Proceedings of the IVth French-German Encounter on Mathematics and Physics, CIRM, Marseille, France, February/March 1988

'Et moi, "'f si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point aile':' human race. It has put common sense back Jules Verne where it belongs, 011 the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be able to do something with it. Eric T. Bell o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non Iinearities 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'etre of this series_ This series, Mathematics and Its Applications, started in 1977. Now that over one hundred volumes have appeared it seems opportune to reexamine its scope. At the time I wrote ''Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches.

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White Noise and Stochastic Analysis.- Quelques Remarques sur le Cut-Locus sous-Riemannien.- Simulation on Random Graphs of the Epidemic Dynamics of Sexually Transmitted Diseases - A New Model for the Epidemiology of AIDS.- Sur une version à deux dimensions du modele de Ginzburg et Landau pour la supraconductivité.- Differential Calculus and Integration by Parts on Poisson Space.- to Entire Cyclic Cohomology (of Z/2-Graded Banach Algebras).- Stochastic Analysis, Mathematical Structures and Distributions Methods.- Ward Identities for Conformal Models.- Dynamical Systems in Plasma Theory.- Bosonic Strings and Measures on Infinite Dimensional Manifolds.- A Reaction-Diffusion Model for Moderately Interacting Particles.- Nondegeneracy in the Perturbation Theory of Integrable Dynamical Systems.- Energy Forms in Terms of White Noise.- Linear Stability and the Parameter Modulation Approach for Solitary Waves in Hamiltonian Systems with Symmetries.