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Publication year : 2023 ✕Publisher : Tübitak ✕
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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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The inequalities on dual numbers and their topological structures

Olgun DURMAZ

Inequalities are frequently used in various fields of mathematics to prove theorems. The existence of inequalities contributes significantly to the foundations of such branches. In this paper, we study the properties of order relations in the system of dual numbers, which is inspired by order relations defined on real numbers. Besides, some special inequalities that are used in various fields of mathematics, such as Cauchy-Schwarz, Minkowski, and Chebyshev are studied in this framework. An example is also provided to validate our research findings. Keywords: dual numbers; dual absolute value; ...More

Article 2023 Fen Fakültesi Turkish Journal of Mathematics47 ( 5 ) 28 Views
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