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Zylinder-knoten und symmetrische VereinigungenLamm, Christoph. January 1999 (has links)
Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1999. / Includes bibliographical references (p. [85]-87).
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Knotted varieties ...Stafford, Anna Adelaide, January 1935 (has links)
Thesis (PH. D.)--University of Chicago, 1933. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." Bibliography: p. 28.
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Braid index of satellite linksNutt, Ian John January 1995 (has links)
No description available.
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The existence of energy minimizers for knots and linksSargrad, Scott. January 2004 (has links)
Thesis (B.A.)--Haverford College, Dept. of Mathematics, 2004. / Includes bibliographical references.
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Elementary surgery along torus knots and solvable fundamental groups of closed 3-manifoldsMoser, Louise Elizabeth, January 1970 (has links)
Thesis (Ph. D.)--University of Wisconsin--Madison, 1970. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.
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On Vassiliev invariants and Cn̳-moves for knots /Yamada, Harumi. January 2005 (has links) (PDF)
Thesis (Ph. D.)--Waseda University, 2005. / Accompanied by summary (4 leaves ; 30 cm.) in Japanese. On t.p. "n̳" of "Cn-moves" is subscript. Includes bibliographical references (leaves 43-46). "List of papers by Harumi Yamada": leaf 47.
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Knotengruppen Darstellungen und Invarienten von endlichem TypEisermann, Michael. January 1900 (has links)
Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2000. / Includes bibliographical references (p. 127-131).
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Khovanov Homology as an Generalization of the Jones Polynomial in Kauffman TermsTram, Heather 01 August 2016 (has links)
This paper explains the construction of Khovanov homology of which begins by un derstanding how Louis Kauffman generalizes the Jones polynomial using a state sum model of the bracket polynomial for an unoriented knot or link and in turn recovers the Jones polynomial, a knot invariant for an oriented knot or link. Kauffman associates the unknot by the polynomial (−A2 − A−2) whereas Khovanov associates the unknot by (q + q−1) through a change of variables. As an oriented knot or link K with n crossings produces 2n smoothings, Khovanov builds a commutative cube {0,1}n and associates a graded vector space to each smoothing in the cube. By defining a differential operator on the directed edges of the cube so that adjacent states differ by a type of smoothing for a fixed cross ing, we can form chain groups which are direct sums of these vector spaces. Naturally we get a bi-graded (co)chain complex which is called the Khovanov complex. The resulting (co)homology groups of these (co)chains turns out to be invariant under the Reidemeister moves and taking the Euler characteristic of the Khovanov complex returns the very same Jones polynomial that we started with.
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Virtual TribracketsPico, Shane 01 January 2018 (has links)
The goal of this paper is to introduce a new algebraic structure for coloring regions in the planar complement of an oriented virtual knot or link diagram that I will refer to as virtual tribrackets. I will begin with an overview of classical knot theory where I introduce knot diagrams and ways of calculating knot invariants. This paper progresses into virtual knots and links, their geometric interpretations as well as their virtual moves, and some invariant examples for the virtual case. This informations allows me to introduce tribrackets, which is a labeling method used to define counting invariants for classical knots and link diagrams. Finally, this paper properly defines and proves the use of virtual tribackets in defining invariants for virtual knots as well as providing examples from [6] which more precisely show that these invariants can distinguish between certain virtual knots.
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Fitting spline functions by the method of least squaresSmith, John Terry January 1967 (has links)
A spline function of degree k with knots S₀, S₁,...,Sr is a C[superscript]k-1 function which is a polynomial of degree at most k in each of the intervals (-∞, S₀), (S₀, S₁),…, (Sr,+∞). The Gauss-Markoff Theorem can be used to estimate by least squares the coefficients of a spline function of given degree and knots.
Estimating a spline function of known knots without full knowledge of the degree entails an extension of the Gauss-Markoff technique. The estimation of the degree when the knots are also unknown has a possible solution in a method employing finite differences.
The technique of minimizing sums of squared residuals forms the basis for a method of estimating the knots of a spline function of given degree. Estimates for the knots may also be obtained by a method of successive approximation, provided additional information about the spline function is known. / Science, Faculty of / Mathematics, Department of / Graduate
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