Series: Research Notes in Mathematics Series Volume: 436
ISBN: 1-58488-490-8
Publication Date: 8/30/2004
Number of Pages: 264
Offers a comprehensive, mathematically rigorous treatment of many-body
physics
Presents many new results and clarifies difficult concepts
Provides a full introduction to the Feldman, Knoerrer &
Trubowitz Fermio-liquid construction
Follows a methodical, step-by-step method of calculation and
definition
Mathematical Methods of Many-Body Quantum Field Theory offers a
comprehensive, mathematically rigorous treatment of many-body
physics. It develops the mathematical tools for describing
quantum many-body systems and applies them to the many-electron
system. These tools include the formalism of second quantization,
field theoretical perturbation theory, functional integral
methods, bosonic and fermionic, and estimation and summation
techniques for Feynman diagrams. Among the physical effects
discussed in this context are BCS superconductivity, s-wave and
higher l-wave, and the fractional quantum Hall effect. While the
presentation is mathematically rigorous, the author does not
focus solely on precise definitions and proofs, but also shows
how to actually perform the computations.
Presenting many recent advances and clarifying difficult
concepts, this book provides the background, results, and detail
needed to further explore the issue of when the standard
approximation schemes in this field actually work and when they
break down. At the same time, its clear explanations and
methodical, step-by-step calculations shed welcome light on the
established physics literature.
Series: Texts in Statistical Science Series Volume: 64
ISBN: 1-58488-322-7
Publication Date: 12/22/2004
Number of Pages: 504
Covers the three main types of spatial data: geostatistical data,
lattice data, and point patterns in theory and application
Adopts a modeling approach that ties the material into well known
areas like linear models and Monte Carlo testing
Requires no previous exposure to measure theory and includes the
necessary background material from stochastic process theory
Spatial statistics -- one of the fastest growing areas of
statistics -- has applications across a wide range of disciplines.
Statistical Methods for Spatial Data Analysis takes a model-based
approach and covers the theory and applications of all three
major types of spatial data: geostatistical, lattice, and point
pattern. The book is rich in applications and incorporates
discussions on important recent developments in the field, such
as spatial models for nonstationary data and generalized linear
model extensions to spatial data. The authors also incorporate
the use of SAS for problem solving and make the relevant code and
various data sets available for download from the publisher's Web
site.
Table of Contents
Introduction. Mapped Point Patterns. Semivariogram Analysis and
Estimation. Geostatistics I. Spatial Prediction and Ordinary
Kriging. Spatial Regression Models. Geostatistics II. Kriging
Methods. Models for Lattic Data. Miscellaneous Topics. Appendices.
Series: Numerical Insights Volume: 4
ISBN: 1-58488-49-24
Publication Date: 10/27/2004
Number of Pages: 240
Provides a theoretical framework necessary for the successful use
of multigrid methods for (systems of) partial differential
equations
Allows for local Fourier analysis via a simple mouse click,
courtesy of accompanying software (LFA) and GUI (xlfa)
Includes case studies for two- and three-dimensional problems,
including Poisson, convection diffusion, and biharmonic equation,
the Oseen and Stokes equations, a linear shell problem and
elasticity systems
Presents the recently-developed three-grid analysis, allowing
investigation of real multigrid effects
Before applying multigrid methods to a project, mathematicians,
scientists, and engineers need to answer questions related to the
quality of convergence, whether a development will pay out,
whether multigrid will work for a particular application, and
what the numerical properties are. Practical Fourier Analysis for
Multigrid Methods uses a detailed and systematic description of
local Fourier k-grid (k=1,2,3) analysis for general systems of
partial differential equations to provide a framework that
answers these questions.
This volume contains software that confirms written statements
about convergence and efficiency of algorithms and is easily
adapted to new applications. Providing theoretical background and
the linkage between theory and practice, the text and software
quickly combine learning by reading and learning by doing. The
book enables understanding of basic principles of multigrid and
local Fourier analysis, and also describes the theory important
to those who need to delve deeper into the details of the subject.
The first chapter delivers an explanation of concepts, including
Fourier components and multigrid principles. Chapter 2 highlights
the basic elements of local Fourier analysis and the limits to
this approach. Chapter 3 examines multigrid methods and
components, supported by a user-friendly GUI. Chapter 4 provides
case studies for two- and three-dimensional problems. Chapters 5
and 6 detail the mathematics embedded within the software system.
Chapter 7 presents recent developments and further applications
of local Fourier analysis for multigrid methods.
Series: Chapman & Hall/CRC Applied Mathematics &
Nonlinear Science
ISBN: 1-58488-389-8
Publication Date: 9/26/2005
Number of Pages: 320
" Offers the most mathematically comprehensive treatment of
the subject currently available
" Provides many illustrations of circuits and devices to
promote understanding of the concepts
" Includes discussions on quantum circuit design and quantum
error correcting codes
The design and construction of the quantum computer is one of the
most exciting and challenging goals of the scientific community.
This book provides an introductory yet comprehensive treatment of
the mathematical theory underlying quantum computation. The
author adopts the formal, axiomatic style of stating and proving
lemmas, propositions, and theorems, but does so in a way that
keeps the treatment self-contained and accessible to a broad,
multidisciplinary audience. Numerous diagrams of circuits and
devices support the text. Plentiful exercises and examples
reinforce the concepts and make this book suitable for graduate-level
course work as well as a valuable reference for researchers and
practitioners.
Table of Contents
Introduction to Quantum Mechanics and Quantum Computing Devices.
Quantum Circuits and Universality of Quantum Gates. Quantum
Computing Complexity. Quantum Fourier Transforms. Quantum Search
Algorithms. Shoris Quantum Algorithm for Factoring Integers.
Quantum Error Correcting Codes.
Series: Chapman & Hall/CRC Computer Science & Data
Analysis Volume: 5
ISBN: 1-58488-366-9
Publication Date: 11/24/2004
Number of Pages: 424
" Presents MATLAB code for virtually all algorithms covered
in the book for better understanding
" Provides pseudo-code to implement the algorithms presented
using other software packages
" Includes MATLAB code that is robust in nature to make the
book accessible to many more people and useable for several years
Exploratory Data Analysis with MATLAB is the first book to put a
computational emphasis on the methods used to visualize and
summarize data before making model assumptions to generate
hypotheses. The authors use MATLAB code and algorithmic
descriptions to provide the user with state-of-the-art techniques
for finding patterns and structure in data. They also focus on
the computational aspects of these methodologies as opposed to
theoretical. Many annotated references to papers and books help
to provide the theoretical aspects of the topic. The approach
taken by the authors helps to make exploratory data analysis
accessible to a wide range of users.