65 research outputs found
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
Introduction to disoriented knot theory
No full textThis paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot, disoriented crossing and Reidemesiter moves for disoriented diagrams, numerical invariants such as the linking number and the complete writhe, the polynomial invariants such as the bracket polynomial, the Jones polynomial for the disoriented knots and links
An oriented state model for the Jones polynomial and its applications alternating links
No full textIn this paper, we de. ne a polynomial invariant of regular isotopy, G(L), for oriented knot and link diagrams L. From G(L) by multiplying it by a normalizing factor, we obtain an ambient isotopy invariant, N-L, for oriented knots and links. We compare the polynomial N-L with the original Jones polynomial and with the normalized bracket polynomial. We show that the polynomial NL yields the Jones polynomial and the normalized bracket polynomial. As examples, we give the polynomial G(L) of some knot and link diagrams and compute the polynomial GL for torus links of type (2, n), and applying computer algebra ( MAPLE) techniques, we calculate the polynomial G(L) of torus links of type (2, n). Furthermore we give its applications to alternating links. (c) 2007 Elsevier Inc. All rights reserved
Manufacturing automation : metal cutting mechanics, machine tool vibrations, and CNC design / Yusuf Altintas.
No full textengineering bookfair2015Includes bibliographical references and index.xii, 366 pages :"Metal cutting is a widely used method of producing manufactured products. The technology of metal cutting has advanced considerably along with new materials, computers, and sensors. This new edition treats the scientific principles of metal cutting and their practical application to manufacturing problems. It begins with metal cutting mechanics, principles of vibration, and experimental modal analysis applied to solving shop floor problems. Notable is the in-depth coverage of chatter vibrations, a problem experienced daily by manufacturing engineers. The essential topics of programming, design, and automation of CNC (computer numerical control) machine tools, NC (numerical control) programming, and CAD/CAM technology are discussed. The text also covers the selection of drive actuators, feedback sensors, modeling and control of feed drives, the design of real time trajectory generation and interpolation algorithms, and CNC-oriented error analysis in detail. Each chapter includes examples drawn from industry, design projects, and homework problems. This book is ideal for advanced undergraduate and graduate students, as well as practicing engineers"--Provided by publisher
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
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)
Computer algebra and colored Jones polynomials
No full textIn this paper, we apply computer algebra (MAPLE) techniques to calculate the N-colored Jones polynomial of the trefoil knot and the figure eight knot. For this purpose, a computer program was developed. When an integer N >= 2 is given, the program calculates the N-colored Jones polynomial of the trefoil and the figure eight knot. (c) 2006 Elsevier Inc. All rights reserved
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
A new approach for soft topology and soft function via soft element
No full textIn 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 soft function and soft continuity and give an application of the soft function as soft set approach to the rotation inE3
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