Series: Springer Tracts in Modern Physics, Vol. 244
1st Edition., 2011, XII, 194 p. 11 illus.
Hardcover, ISBN 978-3-642-24383-7
Due: November 30, 2011
This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane-Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics. This manifests itself through topological choices for the fractional momentum spacings. The general model is derived by mapping exact models of quantized Hall states onto spin chains. The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.
Content Level ≫ Research
Keywords ≫ Abelian and non-Abelian statistics - Critical model - Exact models - Haldane-Shastry Model - Integrable models - Laughlin state - Pfaffian state - Quantum Hall states - Spin chains - Wess-Zumino Witten model
Related subjects ≫ Complexity - Materials - Quantum Physics - Theoretical, Mathematical & Computational Physics
Introduction and summary.- Three models and a ground state.- From a Laughlin state to the Haldane-Shastry model.- From a bosonic Pfaffian state to an S = 1 spin chain.- Generalization to arbitrary spin S.- Conclusions and unresolved issues.- Spherical coordinates.- Fourier sums for one-dimensional lattices.- Angular momentum algebra.- Tensor decompositions of spin operators.
Series: Developments in Mathematics, Vol. 25
2012, 2012, XV, 217 p. 49 illus.
Hardcover, ISBN 978-1-4614-1796-5
n elementary introduction to inverse limits through inverse limits on [0,1] is included in the first chapter
The general theory of inverse limits is presented for compact Hausdorff spaces over directed sets using set valued functions in chapter two
Special topics from continuum theory such as indecomposability are discussed in detail An appendix containing mostly an introduction to the topology of the Hilbert cube is included
An extensive bibliography listing much of the literature on inverse limits is a part of the book
Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also can turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introductory study of inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families.
This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book.
Content Level ≫ Research
Keywords ≫ chaos - continua - dynamics - inverse limits - mappings and set valued functions
Related subjects ≫ Dynamical Systems & Differential Equations - Geometry & Topology
1 Inverse Limits on Intervals. -2 Inverse Limits in a General Setting . -3 INVERSE LIMITS IN CONTINUUM THEORY . -4 BROWN’S APPROXIMATION THEOREM . -AN INTRODUCTION TO THE HILBERT CUBE. ?References. -Index
2012, XLIV, 3492 p. 1547 illus., 665 in color.
In 6 volumes, not available separately.
print (book), Hardcover, ISBN 978-1-4614-1799-6
Presents the fundamental tools and approaches that underlie all large-scale modeling
Addresses a multidisciplinary audience in computer science, pure and applied mathematics, engineering, physics, and economics
Includes a glossary of important terms and a concise definition of the subject for each entry
Gathers together more than 200 peer-reviewed entries from the 11-volume Encyclopedia of Complexity and Systems Science
Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The recognition that the collective behavior of the whole system cannot be simply inferred from an understanding of the behavior of the individual components has led to the development of numerous sophisticated new computational and modeling tools with applications to a wide range of scientific, engineering, and societal phenomena.
Computational Complexity: Theory, Techniques and Applications presents a detailed and integrated view of the theoretical basis, computational methods, and state-of-the-art approaches to investigating and modeling of inherently difficult problems whose solution requires extensive resources approaching the practical limits of present-day computer systems. This comprehensive and authoritative reference examines key components of computational complexity, including cellular automata, graph theory, data mining, granular computing, soft computing, wavelets, and more.
Content Level ≫ Research
Keywords ≫ Agent-Based Modeling and Simulation - Cellular Automata, Mathematical Basis of - Complex Networks and Graph Theory - Complex computing book - Computational complexity book - Data Mining and Knowledge Discovery - Fuzzy math book - Game Theory - Granular Computing - Intelligent Systems - Probability and Statistics in Complex Systems - Quantum Information Science - Social Network Analysis - Soft Computing - Unconventional Computing - Wavelets
Related subjects ≫ Complexity - Database Management & Information Retrieval - Theoretical Computer Science
Agent-Based Modeling and Simulation.- Cellular Automata, Mathematical Basis of Complex Networks and Graph Theory.- Data Mining and Knowledge Discovery.- Game Theory.- Granular Computing.- Intelligent Systems.- Probability and Statistics in Complex Systems.- Quantum Information Science.- Social Network Analysis.- 3 entries from the section Social Science, Physics and Mathematical Applications: Minority Games; Rational, Goal-Oriented Agents; and Social Processes, Simulation Models in Soft Computing.- Unconventional Computing.- Wavelets.
Series: Texts in Applied Mathematics, Vol. 40
2012, X, 518p.
Hardcover, ISBN 978-1-4614-1685-2
Due: December 22, 2011
Concentration is on applications in population biology, epidemiology, and resource management
This textbook provides an introduction to the field of mathematical biology through the integration of classical applications in ecology with more recent applications to epidemiology, particularly in the context of spread of infectious diseases. It integrates modeling, mathematics, and applications in a semi-rigorous way, stating theoretical results and giving references but not necessarily giving detailed proofs, providing a solid introduction to the field to undergraduates (junior and senior level), graduate students in applied mathematics, ecology, epidemiology or evolutionary biology, sustainability scientists, and to researchers who must routinely read the practical and theoretical results that come from modeling in ecology and epidemiology.
This new edition has been updated throughout. In particular the chapters on epidemiology have been updated and extended considerably, and there is a new chapter on spatially structured populations that incorporates dispersal. The number of problems has been increased and the number of projects has more than doubled, in particular those stressing connections to data. In addition some examples, exercises, and projects include use of Maple and Matlab.
Content Level ≫ Graduate
Keywords ≫ Epidemiology - Mathematical Biology - Mathematical Ecology - Population Biology - Population Dynamics - Population Ecology - Resource Management
Related subjects ≫ Ecology
Preface * Ackn. * Prologue * Part I: Simple Single-Species Models * 1 Continuous Population Models * 2 Discrete Population Models * 3 Continuous single-species Population Models with Delays * Part II: Models for Interacting Species * 4 Introduction and Mathematical Preliminaries * 5 Continuous models for two interacting populations * 6 Harvesting in two-species models * Part III: Structured Population Models * 7 Basic ideas of Mathematical Epidemiology * 8 Models for population with age structure * Epilogue * Answers to selected Exercises * References
Series: Springer Monographs in Mathematics
2012, 2012, X, 210 p. 1 illus. in color.
Hardcover, ISBN 978-3-642-25619-6
Due: March 31, 2012
Presents an elementary proof of a very fundamental and beautiful mathematical result
First complete presentation of this results in the mathematical literature
It can be read by almost anyone with a basic graduate education
One of the most elementary questions in mathematics is whether an area minimizing surface spanning a contour in three space is immersed or not; i.e. does its derivative have maximal rank everywhere.
The purpose of this monograph is to present an elementary proof of this very fundamental and beautiful mathematical result. The exposition follows the original line of attack initiated by Jesse Douglas in his Fields medal work in 1931, namely use energy as opposed to area. Remarkably, the author shows how to calculate arbitrarily high orders of derivatives of the Douglas Energy defined on the infinite dimensional manifold of all surfaces spanning a contour, breaking new ground in the Calculus of Variations, where normally only the second derivative or variation is calculated.
The monograph begins with easy examples leading to a proof in a large number of cases that can be presented in a graduate course in either manifolds or complex analysis. Thus this monograph requires only the most basic knowledge of analysis, complex analysis and topology and can therefore be read by almost anyone with a basic graduate education.
Content Level ≫ Research
Keywords ≫ 30B10, 49J50, 49Q05, 53A10, 58E12, 58C20 - Branch Points - Immersed Minimal Surfaces - Minimal Surfaces - Plateau's Problem
Related subjects ≫ Analysis - Geometry & Topology
1.Introduction.- 2.Higher order Derivatives of Dirichlets' Energy.- 3.Very Special Case; The Theorem for n + 1 Even and m + 1 Odd .- 4.The First Main Theorem; Non-Exceptional Branch Points.- 5.The Second Main Theorem: Exceptional Branch Points; The Condition k > l.- 6.Exceptional Branch Points Without The Condition k > l.- 7.New Brief Proofs of the Gulliver-Osserman-Royden Theorem .- 8.Boundary Branch Points.- Scholia.- Appendix.- Bibliography.