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Seit der Entdeckung der Inselzellen des Pankreas durch LANGERHANS sind 106 Jahre, seit der experimentellen Erzeugung eines Diabetes durch v. MERING und MINKOWSKI 86 Jahre und seit der Gewinnung des Insulins aus tierischen Pankreata durch BANTING und BEST 54 Jahre vergangen. Trotzdem ist ein giiltiges Gesamtkonzept des Diabetes noch nicht gefunden. Atiologie und viele Fragen der Pathogenese bleiben weiterhin im Dunkeln. Unser Wissen iiber Klinik und Therapie, aber auch urn die einzelnen pathoge netischen Schritte bei der Entstehung der Krankheit hat sich dennoch auBeror dentlich vergroBert. Manche Probleme, die in der letzten Auflage nur angedeutet werden konnten, haben sich als weit schwieriger und komplizierter erwiesen, als man damals annehmen konnte. Mit dem schnell en Fortschritt und der An sammlung von Fakten kam es auch zu ganz neuen Problemstellungen. Nach einer Stagnation wahrend des zweiten Weltkrieges hat sich die Grund lagenforschung in den fiinfziger Jahren, angeregt durch die Moglichkeit des Nach weises extrem kleiner Insulinmengen im Blut, durch die Strukturanalyse des Insulinmolekiils und seine spatere Synthese und durch die Entdeckung der ora len Antidiabetika auBerordentlich entwickelt. Dies schlieBt eine genauere Kennt nis der B-Zelle, besonders durch elektronenmikroskopische Forschung, der Immunpathologie des Insulins, der Einwirkungsmoglichkeit des Insulins am Erfolgsorgan und des Sekretionsmodus des Insulins ein, weiterhin die Kenntnis anderer hormoneller Faktoren, den Ausbau un serer genetischen und epidernio logischen Vorstellungen sowie die Verbesserung der Methoden zur Erzeugung eines experimentellen Diabetes im Tierversuch.

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.In 10 chapters and one appendix, it provides a comprehensive treatment from abstract foundations to applications in physics and engineering. The focus is on non-self-adjoint problems. Bounded operators are associated to these problems, and Chapter 1 provides an in depth investigation of eigenfunctions and associated functions for bounded Fredholm valued operators in Banach spaces. Since every n-th order differential equation is equivalentto a first order system, the main techniques are developed for systems. Asymptotic fundamentalsystems are derived for a large class of systems of differential equations. Together with boundaryconditions, which may depend polynomially on the eigenvalue parameter, this leads to the definition of Birkhoff and Stone regular eigenvalue problems. An effort is made to make the conditions relatively easy verifiable; this is illustrated with several applications in chapter 10.The contour integral method and estimates of the resolvent are used to prove expansion theorems.For Stone regular problems, not all functions are expandable, and again relatively easy verifiableconditions are given, in terms of auxiliary boundary conditions, for functions to be expandable.Chapter 10 deals exclusively with applications; in nine sections, various concrete problems such asthe Orr-Sommerfeld equation, control of multiple beams, and an example from meteorology are investigated.Key features:• Expansion Theorems for Ordinary Differential Equations • Discusses Applications to Problems from Physics and Engineering • Thorough Investigation of Asymptotic Fundamental Matrices and Systems • Provides a Comprehensive Treatment • Uses the Contour Integral Method • Represents the Problems as Bounded Operators • Investigates Canonical Systems of Eigen- and Associated Vectors for Operator Functions

Following the first two volumes "Dendrimers" (TCC vol. 197) and "Dendrimers II" (TCC vol. 210), the third volume dealing with this topic is now appearing in print (the "tetralogy" on dendrimers will soon be completed with the fourth volume). The present volume comprises a collection of up-to-date reviews written by renowned pioneers of research in the dendrimer field, three of whom lectured at the 1. International Dendrimer Symposium (IDS-1 1999) in Frankfurt. A focus of this volume is the variety of material properties of soft and shape-persistent dendrimers. As its predecessors did, this volume breaks through the frontiers to neighboring disciplines and, in an interdisciplinary approach, addresses topics such as polydisperse, hyperbranched macromolecules (dendritic polymers), the analysis of shape and density by small-angle scattering techniques, finely dispersed metals (dendrimers as catalysts), and nanotechnology close to potential applications.

The book, based on a course of lectures by the authors at the Indian Institute of Technology, Guwahati, covers aspects of infinite permutation groups theory and some related model-theoretic constructions. There is basic background in both group theory and the necessary model theory, and the following topics are covered: transitivity and primitivity; symmetric groups and general linear groups; wreatch products; automorphism groups of various treelike objects; model-theoretic constructions for building structures with rich automorphism groups, the structure and classification of infinite primitive Jordan groups (surveyed); applications and open problems. With many examples and exercises, the book is intended primarily for a beginning graduate student in group theory.