Series: Pseudo-Differential Operators, Tentative volume 9
2012, 250 p.
Softcover, ISBN 978-3-0348-0293-2
Due: August 31, 2012
Numerous examples are worked, out illustrating each result
The applications to various fields are discussed in elementary fashion
The methods are extended to operators other than the standard ones
The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar. This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner.
Content Level ā Research
Related subjects ā Analysis - Dynamical Systems & Differential Equations
To Be Published 1st May 2012 248 pages
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Hardback: 978-1-46-650719-7:
The divergence theorem and resulting integration by parts formula are among the most frequently used tools of mathematical analysis. Written by a major contributor to the field who has worked on the divergence theorem for over thirty years, this book presents divergence theorems along with all of the important concepts and machinery to rigorously validate the results. The text incorporates new material on bounded variation sets and bounded variation functions. It also addresses dyadic figures, bounded and unbounded vector fields, and mean divergence.
DYADIC FIGURES: Preliminaries. Divergence Theorem for Dyadic Figures. Removable Singularities. SETS OF FINITE PERIMETER: Perimeter. BV Functions. Locally BV Sets. THE DIVERGENCE THEOREM: Bounded Vector Fields. Unbounded Vector Fields. Mean Divergence. Charges. The Divergence Equation.
To Be Published 15th August 2012 250 pages
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Potential theory describes the behavior of gravitational, magnetic, and fluid potentials. This introductory-level book covers the classical three-dimensional Euclidean setting involving the Laplacian and its surface counterpart based on the Beltrami operator. This approach provides a connecting link between two areas of geomathematical research: the exterior of the earth and the earthfs surface in its spherical manifestation. The text discusses the approximation of gravitational potential from gravity measurement, the separation of the magnetic field into interior and exterior, and ionspheric current systems from magnetic field measurements.
Introduction
Preliminaries
Basic Notations
Differential Operators
Integral Formulas
Legendre Polynomials
Scalar Spherical Harmonics
Vector Spherical Harmonics
METHODS IN EUCLIDEAN SPACE
Basic Concepts of Potential Theory
Volume Potentials and Greenfs Formulas
Limit and Jump Relations for Layer Potentials
Dirichlet and Neumann Boundary Value Problems
Oblique Derivative Problems
Dense Function Systems
Geomagnetism
Geomagnetic Background
Mie and Helmholtz Decomposition
Gauss Representation and Boundary Value Problems
Separation of Sources
Gravitation
Observables and the Gravity Potential
Boundary Value Problems of Physical Geodesy
Density Distributions
METHODS ON THE SPHERE
Basic Concepts of Potential Theory
Global Considerations
Surface Potentials and Green's Formulas
Limit and Jump Relations for Layer Potentials
Dirichlet and Neumann Boundary Value Problems
Dense Function Systems
Geomagnetism
Mie and Helmholtz Decomposition
Separation of Sources
Ionospheric Current Systems
Gravitation
Geoid Undulations and Deflections of the Vertical
Exercises and Literature appear at the end of each chapter.
To Be Published 15th August 2012 512 pages
Series: Chapman & Hall/CRC Texts in Statistical Science
Hardback: 978-1-43-981512-0:
This text covers statistical modeling using generalized linear mixed models (GLMMs) as the organizing tool. After an overarching introduction to modeling from a contemporary perspective, the book presents the main theory and methods used for setting up estimation and inference for GLMMs. It also describes the major classes of applications with case studies from biostatistics and epidemiology. SAS is included throughout while R is used when SAS does not work well with the GLMM.
To Be Published 31st October 2012 320 pages
Series: Chapman & Hall/CRC Texts in Statistical Science Series
Hardback: 978-1-43-987880-4
Unique in its presentation of topics from both classical and Bayesian perspectives, this second edition balances both sides elegantly and describes the relative strengths and weaknesses of the different approaches in each case. It covers all the key topics of standard inference courses, including point and interval estimation, hypothesis testing, prediction, approximation, and linear models. Along with real data examples and exercises for self-study, this edition offers numerous updates that reflect recent developments.