2015) Ege, Ozgur; Karaca, IsmetDaha fazla In this paper, we prove Banach fixed point theorem for digital images. We also give the proof of a theorem which is a generalization of the Banach contraction principle. Finally, we deal with an application of Banach fixed point theorem to image processing. (C) 2015 All rights reserved.Daha fazla Öğe CERTAIN TOPOLOGICAL METHODS FOR COMPUTING DIGITAL TOPOLOGICAL COMPLEXITY(Kangwon-Kyungki Mathematical Soc, 2023) Is, Melih; Karaca, IsmetDaha fazla In this paper, we examine the relations of two closely related concepts, the digital Lusternik-Schnirelmann category and the digital higher topological com-plexity, with each other in digital images. For some certain digital images, we in-troduce -top ological groups in the digital topological manner for having stronger ideas about the digital higher topological complexity. Our aim is to improve the understanding of the digital higher topological complexity. We present examples and counterexamples for -top ological groups.Daha fazla Öğe COHOMOLOGICAL APPROACH TO REFLEXIVE GRAPHS(Util Math Publ Inc, 2019) Ege, Ozgur; Karaca, IsmetDaha fazla In this paper, we construct a cohomology structure for reflexive graphs. We also prove the Universal coefficient theorem for singular cohomology in graphs. We show that the Kunneth theorem doesn't yield for graphs.Daha fazla Öğe Cohomology Theory for Digital Images(Editura Acad Romane, 2013) Ege, Ozgur; Karaca, IsmetDaha fazla In this paper we propose a mathematical framework that can be used for de fining cohomology of digital images. We state the Eilenberg-Steenrod axioms and the Universal Coefficient Theorem for this cohomology theory. We show that the Kunneth formula doesn't hold. A cup product is defined and its main properties are proved.Daha fazla Öğe Cohomology Theory for Digital Images(Editura Acad Romane, 2013) Ege, Ozgur; Karaca, IsmetDaha fazla In this paper we propose a mathematical framework that can be used for de fining cohomology of digital images. We state the Eilenberg-Steenrod axioms and the Universal Coefficient Theorem for this cohomology theory. We show that the Kunneth formula doesn't hold. A cup product is defined and its main properties are proved.Daha fazla Öğe Common Fixed Point Results on Complex Valued G(b)-Metric Spaces(Chiang Mai Univ, Fac Science, 2018) Ege, Ozgur; Karaca, IsmetDaha fazla In this study, we introduce some notions such as coincidence point, compatible and occasionally weakly compatible maps in complex valued G(b)-metric spaces. Then using these notions we prove some new common fixed point theorems in complex valued G(b)-metric spaces.Daha fazla Öğe Computing Higher Dimensional Digital Homotopy Groups(Natural Sciences Publishing Corp-Nsp, 2014) Meric, Elif Tugce; Vergili, Tane; Karaca, IsmetDaha fazla In this paper, we study out a method for computing digital homotopy groups in higher dimensions. We investigate the relation between a digital image and its nth homotopy group when n is greater than 1 and show that a digital covering map which is a radius 2 local isomorphism induces an isomorphism between digital homotopy groups in higher dimensions.Daha fazla Öğe Digital Co-Hopf Spaces(Univ Nis, Fac Sci Math, 2020) Ege, Ozgur; Karaca, IsmetDaha fazla In this work, we deal with co-Hopf space structure of digital images. We prove that a pointed digital image having the same digital homotopy type as a digital co-Hopf space is itself a digital co-Hopf space. We conclude that a kappa-deformation retract of a digital co-Hopf space is a digital co-Hopf space. We also show that the digital equivalences are digital co-Hopf homomorphisms.Daha fazla Öğe Digital Fibrations(Natl Acad Sciences India, 2017) Ege, Ozgur; Karaca, IsmetDaha fazla In this paper, digital fibrations were introduced. Theorems related to digital fibrations were proved. Homology properties of digital fibrations with counter examples were studied and an application for digital fibrations was also described.Daha fazla Öğe Digital fixed points, approximate fixed points, and universal functions(Univ Politecnica Valencia, Editorial Upv, 2016) Boxer, Laurence; Ege, Ozgur; Karaca, Ismet; Lopez, Jonathan; Louwsma, JoelDaha fazla A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).Daha fazla Öğe Digital homotopy fixed point theory(Elsevier France-Editions Scientifiques Medicales Elsevier, 2015) Ege, Ozgur; Karaca, IsmetDaha fazla In this paper, we construct a framework which is called the digital homotopy fixed point theory. We get new results associating digital homotopy and fixed point theory. We also give an application on this theory. (C) 2015 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.Daha fazla Öğe THE DIGITAL SMASH PRODUCT(Amer Inst Mathematical Sciences-Aims, 2020) Cinar, Ismet; Ege, Ozgur; Karaca, IsmetDaha fazla In this paper, we construct the smash product from the digital viewpoint and prove some its properties such as associativity, distributivity, and commutativity. Moreover, we present the digital suspension and the digital cone for an arbitrary digital image and give some examples of these new concepts.Daha fazla Öğe Digital topological complexity numbers(Scientific Technical Research Council Turkey-Tubitak, 2018) Karaca, Ismet; Is, MelihDaha fazla The intersection of topological robotics and digital topology leads to us a new workspace. In this paper we introduce the new digital homotopy invariant digital topological complexity number TC(X, kappa) for digital images and give some examples and results about it. Moreover, we examine adjacency relations in the digital spaces and observe how TC(X, kappa) changes when we take a different adjacency relation in the digital spaces.Daha fazla Öğe Examples of self-dual codes over some sub-Hopf algebras of the Steenrod algebra(Scientific Technical Research Council Turkey-Tubitak, 2017) Vergili, Tane; Karaca, IsmetDaha fazla Codes over the finite sub-Hopf algebras A (n) of the (mod 2) Steenrod algebra A were studied by Dougherty and Vergili. In this paper we study some Euclidean and Hermitian self-dual codes over A (n) by considering Milnor basis elements.Daha fazla Öğe Explicit motion planning in digital projective product spaces(Scientific And Technological Research Council Turkey, 2022) Fisekci, Seher; Karaca, IsmetDaha fazla We introduce digital projective product spaces based on Davis' projective product spaces. We determine an upper bound for the digital LS-category of digital projective product spaces. In addition, we obtain an upper bound for the digital topological complexity of these spaces through an explicit motion planning construction, which shows digital perspective validity of results given by S. Fi?sekci? and L. Vandembroucq. We apply our outcomes on specific spaces in order to be more clear.Daha fazla Öğe GRAPH TOPOLOGY ON FINITE DIGITAL IMAGES(Util Math Publ Inc, 2018) Ege, Ozgur; Karaca, IsmetDaha fazla The main goal of this work is to present a topology, called a graph topology, on finite digital images. We deal with some properties of this topology such as k-connectivity and digital continuous mapping. We finally show that the property of being graph topology is a topological invariant between digital isomorphic finite digital images.Daha fazla Öğe Higher Topological Complexity for Fibrations(Univ Nis, Fac Sci Math, 2022) Is, Melih; Karaca, IsmetDaha fazla We introduce the higher topological complexity (TCn) of a fibration in two ways: the higher homotopic distance and the Schwarz genus. Then we have some results on this notion related to TC, TCn or cat of a topological space or a fibration. We also show that TCn of a fibration is a fiber homotopy equivalence.Daha fazla Öğe The higher topological complexity in digital images(Univ Politecnica Valencia, Editorial Upv, 2020) Is, Melih; Karaca, IsmetDaha fazla Y. Rudyak develops the concept of the topological complexity TC(X) defined by M. Farber. We study this notion in digital images by using the fundamental properties of the digital homotopy. These properties can also be useful for the future works in some applications of algebraic topology besides topological robotics. Moreover, we show that the cohomological lower bounds for the digital topological complexity TC(X, kappa) do not hold.Daha fazla