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Department : Uygulamalı Matematik ... ✕Researcher : İsmet ALTINTAŞ ✕
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Prof. Dr. İsmet ALTINTAŞFen Fakültesi
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An invariant of regular isotopy for disoriented links

İsmet ALTINTAŞ

In this paper, we define a two-variable polynomial invariant of regular isotopy, M_K for a disoriented link diagram K. By normalizing the polynomial M_K using complete writhe, we obtain a polynomial invariant of ambient isotopy, N_K, for a disoriented link diagram K. The polynomial N_K is a generalization of the expanded Jones polynomial for disoriented links and is an expansion of the Kauffman polynomial F to the disoriented links. Moreover, the polynomial M_K is an expansion of the Kauffman polynomial L to the disoriented links.

Article 2023 Fen Fakültesi Turkish Journal of Mathematics47 ( 1 ) 50 Views
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On elementary soft compact topological spaces

İsmet ALTINTAŞ

This paper is a work on elementary soft (𝜖-soft) compact spaces. We first define the cofinite 𝜖- soft compact space and prove that the image of an 𝜖-soft compact space under a soft continuous mapping is 𝜖-soft compact space. We then examine the relationship between 𝜖-soft compact space and classical compact space and give an illustrative example.

Article 2021 Fen Fakültesi MANAS Journal of Engineering (MJEN)9 ( 2 ) 59 Views
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Soft partial metric spaces

İsmet ALTINTAŞ | Peyil Esengul Kızı

This paper is an introduction to soft partial metric spaces. The aim is to create a soft topological model for a programming language described as a soft logic system, like in classical partial metric studies. Since the soft metric spaces have Hausdorff properties, they are not useful in examining non-Hausdorff soft topologies. This paper proposes a generalized soft metric for non-Hausdorff soft topologies and a new approach that guides how to expand soft metric implements like the Banach theorem to such topologies.

Article 2022 Fen Fakültesi Soft Computing28 ( 18 ) 24 Views
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Redefining disoriented knots and diagrammatic methods

İsmet ALTINTAŞ

Altintas (2018) introduced a new concept with the name of disoriented knot. He defined a disoriented knot as an embedding of a disoriented circle with two arcs into Double-struck capital R3. In this paper, we redefine a disoriented knot as an embedding of a disoriented circle with 2n arcs into Double-struck capital R3 and expand the diagrammatic invariants and methods of classical knot theory such as connected sum, Reidemeister moves, Gauss codes, and Gauss diagrams to disoriented knot theory. Thus, we create the basic diagrammatic invariants and methods of disoriented knot theory.

Article 2022 Fen Fakültesi Mathematical Methods in the Applied Sciences45 ( Special Issue: 18 ) 41 Views
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A new approach for soft topology and soft function via soft element

İsmet ALTINTAŞ

In this article, we give some new properties of elementary operations on soft sets and then we introduce a new soft topology by using elementary operations over a universal set with a set of parameters called elementary soft topology. Also, we define a topology, members of which are collections of the soft elements and give the relation between this topology and elementary soft topology. We show that this new soft topology is different from those previously defined soft topologies. We prove some of the properties of the topological concepts we investigate in this topology. Finally, we describe ...More

Article 2020 Fen Fakültesi Mathematical Methods in the Applied Sciences44 ( 9 ) 68 Views
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Countable and separable elementary soft topological space

İsmet ALTINTAŞ

This paper is an introduction to countable and separable elementary soft topological spaces, which includes concepts such as dense soft set, first countability, second countability, separability and Lindelof properties and some basic properties of them in the elementary soft topological spaces.

Article 2020 Fen Fakültesi Mathematical Methods in the Applied Sciences44 ( 9 ) 39 Views
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Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping

İsmet ALTINTAŞ

In this article, we describe the concepts such as sequentially soft closeness, sequential compactness, totally boundedness and sequentially continuity in any soft cone metric space and prove their some properties. Also, we examine soft closed set, soft closure, compactness and continuity in an elementary soft topological cone metric space. Unlike classical cone metric space, sequential compactness and compactness are not the same here. Because the compactness is an elementary soft topological property and cannot be defined for every soft cone metric space. However, in the restricted soft cone ...More

Article 2020 Fen Fakültesi Turkish Journal of Mathematics44 ( 6 ) 61 Views
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