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One-Cocycles And Knot Invariants

by Thomas Fiedler

97,96€ + 10% CARD

 One-Cocycles and Knot Invariants is about classical knots, i.e., smooth oriented knots in 3-space. It introduces discrete combinatorial analysis in knot theory in order to solve a global tetrahedron equation. This new technique is then used to construct combinatorial 1-cocycles in a certain moduli space of knot diagrams. The construction of the moduli space makes use of the meridian and the longitude of the knot. The combinatorial 1-cocycles are therefore lifts of the well-known Conway polynomial of knots, and they can be calculated in polynomial time. The 1-cocycles can distinguish loops consisting of knot diagrams in the moduli space up to homology. They give knot invariants when they are evaluated on canonical loops in the connected components of the moduli space. They are a first candidate for numerical knot invariants which can perhaps distinguish the orientation of knots.Contents: <ul><li>Introduction</li><li>The 1-Cocycles from the Conway Polynomial</li><li>Proofs</li><li>The Examples</li><li>Two Forgotten Linear 1-Cocycles</li><li>An Eclectic 1-Cocycle</li></ul>Readership: This title will be particularly useful for academic researchers and PhD students.Key Features:<ul> <li>The main problem in knot theory in 3-space, namely giving a system of calculable numerical knot invariants, which distinguish all smooth oriented classical knots, is still open since the first mathematical paper about knots in 1771. This title makes an essential step towards a potential solution to this problem. So far, the construction of knot invariants in 3-space was mainly based on representation theory and hence on algebra. The book introduces combinatorial analysis as a new tool in order to study classical knots, by studying families of knot diagrams instead of individual diagrams. The basis of this new technique was laid in the previous title Polynomial One-cocycles for Knots and Closed Braids. This new book develops this technique further to its full power</li></ul></ul>
ENGLISH

On Complementarity: A Universal Organizing Principle - A Universal Organizing Principle

by Avrin Jack Shulman Avrin

79,50€ + 10% CARD

 It is not uncommon for the Principle of Complementarity to be invoked in either Science or Philosophy, viz. the ancient oriental philosophy of Yin and Yang whose symbolic representation is portrayed on the cover of the book. Or Niels Bohr''s use of it as the basis for the so-called Copenhagen interpretation of Quantum Mechanics. This book arose as an outgrowth of the author''s previous book entitled ''Knots, Braids and Moebius Strips,'' published by World Scientific in 2015, wherein the Principle itself was discovered to be expressible as a simple 2x2 matrix that summarizes the algebraic essence of both the well-known Microbiology of DNA and the author''s version of the elementary particles of physics. At that point, the possibility of an even wider utilization of that expression of Complementarity arose.The current book, features Complementarity, in which the matrix algebra is extended to characterize not only DNA itself but the well-known process of its replication, a most gratifying outcome. The book then goes on to explore Complementarity, with and without its matrix expression, as it occurs, not only in much of physics but in its extension to cosmology as well.
ENGLISH

Geometry Of The Universe, The

by Rourke Colin Rourke

79,50€ + 10% CARD

 Cosmology, the study of the universe, arouses a great deal of public interest, with serious articles both in the scientific press and in major newspapers, with many of the theories and concepts (e.g. the ''big bang'' and ''black holes'') discussed, often in great depth.Accordingly the book is divided into three parts:Part 1 is readable (and understandable) by anyone with a nodding acquaintance with the basic language of cosmology: events, lights paths, galaxies, black holes and so on. It covers the whole story of the book in a way as untechnical as possible given the scope of the topics covered.Part 2 covers the same ground again but with enough technical details to satisfy a reader with basic knowledge of mathematics and/or physics.Part 3 consists of appendices which are referred to in the other parts and which also contain the highly technical material omitted from Section 2.
ENGLISH

Geometric Foundations Of Design: Old And New

by Kappraff Jay Kappraff

53,00€ + 10% CARD

 This book is meant to serve either as a textbook for an interdisciplinary course in Mathematics of Design, or as a trade book for designers. It will also be of interest for people interested in recreational mathematics showing the connection between mathematics and design. Topics from the book can also be adapted for use in pre-college mathematics. Each chapter will provide the user with ideas that can be incorporated in a design. Background materials will be provided to show the reader the mathematical principles that lie behind the designs.
ENGLISH

Mathematics Of Harmony As A New Interdisciplinary Direction And &Quote;Golden&Quote; Paradigm Of Modern Science-Volume 3:The &Quote;Golden&Quote; Para - Volume 3: The Golden Paradigm Of Modern Science: Prerequisite For The Golden Revolution In Mathematics, Computer Science, And Theoretical Natural Scie

by Stakhov Alexey Stakhov

79,50€ + 10% CARD

 Volume III is the third part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and ''Golden'' Paradigm of Modern Science. ''Mathematics of Harmony'' rises in its origin to the ''harmonic ideas'' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the ''Universe Harmony,'' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors'' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the ''Mathematics of Harmony,'' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet''s formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
ENGLISH

Mathematics Of Harmony As A New Interdisciplinary Direction And &Quote;Golden&Quote; Paradigm Of Modern Science - Volume 2: Algorithmic Measurement Th - Volume 2: Algorithmic Measurement Theory, Fibonacci And Golden Arithmetic'S And Ternary Mirror-Symmetrical Arithmetic

by Stakhov Alexey Stakhov

92,75€ + 10% CARD

 Volume II is the second part of the 3-volume book Mathematics of Harmony as a New Interdisciplinary Direction and ''Golden'' Paradigm of Modern Science. ''Mathematics of Harmony'' rises in its origin to the ''harmonic ideas'' of Pythagoras, Plato and Euclid, this 3-volume book aims to promote more deep understanding of ancient conception of the ''Universe Harmony,'' the main conception of ancient Greek science, and implementation of this conception to modern science and education.This 3-volume book is a result of the authors'' research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the ''Mathematics of Harmony,'' a new interdisciplinary direction of modern science. This direction has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the generalized Binet''s formulas), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational bases, Fibonacci computers, ternary mirror-symmetrical arithmetic).The books are intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
ENGLISH

Combinatorial Physics

by Bastin Ted Bastin, Kauffman Louis H Kauffman e Kilmister Clive W Kilmister

26,50€ + 10% CARD

 Abandoning the intuitive continuum concepts in physics, the authors build up constructively a combinatorial mathematics of process. This change alone makes it possible to calculate the coupling constants of the fundamental fields which are the bridge between the combinatorial world and dynamics.
ENGLISH

Nonstandard Logics And Nonstandard Metrics In Physics

by Honig W M Honig

46,38€ + 10% CARD

 This work presents two mathematical techniques: non-standard logics and non-standard metrics. The techniques are applied to current problems in physics, such as the hidden variable problem and the local and nonlocal problems.
ENGLISH

Symmetric Bends: How To Join Two Lengths Of Cord

by Miles Roger E Miles

22,53€ + 10% CARD

 This book presents a mathematical theory of symmetric bends, together with a simple explanation of how such bends may be invented. Also discussed are the additionally symmetric "triply symmetric" bends. Full details, including colour pictures, are given of the "best 60" known symmetric bends.
ENGLISH

How Surfaces Intersect In Space: An Introduction To Topology (2nd Edition)

by Carter J Scott Carter

31,80€ + 10% CARD

 This text illustrates standard examples in low dimensional topology. It begins at the most basic level (the intersection of coordinate planes) and gives hands on constructions of examples in topology: the projective plane, Poincare's example of a homology sphere and lens spaces.
ENGLISH

Random Knotting And Linking

42,40€ + 10% CARD

 The papers in this volume reflect the diversity of interest across science and mathematics in the area of random knotting, from topology and statistical mechanics to theoretical chemistry and wet-lab molecular biology.
ENGLISH

Knots And Applications

60,95€ + 10% CARD

 This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology.
ENGLISH

Gems, Computers And Attractors For 3-Manifolds

by Lins Sostenes Lins

63,60€ + 10% CARD

 This text provides a guide to dealing with 3-manifolds by computers, with an emphasis on presenting algorithms which are used for solving the homeomorphism problem for the smallest of these objects. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included.
ENGLISH

Knots And Physics (Second Edition)

by Kauffman Louis H Kauffman

39,75€ + 10% CARD

 An introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical framework, create a context that naturally includes a wide range of interrelated topics in topology and mathematical physics.
ENGLISH

Quantum Topology

56,98€ + 10% CARD

 Discusses topics in the field of quantum topology, including: knot theory, exotic spheres and global gravitational anomolies; construction of 4D topological quantum field theories; computing the arf invariants of links; and the Casson invariants for two-fold branched covers of links.
ENGLISH

How Surfaces Intersect In Space: An Introduction To Topology

by Carter J Scott Carter

26,50€ + 10% CARD

 This is a book of marvelous pictures that illustrates standard examples in low dimensional topology. The text starts at the most basic level (the intersection of coordinate planes) and gives hands on constructions of the most beautiful examples in topology: the projective plane, Poincare''s example of a homology sphere, lens spaces, knotted surfaces, 2-sphere eversions, and higher dimensional manifolds. The text carefully explains the importance of the examples and the techniques without being bogged down in a morass of technicalities.Chapter 1 opens with the classification of orientable surfaces, and the meaning of space. Chapter 2 discusses examples of non-orientable surfaces including models of the projective plane and the Klein bottle. Chapter 3 discusses how curves fit on surfaces and gives a general discussion of knotted strings in space. In Chapter 4, some examples of other 3-dimensional spaces are described. These include the 3-dimensional sphere, lens spaces, and the quaternionic projective space. In Chapter 5, the author reviews the movie techniques of studying surfaces in 4-dimensions. He shows how to move among the standard examples of Klein bottles, and he gives a "movie move" decomposition of turning the 2-sphere inside out. In the final Chapter, higher dimensional spaces are examined from the same elementary point of view.The book is a guide book to a wide variety of topics. It will be of value to undergraduates who want to learn geometric topology and to graduate students who want examples with which they can make computations and who need an elementary description of topological spaces. Finally, the book should be interesting to other scientists and mathematicians who want to learn some examples of topological spaces.
ENGLISH

Knots And Physics (Third Edition)

by Kauffman Louis H Kauffman

87,45€ + 10% CARD

 An introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. A selection of papers by the author are included at the end of the book, including a paper entitled "Knot Theory and Functional Integration", which is new to the third edition.
ENGLISH

Gauge Fields, Knots And Gravity

by Baez John C Baez e Muniain Javier P Muniain

62,28€ + 10% CARD

 Introduces the mathematics needed to understand gravity. The book includes a rapid course on manifolds and differential forms, and covers: vector bundles, connections and curvature; the relation of gauge theory to the newly-discovered knot invariants; and Riemannian geometry.
ENGLISH

Mathematics Of Harmony: From Euclid To Contemporary Mathematics And Computer Science

by Stakhov Alexey Stakhov

84,80€ + 10% CARD

 Provides an introduction to the subject of the "Mathematics of Harmony". This book is intended for mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science.
ENGLISH

Linknot: Knot Theory By Computer

by Jablan Slavik Vlado Jablan e Sazdanovic Radmila Sazdanovic

63,60€ + 10% CARD

 Provides a view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics. This book covers basic notions in knot theory, as well as methods for handling open problems such as unknotting number and non-algebraic tangles.
ENGLISH

Self-Evolving Cosmos, The: A Phenomenological Approach To Nature'S Unity-In-Diversity

by Rosen Steven M Rosen

63,60€ + 10% CARD

 Offers a different way of thinking about two significant problems confronting modern theoretical physics: the unification of the forces of nature and the evolution of the universe. In bringing out the inadequacies of the prevailing approach to these questions, this book demonstrates the need for more than just a different theory.
ENGLISH

Zero To Infinity: The Foundations Of Physics

by Rowlands Peter Rowlands

79,50€ + 10% CARD

 Proposes a fundamental description of process in a universal computational rewrite system. This book takes the rewrite structure more generally as a description of process, and shows how it can be applied to large-scale structures beyond the realm of fundamental physics.
ENGLISH

Intelligence Of Low Dimensional Topology 2006

99,38€ + 10% CARD

 Features the contributions from the international conference "Intelligence of Low Dimensional Topology 2006," which took place in Hiroshima in 2006. This book aims to promote research in low dimensional topology with the focus on knot theory and related topics. It contains papers that include comprehensive reviews and results.
ENGLISH

Topological Library - Part 1: Cobordisms And Their Applications

86,13€ + 10% CARD

 Collecting the original works in topology written in the 50s-60s, this work covers the ensemble of methods created in topology starting from approximately 1950, that is, from Serre's celebrated "Singular homologies of fibre spaces". It is also a translation of the Russian edition published in 2005 with Milnor's lectures on the h-cobordism omitted.
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