adex theory how the ade coxeter graphs unify mathematics and physics 57 series on knots and everything

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Adex Theory

Author : Saul Paul Sirag
ISBN : 9789814656504
Genre : Mathematics
File Size : 89. 42 MB
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"This book shows how the ADE Coxeter graphs unify at least 20 different types of mathematical structures. These mathematical structures are of great utility in unified field theory, string theory, and other areas of physics."--Provided by publisher.

Mereon Matrix The Everything Connected Through K Nothing

Author : Kauffman Louis H
ISBN : 9789813233577
Genre : Mathematics
File Size : 58. 97 MB
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In this richly illustrated book, the contributors describe the Mereon Matrix, its dynamic geometry and topology. Through the definition of eleven First Principles, it offers a new perspective on dynamic, whole and sustainable systems that may serve as a template information model. This template has been applied to a set of knowledge domains for verification purposes: pre-life-evolution, human molecular genetics and biological evolution, as well as one social application on classroom management. The importance of the book comes in the following ways: The dynamics of the geometry unites all Platonic and Kepler Solids into one united structure and creates 11 unique trefoil knots. Its topology is directly related to the dynamics of the polyhedra. The Mereon Matrix is an approach to the unification of knowledge that relies on whole systems modelling. it is a framework charting the emergence of the Platonic and Kepler solids in a sequential, emergent growth process that describes a non-linear whole system, and includes a process of 'breathing' as well as multiplying ('birthing'); This dynamic/kinematic structure provides insight and a new approach to General Systems Theory and non-linear science, evolving through a new approach to polyhedral geometry. A set of 11 First Principles is derived from the structure, topology and dynamics of the Mereon Matrix, which serve well as a template information model. The Mereon Matrix is related to a large number of systems, physical, mathematical, and philosophical, and in linking these systems, provides access to new relationships among them by combining geometry with process thinking. The new perspective on systems is hypothesized as universal -- this is, applicable in all areas of science, natural and social. Such applicability has been demonstrated for applications as diverse as pre-life evolution, biological evolution and human molecular genetics, as well as a classroom management system for the educational system. Care has been taken to use images and languaging that are understandable across domains, connecting diverse disciplines, while making this complex system easily accessible. Contents: Prologues: Sustainability: Mathematical Elegance, Solid Science and Social Grace (L Dennis and L H Kauffman) Lynnclaire Dennis & R Buckminster Fuller Investigation (R W Gray) The Matrix We Call Mereon (L H Kauffman) First Things First: Building on the Known: A Quintessential Jitterbug (L Dennis, J Brender McNair, N J Woolf and L H Kauffman) Methodology (J Brender McNair and L Dennis) Philosophical Thoughts and Thinking Aloud Allowed (L Dennis) Belonging -- Education as Transformation (L Dennis) Meme, Pattern and Perspective (L Dennis, N J Woolf and L H Kauffman) Including and Beyond the Point: The Context -- Form Informing Function (L Dennis, J Brender McNair, N J Woolf and L H Kauffman) Flow and Scale (L Dennis and L H Kauffman) The Core -- Sharp Distinctions to Elegant Curves (L Dennis and L H Kauffman) Connections, Ligatures and Knots: Mereon Thoughts -- Knots and Beyond (L H Kauffman) The Mereon Trefoil -- Asymmetrical with Perfect Symmetry (L Dennis) Applying Mereon to Knowledge Domains: Exploring the Mereon Matrix (and Beyond) with the CymaScope Technology (L Dennis and P McNair) The Origin of Matter: Life, Learning and Survival (N J Woolf and L Dennis) ATCG -- An Applied Theory for Human MoleCular Genetics (J Brender McNair, P McNair,

New Horizons For Second Order Cybernetics

Author : Muller Karl H
ISBN : 9789813226272
Genre : Language Arts & Disciplines
File Size : 33. 34 MB
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In almost 60 articles this book reviews the current state of second-order cybernetics and investigates which new research methods second-order cybernetics can offer to tackle wicked problems in science and in society. The contributions explore its application to both scientific fields (such as mathematics, psychology and consciousness research) and non-scientific ones (such as design theory and theater science). The book uses a pluralistic, multifaceted approach to discuss these applications: Each main article is accompanied by several commentaries and author responses, which together allow the reader to discover further perspectives than in the original article alone. This procedure shows that second-order cybernetics is already on its way to becoming an idea shared by many researchers in a variety of disciplines. Contents: Prologue: A Brief History of (Second-Order) Cybernetics (Louis H Kauffman & Stuart A Umpleb)Mapping the Varieties of Second-Order Cybernetics (Karl H Müller & Alexander Riegle)Part I: Exploring Second-Order Cybernetics and Its Fivefold Agenda: Second-Order Cybernetics as a Fundamental Revolution in Science (Stuart A Umpleby)Obstacles and Opportunities in the Future of Second-Order Cybernetics and Other Compatible Methods (Allenna Leonard)Connecting Second-Order Cybernetics' Revolution with Genetic Epistemology (Gastón Becerra)Shed the Name to Find Second-Order Success: Renaming Second-Order Cybernetics to Rescue its Essence (Michael R Lissack)Beware False Dichotomies (Peter A Cariani)Second-Order Cybernetics Needs a Unifying Methodology (Thomas R Flanagan)Viva the Fundamental Revolution! Confessions of a Case Writer (T Grandon Gill)Author's Response: Struggling to Define an Identity for Second-Order Cybernetics (Stuart A Umpleby)Cybernetics, Reflexivity and Second-Order Science (Louis H Kauffman)Remarks From a Continental Philosophy Point of View (Tatjana Schönwälder-Kuntze)Finally Understanding Eigenforms (Michael R Lissack)Eigenforms, Coherence, and the Imaginal (Arthur M Collings)Conserving the Disposition for Wonder (Kathleen Forsythe)Author's Response: Distinction, Eigenform and the Epistemology of the Imagination (Louis H Kauffman)Cybernetic Foundations for Psychology (Bernard Scott)Wielding the Cybernetic Scythe in the Blunting Undergrowth of Psychological Confusion (Vincent Kenny)To What Extent Can Second-Order Cybernetics Be a Foundation for Psychology? (Marcelo Arnold-Cathalifaud & Daniela Thumala-Dockendorff)The Importance — and the Difficulty — of Moving Beyond Linear Causality (Robert J Martin)Obstacles to Cybernetics Becoming a Conceptual Framework and Metanarrative in the Psychologies (Philip Baron)The Social and the Psychological: Conceptual Cybernetic Unification vs Disciplinary Analysis? (Eva Buchinger)Second Thoughts on Cybernetic Unifications (Tilia Stingl de Vasconcelos Guedes)Cybernetics and Synergetics as Foundations for Complex Approach Towards Complexities of Life (Lea Šugman Bohinc)Author's Response: On Becoming and Being a Cybernetician (Bernard Scott)Consciousness as Self-Description in Differences (Diana Gasparyan)On the Too Often Overlooked Complexity of the Tension between Subject and Object (Yochai Ataria)Where Is Consciousness? (Urban Kordeš)Theorizing Agents: Their Games, Hermeneutical Tools and Epistemic Resources (Konstantin Pavlov-Pinus)How

A First Course In Integral Equations

Author : Abdul-Majid Wazwaz
ISBN : 9789814675147
Genre : Mathematics
File Size : 62. 11 MB
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This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods. This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering. Click here for solutions manual.

The Solution Of The K Gv Problem

Author : Peter Schmid
ISBN : 9781860949708
Genre : Mathematics
File Size : 48. 2 MB
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The k(GV) conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product GV is bounded above by the order of V. Here V is a finite vector space and G a subgroup of GL(V) of order prime to that of V. It may be regarded as the special case of Brauer's celebrated k(B) problem dealing with p-blocks B of p-solvable groups (p a prime). Whereas Brauer's problem is still open in its generality, the k(GV) problem has recently been solved, completing the work of a series of authors over a period of more than forty years. In this book the developments, ideas and methods, leading to this remarkable result, are described in detail.

Universal Formulas In Integral And Fractional Differential Calculus

Author : Khavtgai Namsrai
ISBN : 9789814675611
Genre : Mathematics
File Size : 90. 91 MB
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' This reference book presents unique and traditional analytic calculations, and features more than a hundred universal formulas where one can calculate by hand enormous numbers of definite integrals, fractional derivatives and inverse operators. Despite the great success of numerical calculations due to computer technology, analytical calculations still play a vital role in the study of new, as yet unexplored, areas of mathematics, physics and other branches of sciences. Readers, including non-specialists, can obtain themselves universal formulas and define new special functions in integral and series representations by using the methods expounded in this book. This applies to anyone utilizing analytical calculations in their studies. Contents:Mathematical PreparationCalculation of Integrals Containing Trigonometric and Power FunctionsIntegrals Involving xγ, (p + txp)–λ Sine and Cosine FunctionsDerivation of General Formulas for Integrals Involving Powers of x, (a + bx)-Type Binomials and Trigonometric FunctionsIntegrals Involving xγ, 1/(p + txp)–λ, exp[–axγ] and Trigonometric FunctionsIntegrals Containing Bessel FunctionsIntegrals Involving the Neumann Function Nσ(x)Integrals Containing Other Cylindrical and Special FunctionsIntegrals Involving Two Trigonometric FunctionsDerivation of Universal Formulas for Calculation of Fractional Derivatives and Inverse Operators Readership: Undergraduate and graduate students interested in analytic calculations in integral calculus. Researchers from the fields of modern mathematical analysis, theoretical physics and engineering. Non-experts interested in integrals, fractional derivatives and inverse operators. Key Features:Content in this book is easy to readHas simple tables of integration and taking fractional derivatives and calculating complicated inverse operatorsMost valuable tip from the book is a simple and nice way to perform integration showing it as a design culture but not as tedious workKeywords:Mellin Representation;Contour Integration;Analytic Continuation;Taking Residue;L''Hôpital''s Rule;Gamma Function;Psi-Function;Exponential Function;Neumann;Trigonometric;Cylindrical;Struve;Modified Struve;Bessel and Modified Bessel Functions;Probability Integrals;Integral of Frenal;General Formulas for Taking Integrals;Fractional Derivatives;Inverse Operators;Euler Number'

Hyperbolic Geometry And Geometric Group Theory

Author : K.Fujiwara
ISBN : 4864970424
Genre : Geometric group theory
File Size : 82. 86 MB
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The 7th Seasonal Institute of the Mathematical Society of Japan on Hyperbolic Geometry and Geometric Group Theory was held from July 30-August 5, 2014, at the University of Tokyo. This volume, the proceedings of the meeting, collects survey and research articles in this fast-growing field by international specialists. This volume is recommended for researchers and graduate students interested in hyperbolic geometry, geometric group theory, and low-dimensional topology.

Infinite Group Theory From The Past To The Future

Author : Fine Benjamin
ISBN : 9789813204065
Genre : Mathematics
File Size : 49. 99 MB
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The development of algebraic geometry over groups, geometric group theory and group-based cryptography, has led to there being a tremendous recent interest in infinite group theory. This volume presents a good collection of papers detailing areas of current interest. Contents: Groups with the Weak Minimal Condition on Non-Permutable Subgroups (Laxmi K Chatuat and Martyn R Dixon)A Survey: Shamir Threshold Scheme and Its Enhancements (Chi Sing Chum, Benjamin Fine, and Xiaowen Zhang)The Zappa-Szep Product of Left-Orderable Groups (Fabienne Chouraqui)Totally Disconnected Groups From Baumslag-Solitar Groups (Murray Elder and George Willis)Elementary and Universal Theories of Nonabelian Commutative Transitive and CSA Groups (B Fine, A M Gaglione, and D Spellman)Commutative Transitivity and the CSA Property (Benjamin Fine, Anthony Gaglione, Gerhard Rosenberger, and Dennis Spellman)The Universal Theory of Free Burnside Groups of Large Prime Exponent (Anthony M Gaglione, Seymour Lipschutz, and Dennis Spellman)Primitive Curve Lengths on Pairs of Pants (Jane Gilman)Drawing Inferences Under Maximum Entropy From Relational Probabilistic Knowledge Using Group Theory (Gabriele Kern-Isberner, Marco Wilhelm, and Christoph Beierle)On Some Infinite-Dimensional Linear Groups and the Structure of Related Modules (L A Kurdachenko and I Ya Subbotin)On New Analogs of Some Classical Group Theoretical Results in Lie Rings (L A Kurdachenko, A A Pypka and I Ya Subbotin)Log-Space Complexity of the Conjugacy Problem in Wreath Products (Alexei Myasnikov, Svetla Vassileva, and Armin Weiss)Group Presentations, Cayley Graphs and Markov Processes (Peter Olszewski) Readership: Graduate students and researchers in group theory. Keywords: Infinite Group Theory;Combinatorial Group Theory;Geometric Group TheoryReview: Key Features: This book is centered on infinite group theory from a combinatorial and geometric point of view. It also contains material on non-commutative algebraic group-based cryptography

Theory And Applications In Mathematical Physics In Honor Of B Tirozzi S 70th Birthday

Author : Montani Giovanni
ISBN : 9789814713290
Genre : Mathematics
File Size : 32. 29 MB
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The aim of this volume is to make a connection among advanced mathematical tools and application to real problems. There are many different mathematical structures analyzed in the book and all of them are in important applications, like statistics and biology, neural networks and financial markets, asymptotic methods for partial differential equations and the problem of tsunami propagation. Plasma physics has been given a new approach, using focal points in analogy to the theory of tsunami waves.

Woods Hole Mathematics

Author : Nils Tongring
ISBN : 9789812701398
Genre : Mathematics
File Size : 39. 53 MB
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The central theme of this volume is the contemporary mathematics of geometry and physics, but the work also discusses the problem of the secondary structure of proteins, and an overview of arc complexes with proposed applications to macromolecular folding is given. OC Woods Hole has played such a vital role in both my mathematical and personal life that it is a great pleasure to see the mathematical tradition of the 1964 meeting resurrected forty years later and, as this volume shows, resurrected with new vigor and hopefully on a regular basis. I therefore consider it a signal honor to have been asked to introduce this volume with a few reminiscences of that meeting forty years ago.OCO Introduction by R Bott (Wolf Prize Winner, 2000)."

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