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Solitons in Mathematics and Physics
A discussion of the soliton, focusing on the properties that make it physically ubiquitous and the soliton equation mathematically miraculous.
Research in Progress
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Research in Progress
Vols. for 1977- consist of two parts: Chemistry, biological sciences, engineering sciences, metallurgy and materials science (issued in the spring); and Physics, electronics, mathematics, geosciences (issued in the fall).
An Introduction to Structured Population Dynamics
Interest in the temporal fluctuations of biological populations can be traced to the dawn of civilization. How can mathematics be used to gain an understanding of population dynamics? This monograph introduces the theory of structured population dynamics and its applications, focusing on the asymptotic dynamics of deterministic models. This theory bridges the gap between the characteristics of individual organisms in a population and the dynamics of the total population as a whole. In this monograph, many applications that illustrate both the theory and a wide variety of biological issues are given, along with an interdisciplinary case study that illustrates the connection of models with the...
Solitons in Two-Dimensional Shallow Water
Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools?algebraic geometry, algebraic combinatorics, and representation theory, among others?are used to analyze these two-dimensional wave patterns. The author?s primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students.?
Mathematical Models for Communicable Diseases
A self-contained and comprehensive guide to the mathematical modeling of disease transmission, appropriate for graduate students.
Inverse Scattering Theory and Transmission Eigenvalues
Inverse scattering theory is a major theme of applied mathematics, and it has applications to such diverse areas as medical imaging, geophysical exploration, and nondestructive testing. The inverse scattering problem is both nonlinear and ill-posed, thus presenting particular problems in the development of efficient inversion algorithms. Although linearized models continue to play an important role in many applications, an increased need to focus on problems in which multiple scattering effects cannot be ignored has led to a central role for nonlinearity, and the possibility of collecting large amounts of data over limited regions of space means that the ill-posed nature of the inverse scatt...
Integer Programming
This monograph considers pure integer programming problems which concern packing, partitioning or covering. For this class of problems, an algorithmic framework using a duality approach is offered. Furthermore, the author proposes for the first time a general framework for both packing and covering problems characterizing the convex whole of integer solutions.
Reacting Flows
These two volumes represent the culmination of the Special Year `84-'85 in Reacting Flows held at Cornell University. As the proceedings of the 1985 AMS/SIAM Summer Seminar in Applied Mathematics, the volumes focus on both mathematical and computational questions in combustion and chemical reactors. They are addressed to researchers and graduate students in the theory of reacting flows. Together they provide a sound basis and many incentives for future research, especially in computational aspects of reacting flows. Although the theory of reacting flows has developed rapidly, researchers in the two subareas of combustion and chemical reactors have not communicated. The main goal of this seminar was to synthesize the mathematical theory and bring it to the interface with large-scale computing. All of the papers have high research value, but the first five introductory lectures should be especially noted.
The Linear Sampling Method in Inverse Electromagnetic Scattering
A complete description of the linear sampling method for electromagnetic waves, important for those researching inverse electromagnetic scattering theory.
