10 research outputs found
HOMFLY polynomials of torus links as generalized Fibonacci polynomials
No full textThe focus of this paper is to study the HOMFLY polynomial of (2, n)-torus link as a generalized Fibonacci polynomial. For this purpose, we first introduce a form of generalized Fibonacci and Lucas polynomials and provide their some fundamental properties. We define the HOMFLY polynomial of (2, n)-torus link with a way similar to our generalized Fibonacci polynomials and provide its fundamental properties. We also show that the HOMFLY polynomial of (2, n)-torus link can be obtained from its Alexander-Conway polynomial or the classical Fibonacci polynomial. We finally give the matrix representations and prove important identities, which are similar to the Fibonacci identities, for the our generalized Fibonacci polynomial and the HOMFLY polynomial of (2, n)-torus link
A generalization of the Alexander polynomial as an application of the delta derivative
No full textIn this paper, we define the delta derivative in the integer group ring and we show that the delta derivative is well defined on the free groups. We also define a polynomial invariant of oriented knot and link by carrying the delta derivative to the link group. Since the delta derivative is a generalization of the free derivative, this polynomial invariant called the delta polynomial is a generalization of the Alexander polynomial. In addition, we present a new polynomial called the difference polynomial of oriented knot and link, which is similar to the Alexander polynomial and is a special case of the delta polynomial
Topology of soft cone metric spaces
No full textInternational Conference on Functional Analysis in Interdisciplinary Applications (FAIA) -- OCT 02-05, 2017 -- Astana, KAZAKHSTANIn Simsek's paper it was introduced a concept of soft cone metric space via soft elements and some fixed point theorems in soft cone metric space were provided. In this work, we examine topological structures such as open ball, soft neighbourhood and soft open set in soft metric spaces and their some properties, and prove that every soft cone metric space under some condition is a soft topological space according to elementary operations on soft sets.Kyrgyz Turkish Manas University [KTMUBAP-2016.FBE.12]This work is supported by Kyrgyz Turkish Manas University in the framework of Scientific Research Projects (KTMUBAP-2016.FBE.12)
A Generalization of the Alexander Polynomial
No full textIn this paper, we present a generalization of two variables of the Alexander polynomial for a given oriented knot diagram. We define the Alexander polynomial of two variables by an easy method which will be achieved as a result of the interpretation of the crossing point as a particle with input-output spins in the mathematical physics. The classical Alexander polynomial is the case of one of the variables to be equal to 1 in the Alexander polynomial of two variables
HOMFLY polynomials of torus links as generalized Fibonacci polynomials
No full textThe focus of this paper is to study the HOMFLY polynomial of (2, n)-torus link as a generalized Fibonacci polynomial. For this purpose, we first introduce a form of generalized Fibonacci and Lucas polynomials and provide their some fundamental properties. We define the HOMFLY polynomial of (2, n)-torus link with a way similar to our generalized Fibonacci polynomials and provide its fundamental properties. We also show that the HOMFLY polynomial of (2, n)-torus link can be obtained from its Alexander-Conway polynomial or the classical Fibonacci polynomial. We finally give the matrix representations and prove important identities, which are similar to the Fibonacci identities, for the our generalized Fibonacci polynomial and the HOMFLY polynomial of (2, n)-torus link
Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping
No full textIn 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 metric spaces, they are the same. Additionally, we prove some fixed point theorems related to diametrically contractive mapping in a complete soft cone metric space.Kyrgyz-Turkish Manas University [KTMU-2016, FBE.12]This work was supported by Kyrgyz-Turkish Manas University under the project number KTMU-2016.FBE.12. Also, we would like to thank the anonymous referees for suggestions and corrections towards the improvement of the paper
Soft partial metric spaces
No full textThis 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.Kyrgyz-Turkish Manas University [KTMU-BAP-2019.FBE.07]The authors thank the referees for their care and contributing evaluations. This research is supported by Kyrgyz-Turkish Manas University (Project Number: KTMU-BAP-2019.FBE. 07)
Unoriented knot polynomials of torus links as Fibonacci-type polynomials
No full textThe focus of this paper is to study the two-variable Kauffman polynomials [Formula: see text] and [Formula: see text], and the one-variable BLM/Ho polynomial [Formula: see text] of [Formula: see text]-torus link as the Fibonacci-type polynomials and to express the Kauffman polynomials in terms of the BLM/Ho polynomial. For this purpose, we prove that each of the examined polynomials of [Formula: see text]-torus link can be determined by a third-order recurrence relation and give the recursive properties of them. We correlate these polynomials with the Fibonacci-type polynomials. By using the relations between the BLM/Ho polynomials and Fibonacci-type polynomials, we express the Kauffman polynomials in terms of the BLM/Ho polynomials.</jats:p
Countable and separable elementary soft topological space
No full textThis 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
COMPARITIVE STUDY ON VOLATILE AROMA COMPOUNDS OF TWO DIFFERENT GARLIC TYPES (KASTAMONU AND CHINESE) USING GAS CHROMATOGRAPHY MASS SPECTROMETRY (HS-GC/MS) TECHNIQUE
No full textBackround: The medicinal use of garlic is much older than its usage as a food. The medical importance of garlic comes forward for its sulfur-containing components. In this study, it was aimed to compare Kastamonu garlic type with Chinese garlic type based on their aroma profiles. Materials and Methods: Fresh Kastamonu garlic samples harvested from Kastamonu region of Turkey and Chinese garlic samples obtained from Turkish market were used as plant material. Volatile aroma compounds were determined using Headspace Gas Chromatography Mass Spectrometry (HS-GC/MS). Results: Sixteen and twenty aroma components were identified in Kastamonu and Chinese garlic types, respectively. Kastamonu garlic type was found to be richer than Chinese garlic types in terms of sulfur-containing compounds. Diallyl disulphide, which is one of these components, was detected at level of 41.87% and 34.95% in the Kastamonu and Chinese garlic types, respectively. Also di-2-propenyl trisulfide was found only in Kastamonu garlic types. Disulfide, methyl 2-propenyl was determined at similar levels in both garlic types. Conclusion: The majority of garlic grown in Kastamonu region of Turkey is assessed by medical companies. Conclusion: The results of the current study showed that Kastamonu garlic type has important medical properties. Therefore, this garlic can also be used in the medical field, as well as the consumption as food.Kastamonu and Taskopru Agriculture Province Management and Republic of Turkey Ministry of Food, Agriculture and Livestock-General Directorate of Agricultural Research and Policy Projects Coordinating Office [TAGEM/11/AR-GE/20]The author would like to thank the Kastamonu and Taskopru Agriculture Province Management and Republic of Turkey Ministry of Food, Agriculture and Livestock-General Directorate of Agricultural Research and Policy Projects Coordinating Office (TAGEM/11/AR-GE/20), for garlic samples and supporting this study
