Applied mathematics

This volume (>Ie) NEMATICS Mathematical and Physical aspects constitutes the proceedings of a workshop which was held at l'Universite de Paris Sud (Orsay) in May 1990.

Preface to the English edition xiii Basic notations xv Introduction xvii amPl'ER 1.

The phase transformation from liquid to solid is a phenomenon central to a wide range of manufacturing and natural processes.

Probability has been an important part of mathematics for more than three centuries.

Many problems in celestial mechanics, physics and engineering involve the study of oscillating systems governed by nonlinear ordinary differential equations or partial differential equations.

Shape optimization deals with problems where the design or control variable is no longer a vector of parameters or functions but the shape of a geometric domain.

This monograph is written within the framework of the quantum mechanical paradigm.

Mathematical models have been very successful in the study of the physical world.

Foundational questions in logic, mathematics, computer science and physics are constant sources of epistemological debate in contemporary philosophy.

This book contains contributions by sixteen editors of a single journal specialised in real-world applications of mathematics, particularly in engineering.

The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications.

During the past decade there has been a renewed interest in active sonar systems at both low and medium frequencies.

This book is a continuation of the book Green's Functions and Transfer Functions [35] written some ten years ago.

In the study of integrable systems, two different approaches in particular have attracted considerable attention during the past twenty years.

Singularities in Fluids, Plasmas and Optics, which contains the proceedings of a NATO Workshop held in Heraklion, Greece, in July 1992, provides a survey of the state of the art in the analysis and computation of singularities in physical problems drawn from fluid mechanics, plasma physics and nonlinear optics.

This International Conference on Clifford AlgebrfU and Their Application, in Math- ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989.

Volume 1, i.

This volume contains the proceedings of the Colloquium "e;Analysis, Manifolds and Physics"e; organized in honour of Yvonne Choquet-Bruhat by her friends, collaborators and former students, on June 3, 4 and 5, 1992 in Paris.

We have classified the articles presented here in two Sections according to their general content.

This is the first publication which follows an agreement by Kluwer Publishers with the Caribbean Mathematics Foundation (CMF), to publish the proceedings of its mathematical activities.

The theory of difference equations is now enjoying a period of Renaissance.

Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes.

Stochastic hydrology is an essential base of water resources systems analysis, due to the inherent randomness of the input, and consequently of the results.

Topics in Knot Theory is a state of the art volume which presents surveys of the field by the most famous knot theorists in the world.

The European Turbulence Conferences have been organized under the auspices of the European Mechanics Committee (Euromech) to provide a forum for discussion and exchange of recent and new results in the field of turbulence.

This series presents some tools of applied mathematics in the areas of proba- bility theory, operator calculus, representation theory, and special functions used currently, and we expect more and more in the future, for solving problems in math- ematics, physics, and, now, computer science.

In multivariate statistical analysis, elliptical distributions have recently provided an alternative to the normal model.

Integral representations of holomorphic functions play an important part in the classical theory of functions of one complex variable and in multidimensional com- plex analysis (in the later case, alongside with integration over the whole boundary aD of a domain D we frequently encounter integration over the Shilov boundary 5 = S(D)).

Until not too many years ago, the Italian government bond market, though the third largest in the world in terms of size, was characterised by numerous inefficiencies and problems regarding both policy in managing the public debt and the operation of the market.

In the past few years there has been a fruitful exchange of expertise on the subject of partial differential equations (PDEs) between mathematicians from the People's Republic of China and the rest of the world.

This book contains the edited version of the lectures presented at the NATO ADVANCED STUDY INSTITUTE on "e;COMPUTER AIDED ANALYSIS OF RIGID AND FLEXIBLE MECHANICAL SYSTEMS"e;.

Most industrial and natural materials exhibit a macroscopic behaviour which results from the existence of microscale inhomogeneities.

Objectives The current global environmental crisis has reinforced the need for developing flexible mathematical models to obtain a better understanding of environmental problems so that effective remedial action can be taken.

Two central problems in the pure theory of economic growth are analysed in this monograph: 1) the dynamic laws governing the economic growth processes, 2) the kinematic and geometric properties of the set of solutions to the dynamic systems.

It is probably true quite generally that in the history of human thinking the most fruitful developments frequently take place at those points where two different lines of thought meet.

Small noise is a good noise.

Magnetic energy release plays an important role in a wide variety of cosmic objects such as the Sun, stellar coronae, stellar and galactic accretion disks and pulsars.