Jacques Simon - Böcker

This timely and fascinating book is destined to be recognised as THE book on supramolecular engineering protocols. It covers this sometimes difficult subject in an approachable form, gathering together information from many sources. Supramolecular chemistry, which links organic chemistry to materials science, is one of the fastest growth areas of chemistry research. This book creates a correlation between the structure of single molecules and the physical and chemical properties of the resulting materials. By making systematic changes to the component molecules, the resulting solid can be engineered for optimum performance. There is a clearly written development from synthesis of designer molecules to properties of solids and further on to devices and complex materials systems, providing guidelines for mastering the organisation of these systems. Topics covered include:* Systemic chemistry * Molecular assemblies * Notions of symmetry * Supramolecular engineering * Principe de Curie * Organisation in molecular media * Molecular semiconductors * Industrial applications of molecular materialsThis superb book will be invaluable to researchers in the field of supramolecular materials and also to students and teachers of the subject.

This book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics.Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fréchet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces.The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces.Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers without restricting or generalizing the results.

This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics. It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space. The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers, without restricting or generalizing the results.

This book presents a simple and novel theory of integration, both real and vectorial, particularly suitable for the study of PDEs. This theory allows for integration with values in a Neumann space E, i.e. in which all Cauchy sequences converge, encompassing Neumann and Fréchet spaces, as well as "weak" spaces and distribution spaces.We integrate "integrable measures", which are equivalent to "classes of integrable functions which are a.e. equals" when E is a Fréchet space. More precisely, we associate the measure f with a class f, where f(u) is the integral of fu for any test function u. The classic space Lp(Ω;E) is the set of f, and ours is the set of f; these two spaces are isomorphic.Integration studies, in detail, for any Neumann space E, the properties of the integral and of Lp(Ω;E): regularization, image by a linear or multilinear application, change of variable, separation of multiple variables, compacts and duals. When E is a Fréchet space, we study the equivalence of the two definitions and the properties related to dominated convergence.

This book presents a simple and original theory of distributions, both real and vector, adapted to the study of partial differential equations. It deals with value distributions in a Neumann space, that is, in which any Cauchy suite converges, which encompasses the Banach and Fréchet spaces and the same “weak” spaces. Alongside the usual operations – derivation, product, variable change, variable separation, restriction, extension and regularization – Distributions presents a new operation: weighting.This operation produces properties similar to those of convolution for distributions defined in any open space. Emphasis is placed on the extraction of convergent sub-sequences, the existence and study of primitives and the representation by gradient or by derivatives of continuous functions. Constructive methods are used to make these tools accessible to students and engineers.

The present proceedings volume is devoted to two subjects. Stabilization with emphasis on exact controllability: considering a physical system, such as a vibrating plate, one can reach a steady state in a finite time by acting on the boundary. Control of boundaries: given a physical system find the geometry of the domain (optimal shape) which minimizes a cost related to the solution of a boundary value problem in this domain, for example find a minimum drag profile. Many lectures included mathematical analysis as well as engineering applications and numerical simulation.