R. Narasimhan - Böcker

Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem.

The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincar� and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem.

Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.

The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.

This book studies language behaviour in the larger context of modelling or­ ganismic behaviour more generally. It starts out from the basic premise that what is characteristic of organismic behaviour is that an organism uses its behavioural acts to accomplish something in its interactions with the world in which it finds itself. These two features, that an organism has a behav­ ioural repertoire and that it deploys specific behavioural acts from its repertoire in an intentional way, define the agentive nature of an organism. The study of organismic behaviour, then, must primarily concern itself with this agentive aspect of an organism and determine what structures and proces­ ses underlie these intentional organismic acts. We should be able to say what primitive structures and what primitive processes put together in what ways can give rise to the kinds of behavioural acts an organism engages in. Any explanation of behaviour that we formulate in terms of underlying structures and processes must be testable and must be consonant with the observed pheno­ menological aspects of such behaviour.