One service mathematics has rendered the ~l moil ..., Ii j'avait su comment en revenir, je n'y serais point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'(ftre of this series.

Contains the proceedings of a workshop on nonlinear hyperbolic equations held at Varenna, Italy in June 1990.

Written by two international experts in the field, this book is the first unified survey of the advances made in the last 15 years on key non-standard and improperly posed problems for partial differential equations.This reference for mathematicians, scientists, and engineers provides an overview of the methodology typically used to study improperly posed problems. It focuses on structural stability--the continuous dependence of solutions on the initial conditions and the modeling equations--and on problems for which data are only prescribed on part of the boundary. The book addresses continuous dependence on initial-time and spatial geometry and on modeling backward and forward in time. It covers non-standard or non-characteristic problems, such as the sideways problem for a heat or hyberbolic equation and the Cauchy problem for the Laplace equation and other elliptic equations. The text also presents other relevant improperly posed problems, including the uniqueness and continuous dependence for singular equations, the spatial decay in improperly posed parabolicproblems, the uniqueness for the backward in time Navier-Stokes equations on an unbounded domain, the improperly posed problems for dusty gases, the linear thermoelasticity, and the overcoming Holder continuity and image restoration. - Provides the first unified survey of the advances made in the last 15 years in the field - Includes an up-to-date compendium of the mathematical literature on these topics

Provides a novel treatment of many problems in controlled Markov chains based on occupation measures and convex analysis. Includes a rederivation of many classical results, a general treatment of the ergodic control problems and an extensive study of the asymptotic behavior of the self-tuning adaptive controller and its variant, the Kumar-Becker-Lin scheme. Also includes a novel treatment of some multiobjective control problems, inaccessible to traditional methods. Annotation copyrighted by Book News, Inc., Portland, OR

These notes present a rigorous mathematical formulation of quantum mechanics based on the algebraic framework of observables and states. The underlying mathematics is that of topological algebras, locally convex spaces and distribution theory.