Lezioni Lincee – serie

This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.

This book, based on lectures given at the Polytechnic of Milan, gives a broad overview of the field of polymer dynamics. In these lectures the aim is to stress the fundamental concepts of the behaviour of polymers without drawing on the more advanced mathematical formalism which often obscures the natural elegance of the subject matter. Professor De Gennes is one of the most distinguished workers in the field of material science. Therefore this book will be welcomed by both the experienced researcher in the area and the interested layman. It will be of particular value to graduate students.

These notes arise from lectures presented in Florence under the auspices of the Accadamia dei Lincee and deal with an area that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah here presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

The theme of this book is the investigation of globally asymptotic solutions of evolutionary equations. Locally asymptotic solutions of the Navier-Stokes equations and reaction-diffusion equations are the starting point, and by considering perturbed evolutionary equations, global approximations are constructed. The lectures upon which this book is based were warmly received at the universities of Rome and Pavia, and at the Scuola Normale Superiore in Pisa. Here Professor Vishik has collated his lecture notes, and has added an appendix describing his work on attractors deriving from dynamical systems. This is unquestionably a fine addition to the Lezioni Lincee, and will be a necessary addition to the library of all who seek an insight into the solution of evolutionary equations.

The theme of this book is the investigation of globally asymptotic solutions of evolutionary equations. Locally asymptotic solutions of the Navier-Stokes equations and reaction-diffusion equations are the starting point, and by considering perturbed evolutionary equations, global approximations are constructed. The lectures upon which this book is based were warmly received at the universities of Rome and Pavia, and at the Scuola Normale Superiore in Pisa. Here Professor Vishik has collated his lecture notes, and has added an appendix describing his work on attractors deriving from dynamical systems. This is unquestionably a fine addition to the Lezioni Lincee, and will be a necessary addition to the library of all who seek an insight into the solution of evolutionary equations.

This 1994 book is based on a series of six lectures delivered at the University of Sienna under the auspices of the Lezioni Lincee. The content of the book reflects and delineates the author's career in biochemical research. The lectures revolve around the special role which bound carbohydrates play in nature. Also discussed are the properties of membrane glycoproteins, involved in the resistance of cells to drugs. The metabolism of sugars and sialic acids, which form a pivotal role in the author's research, are covered in detail. The book chronicles just some of the huge advances which have been made in biochemistry over the past few decades and will prove an invaluable and entertaining first hand account for researchers and graduate students.

This book describes the experience over 25 years of the senior author with the chemistry of organic free radicals. It begins with a mechanistic study of industrial importance on the pyrolysis of chlorinated alkanes. It continues with a theory on the biosynthesis of phenolate derived alkaloids involving phenolate radical coupling. There follows 20 years of practical work to prove the theory correct, especially in the case of morphine alkaloids. The book then describes the work on nitrile photolysis (Barton reaction) which involved the invention of new radical chemistry leading to a simple synthesis of the important hormone, aldosterone. There follows a description of the invention of an important new method for the deoxygenation of biologically important molecules, especially sugars and nucleosides, using radical chemistry applied to thiocarbonyl derivatives. Some years later, in a logical extension to carboxylic acids, another new reaction was invented which provides carbon, nitrogen, oxygen and other radicals under mild conditions. A final chapter summarizes recent applications of thiocarbonyl group derived radical reactions by other authors.

This 1994 book is based on a series of six lectures delivered at the University of Sienna under the auspices of the Lezioni Lincee. The content of the book reflects and delineates the author's career in biochemical research. The lectures revolve around the special role which bound carbohydrates play in nature. Also discussed are the properties of membrane glycoproteins, involved in the resistance of cells to drugs. The metabolism of sugars and sialic acids, which form a pivotal role in the author's research, are covered in detail. The book chronicles just some of the huge advances which have been made in biochemistry over the past few decades and will prove an invaluable and entertaining first hand account for researchers and graduate students.

Understanding the role of neural activity in the development of the brain has been a major concern of many modern neurobiologists. The reason is plain enough: since the world influences the brain by means of action potentials and synaptic potentials, activity must be the chief cause of the neural changes wrought by experience. This 1994 volume explores the hypothesis that neural activity generated by experience modulates the ongoing growth of the brain during maturation, thus sculpting in each of us a unique nervous system according to the events of our early life. Brain growth is considered at a macroscopic level by examining brain maps and their modular substructure, and at a cellular level by investigating the neuronal interactions that influence the formation and maintenance of these structures. The ways that experience influences the maturation of the brain at both macroscopic and microscopic levels are described, and the conventional wisdom is re-examined.

In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more. It is in two parts, the first being devoted to the study of the asymptotic behaviour at infinity of solutions of a class of non-linear second order elliptic equations in unbounded, in particular cylindrical, domains. Questions of this type occur in many areas of mathematical physics, such as in the theory of travelling waves, homogenisation, boundary layer theory, flame propagation and combustion. The second part contains the most recent results of the author's research in the theory of homogenisation of partial differential equations, and is concerned with questions about partially perforated domains and of solutions with rapidly alternating types of boundary conditions. These asymptotic problems arise naturally in applications. Many of the results here have not appeared in book form before, and this volume sheds light on the subject, raising many ideas and open problems.

The twin themes of computational complexity and information pervade this 1998 book. It starts with an introduction to the computational complexity of continuous mathematical models, that is, information-based complexity. This is then used to illustrate a variety of topics, including breaking the curse of dimensionality, complexity of path integration, solvability of ill-posed problems, the value of information in computation, assigning values to mathematical hypotheses, and new, improved methods for mathematical finance. The style is informal, and the goals are exposition, insight and motivation. A comprehensive bibliography is provided, to which readers are referred for precise statements of results and their proofs. As the first introductory book on the subject it will be invaluable as a guide to the area for the many students and researchers whose disciplines, ranging from physics to finance, are influenced by the computational complexity of continuous problems.

In 1993, Professor Oleinik was invited to give a series of lectures about her work in the area of partial differential equations. This book contains those lectures, and more. It is in two parts, the first being devoted to the study of the asymptotic behaviour at infinity of solutions of a class of non-linear second order elliptic equations in unbounded, in particular cylindrical, domains. Questions of this type occur in many areas of mathematical physics, such as in the theory of travelling waves, homogenisation, boundary layer theory, flame propagation and combustion. The second part contains the most recent results of the author's research in the theory of homogenisation of partial differential equations, and is concerned with questions about partially perforated domains and of solutions with rapidly alternating types of boundary conditions. These asymptotic problems arise naturally in applications. Many of the results here have not appeared in book form before, and this volume sheds light on the subject, raising many ideas and open problems.

The purpose of this book is to present the three basic ideas of geometrical probability, also known as integral geometry, in their natural framework. In this way, the relationship between the subject and enumerative combinatorics is more transparent, and the analogies can be more productively understood. The first of the three ideas is invariant measures on polyconvex sets. The authors then prove the fundamental lemma of integral geometry, namely the kinematic formula. Finally the analogues between invariant measures and finite partially ordered sets are investigated, yielding insights into Hecke algebras, Schubert varieties and the quantum world, as viewed by mathematicians. Geometers and combinatorialists will find this a most stimulating and fruitful story.