Gregory K.

Gregory K. Miller

Probability: Modeling and Applications to Random Processes

ISBN: 0-471-45892-9
Hardcover
480 pages
June 2006

Description

Written by an enthusiastic educator known for his dynamic teaching, Probability: Modeling and Applications to Random Processes focuses on modeling outcomes of random variables and random processes. Filling the need for a solid introductory texts on probability and stochastic processes which explain the material clearly, the bookOs central point is squarely that of the basic probability laws and modeling with probability distributions while exploring their applications and links to random phenomena.

Table of Contents

Preface.
To the Student.
To the Instructor.
Coverage.
Acknowledgments.
Chapter 1. Modeling.
1.1 Choice and Chance.
1.2 The Model Building Process.
1.3 Modeling in the Mathematical Sciences.
1.4 A First Look at a Probability Model: The Random Walk.
1.5 Brief Applications of Random Walks.
Exercises.
Chapter 2. Sets and Functions.
2.1 Operations with Sets.
2.2 Functions.
2.3 The Probability Function and the Axioms of Probability.
2.4 Equally Likely Sample Spaces and Counting Rules.
Rules.
Exercises.
Chapter 3. Probility Laws I: Building on the Axioms.
3.1 The Complement Rule.
3.2 The Addition Rule.
3.3 Extensions and Additional Results.
Exercises.
Chapter 4. Probility Laws II: Results of Conditioning.
4.1 Conditional Probability and the Multiplication Rule.
4.2 Independent Events.
4.3 The Theorem of Total Probabilities and Bayes' Rule.
4.4 Problems of Special Interest: Effortful Illustrations of the Probability Laws.
Exercises.
Chapter 5. Random Variables and Stochastic Processes.
5.1 Roles and Types of Random Variables.
5.2 Expectation.
5.3 Roles, Types, and Characteristics of Stochastic Processes.
Exercises.
Chapter 6. Discrete Random Variables and Applications in Stochastic Processes.
6.1 The Bernoulli and Binomial Models.
6.2 The Hypergeometric Model.
6.3 The Poisson Model.
6.4 The Geometric and Negative Binomial.
Models.
Exercises.
Chapter 7. Continuous Random Variables and Applications in Stochastic Processes.
7.1 The Continuous Uniform Model.
7.2 The Exponential Model.
7.3 The Gamma Model.
7.4 The Normal Model.
Chapter 8. Covariance and Correlation Among Random Variables.
8.1 Joint, Marginal and Conditional Distributions.
8.2 Covariance and Correlation.
8.3 Brief Examples and Illustrations in Stochastic Processes and Times Series.
Exercises.
Bibliography.
Tables.
Index.

Viktor Ivanov / Natalya Ivanova

MATHEMATICAL MODELS OF THE CELL AND CELL ASSOCIATED OBJECTS

Included in series
Mathematics in Science and Engineering, 206

Description

The book contains five main parts: Introduction: Evolutionary System and Development Modelling; Part I: A Survey of MM of CAO (cell associated objects); Part II: MM (mathematical models) of Development; Part III: Introduction to Applications; Appendix: Mathematics of Development. The part I gives the reader a survey of hundreds results in the field of the cell and cell associated objects modelling, which are not easy accessible. The original four parts of the book have no analogy in the literature, except the previous book of the first author 'Model Development and Optimization', KAP, 1999, and the book 'Mathematical Modeling in Economics, Ecology and the Environment', KAP, 1999, by N. Hritonenko, Yu. Yatsenko (Yu. Yatsenko is a pupil of the first author of the cell book). The present book is different from the previous mainly by much more profound investigation of such a complicated object as the cell and by much more detailed description of applications to modelling AIDS, cancers, and life longevity. Key features: - Inlet novel class of non-linear mathematical models based on the general theory of evolutionary systems and their development . - Introducing and proving fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions. - Proof of effective applicability of that class of models to complicated objects such as the cell and the immune network . - Detailed modelling complicated processes such as the cell cycle, protein folding, immune network response, etc. - Detailed analysis of applications to modelling AIDS, cancers, and life longevity. - Introducing and grounding the respective numerical algorithms and software. - Detailed analysis of hundreds of scientific works in the field of mathematical modelling of the cell and cell associated objects.

Audience

Researchers and students, libraries of universities and scientific centres.

Contents

Contents. Preface. Introduction: Evolutionary Systems and Development Modeling. Part 1: SURVEY OF MM OF CAO. Chapter 1: General Methods of Inlet and Analysis of MM. Chapter 2: MM of Enzyme Reactions. Chapter 3: MM of Kinetic Cellular Theory. 4: Some Other MM. Part 2: MM OF DEVELOPMENT. Chapter 5: Base MM. Chapter 6: Examples of CAO and Their MM. Chapter 7: MM of the Cell. Chapter 8: MM of the Immune Network. Chapter 9: MM of Some Other CAO. Part 3: INTRODUCTION TO APPLICATIONS. Chapter 10: AIDS. Chapter 11: Cancers. Chapter 12: On Life Longevity Problems. Chapter 13: On MM of a Disease. Appendix: MATHEMATICS OF DEVELOPMENT. Chapter 14: Investigation of Equations. Chapter 15: Investigation of Optimization Problems. Chapter 16: Numerical Methods and Software. Summary. Bibliography. Index. About the Authors.

Hardbound, ISBN: 0-444-52714-1, 354 pages, publication date: 2006

Steve Awodey

James G. Oxley

Matroid Theory

NEW IN PAPERBACK
ISBN-10: 0-19-920250-8
ISBN-13: 978-0-19-920250-8
Publication date: 6 July 2006
544 pages, numerous b/w line drawings, 234mm x 156mm

Reviews

'Review from previous edition 'It includes more background, such as finite fields and finite projective and affine geometries, and the level of the exercises is well suited to graduate students. The book is well written and includes a couple of nice touches ... this is a very useful book. I recommend it highly both as an introduction to matroid theory and as a reference work for those already seriously interested in the subject, whether for its own sake or for its applications to other fields.' -Neil L. White, University of Florida, AMS Bulletin, Vol. 30, No. 2, April '94
'Whoever wants to know what is happening in one of the most exciting chapters of combinatorics has no choice but to buy and peruse Oxley's treatise' -Gian-Carlo Rota, Massachusetts Institute Technology (The Bulletin of Mathematics)
'This book is an excellent graduate textbook and reference book on matroid theory. The care that went into the writing of this book is evident by the quality of the exposition' -Talmage J. Reid, University of Mississippi (Mathematical Reviews)

Description

Careful, lucid exposition from an author at the forefront of research
Contains over 500 exercises and proofs
Final chapter lists sixty unsolved problems and describes progress towards their solutions

The study of matroids is a branch of discrete mathematics with basic links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical engineering and statics.

This new in paperback version of the classic "Matroid Theory" by James Oxley provides a comprehensive introduction to matroid theory, covering the very basics to more advanced topics. With over 500 exercises and proofs of major theorems, this book is the ideal reference and class text for academics and graduate students in mathematics and computer science. The final chapter lists sixty unsolved problems and describes progress towards their solutions.

Readership: Mathematicians and computer scientists with interests in combinatorics, graph theory, lattice theory, projective geometry, or combinatorial optimization.

Contents

Preface
Preliminaries
1 Basic definitions and examples
2 Duality
3 Minors
4 Connectivity
5 Graphic matroids
6 Representable matroids
7 Constructions
8 Higher connectivity
9 Binary matroids
10 Ternary matroids
11 The Splitter theorem
12 Submodular functions and matroid union
13 Regular matroids
14 Unsolved problems
References
Appendix. Some interesting matroids
Notation
Index

Serge Haroche and Jean-Michel Raimond

Exploring the Quantum
Atoms, Cavities, and Photons

(Hardback)
ISBN-10: 0-19-850914-6
ISBN-13: 978-0-19-850914-1
Publication date: 4 August 2006
576 pages, 228 figures - 156 b+w line drawings and 72 b+w halftones, 246mm x 171mm
Series: Oxford Graduate Texts

Reviews
'This is a wonderfully well-informed book. The authors tackle a difficult subject with beautiful clarity, and elegance. It should be required reading for anyone who wishes to explore the quantum wonders of Nature.' -A. Ekert, University of Cambridge

Description

An introduction to quantum optics for quantum information scientists.
A comprehensive description of the physics of open quantum systems.
Direct demonstrations of quantum concepts, providing illustrations for teaching quantum physics and giving ideas for problem sets at an advanced level.
Useful to readers who are new to the conceptual aspects of the quantum world.
A unified presentation of different subfields of quantum optics: cavity QED, ion traps, and cold atoms in optical lattices.

The counter-intuitive aspects of quantum physics have been for long illustrated by thought experiments, from Einstein's photon box to Schrodinger's cat. These experiments have now become real, with single particles - electrons, atoms or photons - directly unveiling the weird features of the quantum. State superpositions, entanglement and complementarity define a novel quantum logic which can be harnessed for information processing, raising great hopes for applications. This book describes a class of such thought experiments made real. Juggling with atoms and photons confined in cavities, ions or cold atoms in traps, is here an incentive to shed a new light on the basic concepts of quantum physics. Measurement processes and decoherence at the quantum-classical boundary are highlighted. This volume, which combines theory and experiments, will be of interest to students in quantum physics, teachers seeking illustrations for their lectures and new problem sets, researchers in quantum optics and quantum information.

Readership: Students and professionals in physics, quantum information physics and quantum mechanics.

Contents

1 Unveiling the quantum
2 Strangeness and power of the quantum
3 Of spins and springs
4 The environment is watching
5 Photons in a box
6 Seeing light in subtle ways
7 Taming Schrodinger's cats
8 Atoms in a box
9 Entangling matter waves
Appendix: Representation of quantum states in phase space

Terence Tao

Solving Mathematical Problems
A Personal Perspective

(Hardback)
ISBN-10: 0-19-920561-2
ISBN-13: 978-0-19-920561-5
(Paperback)
ISBN-10: 0-19-920560-4
ISBN-13: 978-0-19-920560-8
Publication date: 10 August 2006
150 pages, 234mm x 156mm

Description

Extensive discussion of carefully selected problems
Numerous exercises included
Assumes only a basic level of mathematics

Readership: Students of 14 years and above in pure mathematics

Contents
Preface
1 Strategies in problem solving
2 Examples in number theory
3 Examples in algebra and analysis
4 Euclidean geometry
5 Analytic geometry
6 Sundry examples
References
Index

Juan Luis Vazquez

Smoothing and Decay Estimates for Nonlinear Diffusion Equations
Equations of Porous Medium Type

(Hardback)
ISBN-10: 0-19-920297-4
ISBN-13: 978-0-19-920297-3
Publication date: 17 August 2006
250 pages, 234mm x 156mm
Series: Oxford Lecture Series in Mathematics and Its Applications

Description

Provides a comprehensive and systematic guide to nonlinear diffusion equations
End of chapter notes provide comments, historical notes and recommended reading
Chapter-length list of references

This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.

Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porous medium type"), the aim of this text is to obtain sharp a priori estimates and decay rates for general classes of solutions in terms of estimates of particular problems. These estimates are the building blocks in understanding the qualitative theory, and the decay rates pave the way to the fine study of asymptotics. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including time decay, smoothing, extinction in finite time, and delayed regularity.

Readership: Graduates and researchers in mathematics, the physical sciences and engineering

Contents

Preface
Part I
1 Preliminaries
2 Smoothing effect and time decay. Data in L1(Rn) or M(Rn)
3 Smoothing effect and time decay from Lp or Mp
4 Lower bounds, contractivity, error estimates and continuity
Part II
5 Subcritical range of the FDE. Critical line. Extinction. Backward effect
6 Improved analysis of the critical line. Delayed regularity
7 Extinction rates and asymptotics for 08 Logarithmic diffusion in 2-d and intermediate 1-d range
9 Super-fast FDE
10 Summary of main results for the PME/FDE
Part III
11 Evolution equations of the p-Laplacian type
12 Appendices
Bibliography
Index