Random Knotting and Linking
Random Knotting and Linking

Author: Kenneth C. Millett

Publisher: World Scientific

Published: 1994

Total Pages: 207

ISBN-13: 9810220057

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This volume includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths. The statistical mechanics and topology of surfaces on the d-dimensional simple cubic lattice are investigated. The energy of knots is studied both analytically and numerically. Vassiliev invariants are investigated and used in random knot simulations. A mutation scheme which leaves the Jones polynomial unaltered is described. Applications include the investigation of RNA secondary structure using Vassiliev invariants, and the direct experimental measurement of DNA knot probability as a function of salt concentration in random cyclization experiments on linear DNA molecules. The papers in this volume reflect the diversity of interest across science and mathematics in this subject, from topology to statistical mechanics to theoretical chemistry to wet-lab molecular biology.

Knotted Doughnuts and Other Mathematical Entertainments
Knotted Doughnuts and Other Mathematical Entertainments

Author: Martin Gardner

Publisher: American Mathematical Soc.

Published: 2020-10-06

Total Pages: 278

ISBN-13: 1470463644

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Martin Gardner's Mathematical Games columns in Scientific American inspired and entertained several generations of mathematicians and scientists. Gardner in his crystal-clear prose illuminated corners of mathematics, especially recreational mathematics, that most people had no idea existed. His playful spirit and inquisitive nature invite the reader into an exploration of beautiful mathematical ideas along with him. These columns were both a revelation and a gift when he wrote them; no one--before Gardner--had written about mathematics like this. They continue to be a marvel. This is the original 1986 edition and contains columns published from 1972-1974.

Knot Theory
Knot Theory

Author: Vassily Olegovich Manturov

Publisher: CRC Press

Published: 2004-02-24

Total Pages: 417

ISBN-13: 0203402847

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Since discovery of the Jones polynomial, knot theory has enjoyed a virtual explosion of important results and now plays a significant role in modern mathematics. In a unique presentation with contents not found in any other monograph, Knot Theory describes, with full proofs, the main concepts and the latest investigations in the field. The book is divided into six thematic sections. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. This method allows the encoding of topological objects by words in a finite alphabet. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. This section includes the author's own important results regarding new invariants of virtual knots. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra (DGA) construction. Knot Theory is notable not only for its expert presentation of knot theory's state of the art but also for its accessibility. It is valuable as a professional reference and will serve equally well as a text for a course on knot theory.

The Knot Bible
The Knot Bible

Author: Bloomsbury Publishing

Publisher: A&C Black

Published: 2013-03-15

Total Pages: 288

ISBN-13: 1408155877

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The complete and definitive bible of knots for seafarers. Featuring all the knots, hitches, bends, splices, whipping and decorative knotwork that you would find on a boat, this comprehensive bible of knots will help those who go to sea master every knot they will need. Over 200 knots are scored for strength, reliability, ease of tying (and untying) and usefulness. Step by step photographs show how to tie each knot, and demonstrate how they can be used, such as in the rigging or for tying boats up. Interesting knot know-how sections give extra information about the knot's history, plus helpful tips and techniques, including choosing the right rope for the right task and using the right knot. With a beautiful modern design, and highly illustrated with full colour photographs and instructive diagrams throughout, The Knot Bible remains accessible to all sailors of all levels of experience whilst still being the king of knot books.

Braid Group, Knot Theory, and Statistical Mechanics II
Braid Group, Knot Theory, and Statistical Mechanics II

Author: Chen Ning Yang

Publisher: World Scientific

Published: 1994

Total Pages: 496

ISBN-13: 9789810215248

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The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors.

Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model
Modeling Time-Varying Unconditional Variance by Means of a Free-Knot Spline-GARCH Model

Author: Oliver Old

Publisher: Springer Nature

Published: 2022-07-27

Total Pages: 260

ISBN-13: 3658386185

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The book addresses the problem of a time-varying unconditional variance of return processes utilizing a spline function. The knots of the spline functions are estimated as free parameters within a joined estimation process together with the parameters of the mean, the conditional variance and the spline function. With the help of this method, the knots are placed in regions where the unconditional variance is not smooth. The results are tested within an extensive simulation study and an empirical study employing the S&P500 index.

Plants Reported Resistant Or Tolerant to Root Knot Nematode Infestation
Plants Reported Resistant Or Tolerant to Root Knot Nematode Infestation

Author: Jocelyn Tyler

Publisher:

Published: 1941

Total Pages: 100

ISBN-13:

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This publication is a compilation of reports on all plant species and varieties that have been called either resistant or tolerant to infestation by the root knot nematode, Heterodera marioni (Cornu) Goodey, (formerly called H. radicola (Greef) Mueller). The purpose is twofold: to bring together all available information on the subject in condensed form for the use of growers, plant breeders, and other investigators, and to establish a basis for the contribution of further data. It must not be assumed that all of the plants listed here are recommended as resistant. They intention is rather to present technical source material, not only useful to those who need practical information on particular plants but also suggestive to future workers.

An Invitation to Knot Theory
An Invitation to Knot Theory

Author: Heather A. Dye

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 256

ISBN-13: 1315360098

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The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot Theory An Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research. It provides the foundation for students to research knot theory and read journal articles on their own. Each chapter includes numerous examples, problems, projects, and suggested readings from research papers. The proofs are written as simply as possible using combinatorial approaches, equivalence classes, and linear algebra. The text begins with an introduction to virtual knots and counted invariants. It then covers the normalized f-polynomial (Jones polynomial) and other skein invariants before discussing algebraic invariants, such as the quandle and biquandle. The book concludes with two applications of virtual knots: textiles and quantum computation.