Series: Lecture Notes in Mathematics, Vol. 1983
Subseries: Mathematical Biosciences Subseries ,
2010, Approx. 230 p., Softcover
ISBN: 978-3-642-03443-5
Due: October 2009
About this book
This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
Researchers and graduate students
Electrical impedance tomography
Imaging algorithms
Inverse problems
Mathematical modeling
Ultrasound imaging
1 Multi-Frequency Electrical Impedance Tomography and Magnetic Resonance Electrical Impedance Tomography.- 2 Time Reversing Waves For Biomedical Applications.- 3 The Method of Small-Volume Expansions for Medical Imaging.- 4 Electric and Magnetic Activity of the Brain in Spherical and Ellipsoidal Geometry.- 5 Estimation of Velocity Fields and Propagation on Non-Euclidian Domains. Application to the Exploration of Cortical Spatiotemporal Dynamics.
Series: Springer Monographs in Mathematics
2009, Approx. 250 p., Hardcover
ISBN: 978-0-387-87808-9
Due: November 2009
A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner.
The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions. The physical models discussed in some detail here relate to porous media equation, heat equation with absorption, generalized Fisher's equation, Burgers equation and its generalizations.
A chapter each is devoted to nonlinear diffusion and fluid mechanics. The present book will be found useful by applied mathematicians, physicists, engineers and biologists, and would considerably help understand diverse natural phenomena.
Introduction.- Large Time Asymptotics for Solutions of Nonlinear First-Order Partial Differential Equations.- Large Time Asymptotic Analysis of Some Nonlinear Parabolic Equations ? Some Constructive Approaches.- Self-Similar Solutions as Large Time Asymptotics for Some Nonlinear Parabolic Equations.- Asymptotics in Fluid Mechanics.- Index.
Series: Springer Series in Statistics
2010, Approx. 370 p., Hardcover
ISBN: 978-0-387-92709-1
Due: November 2009
Comparing Distributions refers to the statistical data analysis that encompasses the traditional goodness-of-fit testing. Whereas the latter includes only formal statistical hypothesis tests for the one-sample and the K-sample problems, this book presents a more general and informative treatment by also considering graphical and estimation methods. A procedure is said to be informative when it provides information on the reason for rejecting the null hypothesis. Despite the historically seemingly different development of methods, this book emphasises the similarities between the methods by linking them to a common theory backbone.
This book consists of two parts. In the first part statistical methods for the one-sample problem are discussed. The second part of the book treats the K-sample problem. Many sections of this second part of the book may be of interest to every statistician who is involved in comparative studies.
The book gives a self-contained theoretical treatment of a wide range of goodness-of-fit methods, including graphical methods, hypothesis tests, model selection and density estimation. It relies on parametric, semiparametric and nonparametric theory, which is kept at an intermediate level; the intuition and heuristics behind the methods are usually provided as well. The book contains many data examples that are analysed with the cd R-package that is written by the author. All examples include the R-code.
Because many methods described in this book belong to the basic toolbox of almost every statistician, the book should be of interest to a wide audience. In particular, the book may be useful for researchers, graduate students and PhD students who need a starting point for doing research in the area of goodness-of-fit testing. Practitioners and applied statisticians may also be interested because of the many examples, the R-code and the stress on the informative nature of the procedures.
Olivier Thas is Associate Professor of Biostatistics at Ghent University. He has published methodological papers on goodness-of-fit testing, but he has also published more applied work in the areas of environmental statistics and genomics.
Part I One-sample problems Introduction.- Preliminaries (building blocks).- Graphic tools.- Smooth tests.- Methods based on the empirical distribution function.- Part II Two-sample and K-sample problems Introduction.- Preliminaries (building blocks).- Graphical tools.- Some important two-sample tests.- Smooth tests.- Methods based on the empirical distribution function.- Two final methods and some final thoughts.
Series: Operator Theory: Advances and Applications , Vol. 195
2010, Approx. 310 p., Hardcover
ISBN: 978-3-0346-0173-3
Due: November 2009
This volume contains the proceedings of the eighteenth International Workshop on Operator Theory and Applications (IWOTA), hosted by the Unit for Business Mathematics and Informatics of North-West University, Potchefstroom, South Africa from July 3 to 6, 2007. The conference (as well as these proceedings) was dedicated to Professors Joseph A. Ball and Marinus M. Kaashoek on the occasion of their 60th and 70th birthdays, respectively. This conference had a particular focus on Von Neumann algebras at the interface of operator theory with functional analysis and on applications of operator theory to differential equations.
Postgraduates and researchers in operator theory, functional analysis and differential equations
functional analysis
matrix theory
operator theory
systems theory