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A second part of volume number 10 in the OXFORD LECTURE SERIES IN MATHEMATICS AND ITS APPLICATIONS, which describes compressible fluids-mechanics models and deals with problems associated with the compressible Navier-Stokes equations.

This book is a unique introduction to graph theory, written by one of the founding fathers. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experiences in the area, and provides a fascinating insight into the processes leading to his proofs.

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour.

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour.

This monograph examines the self-avoiding walk, a classical model in statistical mechanics, probability theory and mathematical physics, paying close attention to recent developments in the field, such as models in the hexagonal lattice and the Monte Carlo methods.

One of the most challenging topics in applied mathematics has been the development of the theory of nonlinear partial differential equations. Despite a long history of contributions, there exists no central core theory. This two volume work forms a unique and rigorous treatise on various mathematical aspects of fluid mechanics models.

The discovery of relations between quantum gravity and the theory of knots and links came as a surprise, since the topics had been regarded as quite remote from each other. This volume contains the proceedings of a workshop designed to bring together researchers in knot theory and quantum gravity.

The purpose of this book is to inform mathematicians about the applicability of graph theory to other areas of mathematics, from number theory, to linear algebra, knots, neural networks, and finance. It should be of use to professsional mathematicians and graduate students.

This work forms a unique and authoritative account on various important mathematical developments in fluid mechanics. It offers to the reader a self-contained presentation of the theory of Euler equations describing a perfect incompressible fluid. It complements nicely the fluid mechanics books by P.L. Lions published in the same series: Mathematical Topics in Fluid Mechanics, Volumes I & II.

Fractal geometrics can arise in many different ways mathematically. This book proposes notions of coherent geometric structure, asking what exactly is a fractal "pattern"? A wide range of problems are dealt with, and examples given, which connect to other diverse areas of mathmatics.

Filling the gap between introductory and encyclopedic treatments, this book provides rich and appealing material for a second course in combinatorial optimization. This book is suitable for graduate students as well as a reference for established researchers.

This title discusses various aspects of radio spectrum management. Most chapters in the book concentrate on the mathematical and computational issues related to radio channel assignment and network design, with the first two chapters providing background in terms of the role of regulation and the history of spectrum management.

Written by a well-known expert in the field, the focus of this book is on an innovative mathematical and numerical theory which applies to classical models of physics such as shock waves and balance laws. The text is based on early works in common with P.L. Lions (field medalist).

This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by singular elliptic equations.

This text presents some of the basic material on block designs and orthogonal Latin squares, emphasizing in particular methods of constructing cyclic examples by means of difference systems. It also offers an account of the construction of league tables and tournaments.

Based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. This book contains proofs and explicit calculations, and is useful for graduate students of mathematics.

This text examines degree theory and some of its applications in analysis. Topics described include: degree theory for continuous functions; the multiplication theorem; Hopf's theorem; Brower's fixed point theorem; odd mappings; and Jordan's separation theorem.

This text provides a review of the consistent themes from Dominic Welsh's influential work in combinatorics and discrete probability. Original articles by key academics are set in a broader context by the inclusion of review material. The text will appeal to all those seeking an introduction to the relevant contemporary aspects of these fields.

Aimed at graduates and researchers in algebraic geometry, this collection of edited chapters provides a complete and essentially self-contained account of the construction of 3-fold and 4-fold klt flips.

The present book is the first one in the new subject area of non-integrable Hamiltonian partial differential equations, using the approach of analysis and geometry rather than algebra to study the equations. The book will be an invaluable source of information for postgraduate mathematics students and researchers working in analysis as well as for theoretical physicists interested in the topic.

A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.

The 'factorization method', discovered by Professor Kirsch, is a relatively new method for solving certain types of inverse scattering problems and problems in tomography. The text introduces the reader to this promising approach and discusses the wide applicability of this method by choosing typical examples.

A rigorous mathematical description of the overall properties of fast-oscillating differential equations or integral functionals, which also includes an introduction to the theory of convergence and weak lower semicontinuous functionals. The text is volume number 12 in the OXFORD LECTURE SERIES IN MATHEMATICS AND ITS APPLICATIONS.

The theory of homogenization replaces a real composite material with an imaginary homogeneous one, to describe the macroscopic properties of the composite using the properties of the microscopic structure. This work illustrates the relevant mathematics, logic and methodology with examples.

A timely research text by a leading academic on the mathematical theory of viscous compressible fluids. Containing the most recent results in the field, described in a clear self-contained manner, it is aimed at research mathematicians, theoretical physicists, engineers and graduate students.

Phylogenetic (evolutionary) trees and networks are widely used throughout evolutionary biology, epidemiology, and ecology to infer the historical relationships between species through inherited characteristics. Semple and Steel discuss the mathematics that underlies the reconstruction and analysis of these phylogenetic trees.

This is an updated and extended version of the last part of Dr Pretzel's successful book Error Correcting Codes and Finite Fields. It provides an introduction to the geometry of curves over finite fields. and uses the theory for a detailed investigation of geometric Goppa codes, a new and important area of coding theory.

Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.

Based on lecture notes from the Scuola Normale this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.

An application-oriented introduction to the highly topical area of the development and analysis of efficient fixed-parameter algorithms for hard problems. Aimed at graduate and research mathematicians, algorithm designers, and computer scientists, it provides a fresh view on this highly innovative field of algorithmic research.