Paperback
Series: CBMS-NSF Regional Conference Series in Applied Mathematics
ISBN:9781611971965
Publication date:October 2011
128pages
Dimensions: 247 x 174 mm
Weight: 0.22kg
Diffusion has been used extensively in many scientific disciplines to model a wide variety of phenomena. The Mathematics of Diffusion focuses on the qualitative properties of solutions to nonlinear elliptic and parabolic equations and systems in connection with domain geometry, various boundary conditions, the mechanism of different diffusion rates, and the interaction between diffusion and spatial heterogeneity. The book systematically explores the interplay between different diffusion rates from the viewpoint of pattern formation, particularly Turing's diffusion-driven instability in both homogeneous and heterogeneous environments, and the roles of random diffusion, directed movements and spatial heterogeneity in the classical Lotka?Volterra competition systems. Interspersed throughout the book are many simple, fundamental and important open problems for readers to investigate.
Preface
1. Introduction: the heat equation
2. Dynamics of general reaction-diffusion equations and systems
3. Qualitative properties of steady states of reaction-diffusion equations and systems
4. Diffusion in heterogeneous environments: 2 x 2 Lotka?Volterra competition systems
5. Beyond diffusion: directed movements, taxis, and cross-diffusion
Bibliography
Index.
Hardback
Series: Encyclopedia of Mathematics and its Applications(No. 145)
ISBN:9781107018877
Dimensions: 234 x 156 mm
available from April 2012
This largely self-contained treatment surveys, unites and extends some 20 years of research on direct and inverse problems for canonical systems of integral and differential equations and related systems. Five basic inverse problems are studied in which the main part of the given data is either a monodromy matrix; an input scattering matrix; an input impedance matrix; a matrix valued spectral function; or an asymptotic scattering matrix. The corresponding direct problems are also treated. The book incorporates introductions to the theory of matrix valued entire functions, reproducing kernel Hilbert spaces of vector valued entire functions (with special attention to two important spaces introduced by L. de Branges), the theory of J-inner matrix valued functions and their application to bitangential interpolation and extension problems, which can be used independently for courses and seminars in analysis or for self-study. A number of examples are presented to illustrate the theory.
1. Introduction
2. Canonical systems and related differential equations
3. Matrix valued functions in the Nevanlinna class
4. Interpolation problems, resolvent matrices and de Branges spaces
5. Chains that are matrizants and chains of associated pairs
6. The bitangential direct input scattering problems
7. Bitangential direct input impedance and spectral problems
8. Inverse monodromy problems
9. Bitangential Krein extension problems
10. Bitangential inverse input scattering problems
11. Bitangential inverse input impedance and spectral problems
12. Dirac?Krein systems
Bibliography
Index.
Paperback
Series: London Mathematical Society Lecture Note Series(No. 398)
ISBN:9780521617703
Dimensions: 228 x 152 mm
available from June 2012
The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing, and Fejes Toth's conjecture describing all packings of congruent balls in which every ball touches twelve others. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture.
1. Close packing
2. Trigonometry
3. Volume
4. Hypermap
5. Fan
6. Packing
7. Local fan
8. Tame hypermap
9. Further results.
Hardback
ISBN:9780521769358
Paperback
ISBN:9780521139885
30 b/w illus. 100 exercises
Dimensions: 247 x 174 mm
available from June 2012
This fundamental monograph introduces both the probabilistic and algebraic aspects of information theory and coding. It has evolved from the authors' years of experience teaching at the undergraduate level, including several Cambridge Maths Tripos courses. The book provides relevant background material, a wide range of worked examples and clear solutions to problems from real exam papers. It is a valuable teaching aid for undergraduate and graduate students, or for researchers and engineers who want to grasp the basic principles.
1. Essentials of information theory
2. Introduction to coding theory
3. Further topics from coding theory
4. Further topics from information theory
References
Index.
2011 | Hardcover | * ISBN 978-3-11-026759-4
to be published December 2011
Conveys the techniques of multilevel modeling
Relevant to various disciplines, including economy and health
Uses real-world data and problems and the SASR software
Accessible also to practitioners
Interest in multilevel statistical models for social science and public health studies has been aroused dramatically since the mid-1980s. New multilevel modeling techniques are giving researchers tools for analyzing data that have a hierarchical or clustered structure. Multilevel models are now applied to a wide range of studies in sociology, population studies, education studies, psychology, economics, epidemiology, and public health.
This book covers a broad range of topics about multilevel modeling. The goal of the authors is to help students and researchers who are interested in analysis of multilevel data to understand the basic concepts, theoretical frameworks and application methods of multilevel modeling. The book is written in non-mathematical terms, focusing on the methods and application of various multilevel models, using the internationally widely used statistical software, the Statistics Analysis System (SASR). Examples are drawn from analysis of real-world research data. The authors focus on twolevel models in this book because it is most frequently encountered situation in real research. These models can be readily expanded to models with three or more levels when applicable. A wide range of linear and non-linear multilevel models are introduced and demonstrated.