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Ideal Knots by Andrzej Stasiak,Vsevolod Katritch,Louis H. Kauffman Pdf
In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter.
Ideal Knots by A Stasiak,V Katritch,L H Kauffman Pdf
In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter. Contents:Ideal Knots and Their Relation to the Physics of Real Knots (A Stasiak et al.)Knots with Minimal Energies (Y Diao et al.)The Writhe of Knots and Links (E J Janse van Rensburg et al.)Entropy of a Knot: Simple Arguments About Difficult Problem (A Yu Grosberg)Knots and Fluid Dynamics (H K Moffatt)Möbius-Invariant Knot Energies (R B Kusner & J M Sullivan)Fourier Knots (L H Kauffman)and other papers Readership: Mathematicians, physicists, chemists and biologists. Keywords:Knots;Topology;Theory of Knots;Energy of Knots;Knot's Invariants;Geometry of Knots;Physics of KnotsReviews: “The authors of the articles in this book manage to put together a wide variety of ideas related to the notion of a simple representation of a knot.” Mathematical Reviews
Essential Knots by Neville Olliffe,Madeleine Rowles-Olliffe Pdf
A practical and stylish illustrated guide, 'Essential Knots' shows how to tie each knot with expert guidance on which knot to tie when and why. Each knot is categorised by its use in a particular sport or hobby, with a brief explanation as to why it is the best knot for the job.
Jorge Alberto Calvo,AMS Special Session on Physical Knotting,Kenneth C. Millett,Eric J. Rawdon
Author : Jorge Alberto Calvo,AMS Special Session on Physical Knotting,Kenneth C. Millett,Eric J. Rawdon Publisher : American Mathematical Soc. Page : 356 pages File Size : 40,6 Mb Release : 2002 Category : Knot theory ISBN : 9780821832004
Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$ by Jorge Alberto Calvo,AMS Special Session on Physical Knotting,Kenneth C. Millett,Eric J. Rawdon Pdf
The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volumediscusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering,physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.
THE ASHLEY BOOK OF KNOTS by Clifford W. Ashley Pdf
What else needs to be said about knots? Almost 650 pages of incredible knowledge, presented in a truzly unique manner. This is not a book of knots, it is the BOOK OF KNOTS. Was muss noch über Knoten gesagt werden? Fast 650 Seiten unglaubliches Wissen, präsentiert in einer wahrhaft einzigartigen Weise. Dies ist kein Buch über Knoten, es ist das BUCH DER KNOTEN.
Knots in Hellas '98 - Proceedings of the International Conference on Knot Theory and Its Ramifications by V. F. R. Jones Pdf
There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon–Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected by the following path: hyperbolic structures, PSL(2, C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.
Energy of Knots and Conformal Geometry by Jun O'Hara Pdf
Energy of knots is a theory that was introduced to create a “canonical configuration” of a knot — a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a “canonical configuration” of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments. Contents:In Search of the “Optimal Embedding” of a Knot:α-Energy Functional E(α)On E(2)Lp Norm Energy with Higher IndexNumerical ExperimentsStereo Pictures of E(2)MinimizersEnergy of Knots in a Riemannian ManifoldPhysical Knot EnergiesEnergy of Knots from a Conformal Geometric Viewpoint:Preparation from Conformal GeometryThe Space of Non-Trivial Spheres of a KnotThe Infinitesimal Cross RatioThe Conformal Sin Energy Esin θMeasure of Non-Trivial SpheresAppendices:Generalization of the Gauss Formula for the Linking NumberThe 3-Tuple Map to the Set of Circles in S3Conformal Moduli of a Solid TorusKirchhoff ElasticaOpen Problems and Dreams Readership: Graduate students and researchers in geometry & topology and numerical & computational mathematics. Keywords:Energy of Knots;Optimal Embedding;Conformal Geometry;Möbius Transformation;Infinitesimal Cross RatioReviews:“… this book gives an excellent, state of the art account of many of the important results in this field. A strong point of the book is that almost all proofs of the theorems stated are included.”Zentralblatt MATH
CLICK HERE TO DOWNLOAD A KNOT SAMPLER FROM THE CHAPTER ON "KNOTS FOR HIKING & CAMPING" (Provide us with a little information and we'll send your download directly to your inbox) * Guidelines for selecting the best rope and the best knot for the activity at hand * Knot-tying directions clearly illustrated with photos * New entry in the Mountaineers Outdoor Basics series It's fair to say that climber Clyde Soles is obsessed with ropes and knots and their absolute performance-since he regularly entrusts his life to ropes on sheer rock faces. His unique book explains how to select and use ropes, cordage, and webbing for the outdoors. Invaluable information is provided on rope handling techniques (how to avoid dreaded tangles) and the best methods for rope care and maintenance. Step-by-step directions for tying over 40 knots are clearly illustrated with photographs. Other useful features include a glossary and a knot comparison chart by activity. Chapters include Knots Basics (from Tripod Lashing to the Figure 8 Loop), Knots for Hikers and Climbers (from the Prusik knot to the Autoblock), Knots for Canoeists and Kayakers (from the Buntline hitch to the Bowline on a bight), and more. This is the definitive text on ropes and knots for anyone who plays in the outdoors!
The ultimate visual guide to all types of knots. Avoid getting yourself into a tangle by following detailed step-by-step instructions that show you how to tie and untie more than 100 knots. Whichever knotty scenario you find yourself in, from in your own garden, to up in the mountains or across seas, this reference book will take you from novice to expert rope tier. Covering more than 100 knots for climbing, sailing, horse-riding, survival camping, and fishing as well as for gardening, DIY, medical, and even decorative purposes. The photographs of every step use strands of rope in different colors - so you can clearly see how to tie each knot. You’ll learn all about the fascinating stories behind how many of these knots were first tied as well as their original functions in this knot tying book. Each knot has simple to follow instructions on the features and benefits and what they can be used for. Includes knots such as figure-of-eights, reef knots, highwayman’s hitches, and monkey’s fists. Find out about techniques like sheer lashing and the constrictor knot. The book begins by teaching you all about rope materials and construction and how to maintain them. At the end of the book the glossary and index so you can easily find just the knot you’re in need of. There are more than 1,000 photographs, illustrations, and artworks. Expert author Des Pawson is a founding member of the International Guild of Knot Tyers. One-Stop Practical Guide to Tying and Using Knots Knots: The Complete Visual Guide is arranged by chapters covering Stopper Knots, Binding Knots, Bends, Hitches, Loops, Plaits & Sennits, and Splices & Whippings. It also includes detailed instructions for over 100 knots and fantastic beginner guides to help boy scouts, girl scouts, first-time climbers and everything in between become experienced campers, sailors, and mountaineers. Inside this visual guide, you’ll find: • Accessible text and tables that explain the features and benefits of each knot • Sequence spreads display the top five knots you need for a range of purposes, from sailing and fishing to gardening and gift-wrapping • Fun facts about the oldest knots and their history • Essential information on how to choose the best rope to use and how to maintain them More from DK Books: Don’t miss out on more fascinating visual reference books! Look for The Complete Sailing Manual, How to Garden, and The Survival Handbook from DK Books to build on your new-found knot skills.
I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
Author : I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky Publisher : American Mathematical Society Page : 250 pages File Size : 52,6 Mb Release : 2023-08-21 Category : Mathematics ISBN : 9781470471477
The Diverse World of PDEs by I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky Pdf
This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows. The companion volume (Contemporary Mathematics, Volume 789) is devoted to Algebraic and Cohomological Aspects of PDEs.
From camping to rock climbing, your safety depends on choosing and tying knots correctly. With this handy guide, you can tackle every task from DIY to tying fishing or sailing lines with complete confidence. Knots: The Complete Visual Guide presents the 100 most useful knots for sailing, fishing, camping, climbing, and decorative uses. It explains how to tie highwayman hitches, monkey fists, bowlines, and many other key knots. Its clear uncluttered images show you exactly what to do, taking you from the easiest overhand knot to the decorative Turk's head five-lead four-bight knot. This indispensable book identifies the knot you need. Are you climbing and depend on a failsafe knot? The figure-of-eight's distinctive shape makes it easy to check it has been tied correctly. A slipped-release is useful when you need to untie your knot quickly. And if you ever want to know if a knot has been untied, try the quirky "thief" knot - so-called because a thief will betray their presence by retying it incorrectly. You'll also learn the history behind the different types of knots and the fascinating stories behind how many of them came about. Knots: The Complete Visual Guide is the ideal book to have in hand for whenever a knot is needed.
Learn how to apply the right knot in any situation - secure and strong enough for the job. Such skill can be essential to the safety and enjoyment of leisure pursuits, such as climbing, sailing and fishing. In rescue, life can depend on it. Here Geoffrey Budworth has selected over 100 of the best knots from his lifetime's experience of knots.
Topological Polymer Chemistry by Yasuyuki Tezuka Pdf
There are examples aplenty in the macroscopic world that demonstrate the form of objects directing their functions and properties. On the other hand, the fabrication of extremely small objects having precisely defined structures has only recently become an attractive challenge, which is now opening the door to nanoscience and nanotechnology.In the field of synthetic polymer chemistry, a number of critical breakthroughs have been achieved during the first decade of this century to produce an important class of polymers having a variety of cyclic and multicyclic topologies. These developments now offer unique opportunities in polymer materials design to create unprecedented properties and functions simply based on the form, i.e. topology, of polymer molecules.In this book on topological polymer chemistry, the important developments in this growing area will be collected for the first time, with particular emphasis on new conceptual insights for polymer chemistry and polymer materials. The book will systematically review topological polymer chemistry from basic aspects to practice, and give a broad overview of cyclic polymers covering new synthesis, structure characterization, basic properties/functions and the eventual applications.
Discover the Only Knots You'll Ever Need! The Useful Knots Book is a no-nonsense knot guide on how to tie the 25+ most practical rope knots. It comes with easy to follow instructions, pictures, and tips on when to best use each knot. Teach yourself knot tying today, because it's easy, fun, and useful. Get it now. The Ultimate Knots Guide * Explanations of common knots and ropes terms * Easy to follow instructions and clear pictures * Tips for proper rope care * Advice on how to choose right knot for the job * All the fundamental boy scout knots Learn the 5 Main Types of Knots and When to Use Them * Stopper Knots * Loops * Hitches * Bends * Lashing Discover all the Knots You Need ... in this complete knot tying visual guide. * From basic knots to more advanced ones * Climbing knots * Various bowline knots * Fishing knots * Boating knots * Knots for survival ... and more. Limited Time Only... Get your copy of The Useful Knots Book today and you will also receive: * Free SF Nonfiction Books new releases * Exclusive discount offers * Downloadable sample chapters * Bonus content … and more! Learn how to tie the only knots you'll ever need, because this book has the 25 most practical knots there are. Get it now.