الصفحة 1
الصفحة 1
Number Theory and the Periodicity of Matter
The book launch was held at the University of Pretoria (UP) on 26 March 2008. … It’s a fascinating and original concept and I hope you all get the opportunity to read it. It will challenge your current views of numbers. … If there is a link between numbers and the Periodic Table this will of course have major implications as to the ‘meaning’ on the Periodic Table. It’s great to have original thinkers in our midst
Nexus Network Journal : Leonardo da Vinci : Architecture and Mathematics
The quintessential Renaissance Man, Leonardo da Vinci was well aware of the fundamental importance of mathematics for architecture. This issue of the Nexus Network Journal examines Leonardo’s knowledge of theoretical mathematics, explores how he used concepts of geometry in his designs for architectural projects, and reports on a real-life construction project using Leonardo’s principles. Authors include Sylvie Duvernoy, Kim Williams, Rinus Roelofs, Biagio Di Carlo, Mark Reynolds, João Pedro Xavier, Vesna Petresin, Christopher Glass, and Jane Burry. To complete the issue Rachel Fletcher writes her Geometer’s Angle column on "Dynamic Symmetry", Michael Ostwald reviews A Theory of General Ethics by Warwick Fox, Sarah Clough Edwards reviews Inigo Jones and the Classical Tradition by Christy Anderson, and Sylvie Duvernoy reviews Architecture and Mathematics in Ancient Egypt by Corinna Rossi.
Naive Lie Theory
In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra.
Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces
As K. Nomizu has justly noted [K. Nomizu, 56], Differential Geometry ever will be initiating newer and newer aspects of the theory of Lie groups. This monograph is devoted to just some such aspects of Lie groups and Lie algebras. New differential geometric problems came into being in connection with so called subsymmetric spaces, subsymmetries, and mirrors introduced in our works dating back to 1957 [L.V. Sabinin, 58a,59a,59b]. In addition, the exploration of mirrors and systems of mirrors is of interest in the case of symmetric spaces. Geometrically, the most rich in content there appeared to be the homogeneous Riemannian spaces with systems of mirrors generated by commuting subsymmetries, in particular, so called tri-symmetric spaces introduced in [L.V. Sabinin, 61b]. As to the concrete geometric problem which needs be solved and which is solved in this monograph, we indicate, for example, the problem of the classification of all tri-symmetric spaces with simple compact groups of motions. Passing from groups and subgroups connected with mirrors and subsymmetries to the corresponding Lie algebras and subalgebras leads to an important new concept of the involutive sum of Lie algebras [L.V. Sabinin, 65]. This concept is directly concerned with unitary symmetry of elementary par- cles (see [L.V. Sabinin, 95,85] and Appendix 1). The first examples of involutive (even iso-involutive) sums appeared in the - ploration of homogeneous Riemannian spaces with and axial symmetry. The consideration of spaces with mirrors [L.V. Sabinin, 59b] again led to iso-involutive sums.
Metamorphoses of Hamiltonian Systems with Symmetries
Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.
Mathematical Models of Granular Matter
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
Isomonodromic Deformations and Frobenius Manifolds : An Introduction
The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspectives on, and revealed new links between, many apparently unrelated areas of mathematics and physics. Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations and ends with applications to recent research questions related to mirror symmetry.
Hamiltonian Reduction by Stages
In this volume readers will find for the first time a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. Special emphasis is given to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. Ample background theory on symplectic reduction and cotangent bundle reduction in particular is provided. Novel features of the book are the inclusion of a systematic treatment of the cotangent bundle case, including the identification of cocycles with magnetic terms, as well as the general theory of singular reduction by stages.
Group theory : Application to the physics of condensed matter
Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra. This concise and class-tested book has been pedagogically tailored over 30 years MIT and 2 years at the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory in close connection with applications helps students to learn, understand and use it for their own needs. For this reason, the theoretical background is confined to the first 4 introductory chapters (6-8 classroom hours). From there, each chapter develops new theory while introducing applications so that the students can best retain new concepts, build on concepts learned the previous week, and see interrelations between topics as presented.
Geometry of Quantum Theory ; 2nd ed.
This book a classic on the foundations of quantum theory. This view, which is essentially geometric and relies on the concept of symmetry. The mathematical treatment of symmetry in quantum theory is based on the theory of group representations, and this book includes a self-contained treatment of the parts of this theory that are most useful in quantum physics.
Geometric Topology : Localization, Periodicity and Galois Symmetry : the 1970 MIT notes
The seminal `MIT notes' of Dennis Sullivan were issued in June 1970 and were widely circulated at the time, but only privately. The notes had a major influence on the development of both algebraic and geometric topology, pioneering the localization and completion of spaces in homotopy theory, including P-local, profinite and rational homotopy theory, the Galois action on smooth manifold structures in profinite homotopy theory, and the K-theory orientation of PL manifolds and bundles. This is the first time that this major work has actually been published, and made available to anyone interested in topology.
Geometric and Topological Methods for Quantum Field Theory
This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.
Fundamentals of the Physics of Solids ; Vol. I : Structure and Dynamics
This book aims to deliver a comprehensive and self-contained account of the vast field of solid-state physics. It goes far beyond most classic texts in the presentation of the properties of solids and experimentally observed phenomena, along with the basic concepts and theoretical methods used to understand them and the essential features of various experimental techniques.
From Summetria to Symmetry : The Making of a Revolutionary Scientific Concept
The concept of symmetry is inherent to modern science, and its evolution has a complex history that richly exemplifies the dynamics of scientific change. This study is based on primary sources, presented in context: the authors examine closely the trajectory of the concept in the mathematical and scientific disciplines as well as its trajectory in art and architecture. The principal goal is to demonstrate that, despite the variety of usages in many different domains there is a conceptual unity underlying the invocation of symmetry in the period from antiquity to the 1790s which is distinct from the scientific usages of this term that first emerged in France at the end of the 18th century.
Foundations of Quantum Theory : From Classical Concepts to Operator Algebras
This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory.
Factorization Method in Quantum Mechanics
Introduces the factorization method in quantum mechanics at an advanced level with an aim to put mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the Reader’s disposal.
Earthquake Source Asymmetry, Structural Media and Rotation Effects
This is the first book on rotational effects in earthquakes, a revolutionary concept in seismology. Existing models do no yet explain the significant rotational and twisting motions that occur during an earthquake and cause the failure of structures. This breakthrough monograph thoroughly investigates rotational waves, basing considerations on modern observations of strong rotational ground motions and detection of seismic rotational waves. To describe the propagation of such waves the authors consider structured elastic media that allow for rotational motions and rotational deformations of the ground, sometimes stronger than translational deformations. The rotation and twist effects are investigated and described and their consequences for designing tall buildings and other important structures are presented. The book will change the way the world views earthquakes and will interest scientists and researchers in the fields of Geophysics, Geology and Civil Engineering.
Dynamics of Rotating Systems
This book is structured in two parts: the first introduces classical or basic rotordynamics. The basic assumptions are linearity, steady state operation, and at least some degree of axial symmetry. The second part discusses advanced rotordynamics. More detailed models are covered for rotors departing from the classic configurations studied in rotordynamics. The contents of the second part are more research topics than consolidated applications.
Dentofacial and occlusal asymmetries
Covers all crucial aspects of dentofacial and occlusal asymmetries. Dentofacial and Occlusal Asymmetries covers all crucial aspects of asymmetries encountered in the stomatognathic region regarding diagnosis, treatment planning, management, and prognosis. Divided into three core sections, the first part focuses on the etiology of asymmetry and whether it is congenital or acquired through disease or trauma. The second and third sections go on to discuss localization and management, providing information on topics such as interception, correction, and camouflage.
Crystallography and the World of Symmetry
Symmetry exists in realms from crystals to patterns, in external shapes of living or non-living objects, as well as in the fundamental particles and the physical laws that govern them. In fact, the search for this symmetry is the driving force for the discovery of many fundamental particles and the formulation of many physical laws. While one can not imagine a world which is absolutely symmetrical nor can one a world which is absolutely asymmetrical. These two aspects of nature are intermingled with each other inseparably. This is the basis of the existence of aperiodicity manifested in the liquid crystals and also quasi-crystals also discussed in Crystallography and the World of Symmetry.
