161 pp; hardcover
ISBN-13: 978-0-8218-4417-5
Expected publication date is May 10, 2008.
The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry.
The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius.
Chapters 6-9 deal with many of the most relevant contributions to the subject in the years 1959 to 1974. These include the pinching (or sphere) theorem, Berger's theorem for symmetric spaces, the differentiable sphere theorem, the structure of complete manifolds of non-negative curvature, and finally, results about the structure of complete manifolds of non-positive curvature. Emphasis is given to the phenomenon of rigidity, namely, the fact that although the conclusions which hold under the assumption of some strict inequality on curvature can fail when the strict inequality on curvature can fail when the strict inequality is relaxed to a weak one, the failure can happen only in a restricted way, which can usually be classified up to isometry.
Much of the material, particularly the last four chapters, was essentially state-of-the-art when the book first appeared in 1975. Since then, the subject has exploded, but the material covered in the book still represents an essential prerequisite for anyone who wants to work in the field.
Basic concepts and results
Toponogov's theorem
Homogeneous spaces
Morse theory
Closed geodesics and the cut locus
The sphere theorem and its generalizations
The differentiable sphere theorem
Complete manifolds of nonnegative curvature
Compact manifolds of nonpositive curvature
Bibliography
Additional bibliography
Index
ISBN: 9781584889472
Publication Date: 9/26/2008
Number of Pages: 576
Emphasizes the use of statistical methods and the interpretation of data analysis
Features R datasets and simulation
Includes historical material to supplement concepts
Introduces one and two sample location problems, one way analysis of variance, and simple regression
Presents various applications along with supporting datasets
With an emphasis on explaining how and why statistical methods are used to analyze data, An Introduction to Statistical Inference and its Applications with R introduces several important procedures: one and two sample location problems, one way analysis of variance, and simple linear regression. The book presents numerous applications and supporting datasets throughout along with historical background to illustrate the material. Offering a modern approach that focuses on the interpretation of data, it features an appendix that provides instruction on the use of R as well as datasets and simulation. In addition, R code is available for download on the web.
This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.
The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short ? almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area.
Introduction to Topological Groups
Right (Semi)Topological Groups
Topological Groups: Basic Constructions
Special Classes of Topological Groups
Cardinal Invariants of Topological Groups
Moscow Topological Groups, Completions
Free Topological Groups
R-Factorizable Topological Groups
Compactness in Topological Groups
Actions of Topological Groups on Topological Spaces
Readership: Academics and graduate students in Topology and Algebra.
795pp Pub. date: Scheduled Fall 2008
ISBN 978-90-78677-06-2
This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics and engineering. It treats the dynamics of ray optics, resonant oscillators and the elastic spherical pendulum from a unified geometric viewpoint, by formulating their solutions using reduction by Lie-group symmetries. The only prerequisites are linear algebra, calculus and some familiarity with the Euler?Lagrange variational principles and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.
The ideas and concepts of geometric mechanics are explained in the context of explicit examples. Through these examples, the student develops skills in performing computational manipulations, starting from Fermat's principle, working through the theory of differential forms on manifolds and transferring these ideas to the applications of reduction by symmetry to reveal Lie?Poisson Hamiltonian formulations and momentum maps in physical applications.
The many Exercises and Worked Answers aid the student to grasp the essential aspects of the subject. In addition, the modern language and application of differential forms is explained in the context of geometric mechanics, so that the importance of Lie derivatives and their flows is clear. All theorems are stated and proved explicitly.
The book's many worked exercises make it ideal for both classroom use and self-study. In particular, a substantial appendix containing both introductory examples and enhanced coursework problems with worked answers is included to help the student develop proficiency in using the powerful methods of geometric mechanics.
Fermat’s Principle for Ray Optics
Reviews of the Contributions of Newton Lagrange, Euler, Hamilton, Lie, Poincare and Cartan in the Foundations of Geometric Mechanics
Rotations of a Rigid Body
Differential Forms
Lie Derivatives
Resonances and Symmetry Reduction
Geometric and Dynamic Phases
Elastic Spherical Pendulum
Maxwell?Bloch Equations for Laser-Matter Interaction
Readership: Advanced undergraduate and graduate students in mathematics, physics and engineering; researchers interested in learning the basic ideas in the field; non-experts interested in geometric mechanics, dynamics and symmetry.
380pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-1-84816-195-5
ISBN 978-1-84816-196-2(pbk)
This textbook introduces the tools and language of modern geometric mechanics to advanced undergraduate and beginning graduate students in mathematics, physics, and engineering. It treats the dynamics of rotating, spinning and rolling rigid bodies from a geometric viewpoint, by formulating their solutions as coadjoint motions generated by Lie groups. The only prerequisites are linear algebra, multivariable calculus and some familiarity with Euler?Lagrange variational principles and canonical Poisson brackets in classical mechanics at the beginning undergraduate level.
Variational calculus on tangent spaces of Lie groups is explained in the context of familiar concrete examples. Through these examples, the student develops skills in performing computational manipulations, starting from vectors and matrices, working through the theory of quaternions to understand rotations, and then transferring these skills to the computation of more abstract adjoint and coadjoint motions, Lie?Poisson Hamiltonian formulations, momentum maps and finally dynamics with nonholonomic constraints.
The 120 Exercises and 55 Worked Answers help the student to grasp the essential aspects of the subject, and to develop proficiency in using the powerful methods of geometric mechanics. In addition, all theorems are stated and proved explicitly. The book’s many examples and worked exercises make it ideal for both classroom use and self-study.
Galilean Relativity
Newton, Lagrange and Hamilton’s Treatments of the Rigid Body
Quaternions
Quaternionic Conjugacy and Adjoint Actions
The Special Orthogonal Group SO(3)
The Special Euclidean Group SE(3)
Euler?Poincare & Lie?Poisson Equations on SE(3)
Heavy Top Equations
The Euler?Poincare Theorem
Euler?Poincare Reduction by Symmetry
Lie?Poisson Hamiltonian Form of the Classical Spin Chain
Momentum Maps
Round Rolling Rigid Bodies
Readership: Advanced undergraduate and graduate students in mathematics, physics and engineering; researchers interested in learning the basic ideas in the fields; non-experts interested in geometric mechanics, dynamics and symmetry.
250pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-1-84816-155-9
ISBN 978-1-84816-156-6(pbk)
This volume is a collection of articles written by Professor M Ohya over the past three decades in the areas of quantum teleportation, quantum information theory, quantum computer, etc. By compiling Ohya’s important works in these areas, the book serves as a useful reference for researchers who are working in these fields.
Adaptive Dynamics and Its Applications to Chaos and NPC Problem
Quantum Algorithm for SAT Problem and Quantum Mutual Entropy
New Quantum Algorithm for Studying NP-Complete Problems
Entanglement, Quantum Entropy and Mutual Information
Fundamentals of Quantum Mutual Entropy and Capacity
Compound Channels, Transition Expectations, and Liftings
Complexities and Their Applications to Characterization of Chaos
Complexity, Fractal Dimension for Quantum States
Information Dynamics and Its Applications to Optical Communication Processes
Information Theoretical Treatments of Genes
Some Aspects of Quantum Information Theory and Their Applications to Irreversible Processes
On Compound State and Mutual Information in Quantum Information Theory
Note on Quantum Probability
Quantum Ergodic Channels in Operator Algebras
On Open System Dynamics ? An Operator Algebraic Study
Dynamical Process in Linear Response Theory
Stability of Weiss Ising Model
and other papers
Readership: Researchers in quantum entropy, quantum information theory and mathematical physics.
488pp Pub. date: Feb 2008
ISBN 978-981-279-419-2
This volume covers many topics, including number theory, Boolean functions, combinatorial geometry, and algorithms over finite fields. It contains many new, theoretical and applicable results, as well as surveys that were presented by the top specialists in these areas. New results include an answer to one of Serre's questions, posted in a letter to Top; cryptographic applications of the discrete logarithm problem related to elliptic curves and hyperelliptic curves; construction of function field towers; construction of new classes of Boolean cryptographic functions; and algorithmic applications of algebraic geometry.
On the Semiprimitivity of Cyclic Codes (Y Aubry & P Langevin)
An Optimal Unramified Tower of Function Fields (K Brander)
Galois Invariant Smoothness Basis (J-M Couveignes)
Decoding of Scroll Codes (G Hitching & T Johnsen)
Fuzzy Pairing-based CL-PKC (M Kiviharju)
On Quadratic Extensions of Cyclic Projective Planes (H F Law & P Wong)
On the Number of Boolean Resilient Functions (S Mesnager)
Symmetric Cryptography and Algebraic Curves (F Voloch)
Partitions of Vector Spaces over Finite Fields (Y Zelenyuk)
and other papers
Readership: Mathematicians, researchers in mathematics (academic and industry R&D).
520pp (approx.) Pub. date: Scheduled Summer 2008
ISBN 978-981-279-342-3
This volume presents the written versions of the tutorial lectures given at the Workshop on Computational Prospects of Infinity, held from 18 June to 15 August 2005 at the Institute for Mathematical Sciences, National University of Singapore. It consists of articles by four of the leading experts in recursion theory (computability theory) and set theory. The survey paper of Rod Downey provides a comprehensive introduction to algorithmic randomness, one of the most active areas of current research in recursion theory. Theodore A Slaman's article is the first printed account of the ground-breaking work of Slaman?Woodin and Slaman?Shore on the definability of the Turing jump. John Steel presents some results on the properties of derived models of mice, and on the existence of mice with large derived models. The study was motivated by some of the well-known Holy Grails in inner model theory, including the Mouse Set Conjecture. In his presentation, W Hugh Woodin gives an outline of an expanded version (unpublished) on suitable extender sequences, a subject that was developed in the attempt to understand inner model theory for large cardinals beyond the level of superstrong cardinals.
The volume serves as a useful guide for graduate students and researchers in recursion theory and set theory to some of the most important and significant developments in these subjects in recent years.
Five Lectures on Algorithmic Randomness (R Downey)
Global Properties of the Turing Degrees and the Turing Jump (T A Slaman)
Derived Models Associated to Mice (J R Steel)
Tutorial Outline: Suitable Extender Sequences (W H Woodin)
Readership: Graduate students, researchers in recursion theory (computability theory) and set theory, as well as logic in general.
250pp Pub. date: Scheduled Fall 2008
ISBN 978-981-279-653-0