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Excerpt from Ergebnisse Einer Zoologischen Forschungsreise in den Südöstlichen Molukken (Aru-und Kei-Inseln), Vol. 1: Im Auftrag der Senckenbergischen Naturforschenden GesellschaftHerr Prof. Dr. Fritz Römer, der verstorbene hochverdiente Direktor des Sencken bergischen Museums, hat mir in umfassender Weise bei den Vorbereitungen für die Reise seine Hilfe geliehen und seiner reichen Erfahrung‚ seiner tatkräftigen Unterstützung habe ich es zuzuschreiben‚ wenn sich die Ausrüstung allen Anforderungen gewachsen zeigte. Ferner hat mich ein hervorragender Kenner des ostindischen Archipels, Herr Prof. Dr. Max Web er in Eerbeek aufs beste beraten und seinen wertvollen Empfehlungen haben wir viel zu verdanken; ebenso war Herr Dr. Fritz Sarasin in Basel' so freundlich, uns mit Rat und Tat zu unterstützen.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

The object of this book is a presentation of the major results relating to two geometrically inspired problems in analysis. One is that of determining which metric spaces can be isometrically embedded in a Hilbert space or, more generally, P in an L space; the other asks for conditions on a pair of metric spaces which will ensure that every contraction or every Lipschitz-Holder map from a subset of X into Y is extendable to a map of the same type from X into Y. The initial work on isometric embedding was begun by K. Menger [1928] with his metric investigations of Euclidean geometries and continued, in its analytical formulation, by I. J. Schoenberg [1935] in a series of papers of classical elegance. The problem of extending Lipschitz-Holder and contraction maps was first treated by E. J. McShane and M. D. Kirszbraun [1934]. Following a period of relative inactivity, attention was again drawn to these two problems by G. Minty's work on non-linear monotone operators in Hilbert space [1962]; by S. Schonbeck's fundamental work in characterizing those pairs (X,Y) of Banach spaces for which extension of contractions is always possible [1966]; and by the generalization of many of Schoenberg's embedding theorems to the P setting of L spaces by Bretagnolle, Dachuna Castelle and Krivine [1966].

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.  Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated.This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality.  Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.  Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated.This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality.  Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.

Since the elassie work on inequalities by HARDY, LITTLEWOOD, and P6LYA in 1934, an enonnous amount of effort has been devoted to the sharpening and extension of the elassieal inequalities, to the discovery of new types of inequalities, and to the application of inqualities in many parts of analysis. As examples, let us eite the fields of ordinary and partial differential equations, whieh are dominated by inequalities and variational prineiples involving functions and their derivatives; the many applications of linear inequalities to game theory and mathe­ matieal economics, which have triggered a renewed interest in con­ vexity and moment-space theory; and the growing uses of digital com­ puters, which have given impetus to a systematie study of error esti­ mates involving much sophisticated matrix theory and operator theory. The results presented in the following pages reflect to some extent these ramifications of inequalities into contiguous regions of analysis, but to a greater extent our concem is with inequalities in their native habitat. Since it is elearly impossible to give a connected account of the burst of analytic activity of the last twenty-five years centering about inequalities, we have d. eeided to limit our attention to those topies that have particularly delighted and intrigued us, and to the study of whieh we have contributed.

Der Computer hat sich an allgemeinbildenden Schulen - nicht nur in Nordrhein-Westfalen, sondern in fast allen Bundesländern - mit einer Geschwindigkeit durchgesetzt, die für Innovationen in diesem Bereich durchaus als außergewöhnliche bezeichnet werden kann. So ist es in der langjährigen Geschichte des Gymnasiums ein einmaliger Vorgang, daß ein Fach, das erst seit kurzem, seit der "Bonner Vereinbarung zur Neugesaltung der gymnasialen Oberstufe in der Sekundarstufe 11" der Kultusministerkonferenz vom Juli 1972 im Kanon der Obberstufenfächer erwähnt wird, nach einer nur kurzen Versuchs zeit innerhalb weniger Jahre nun einen respektab­ len Platz im Kreise der etalierten Fächer einnimmt. Macht man beispielsweise die Schüler zahlen und die erteilten Wochenstunden zum Maßstab, so hat das Fach Informatik in gut zehn Jahren eine Stellung erreicht, für die andere Fächer wie Physik und Chemie fast 100 Jahre benötigt haben. Die Phase des stürmischen Wachstums, die um 1981 begann, als die ersten Schulversuche abgeschlossen waren, die Richtlinien für das Fach vorlagen und preisgünstige Computer marktgängig wurden - was sicher ein sehr wesentlicher Faktor war -, dürfte für die Sekun­ darstufe 11 des Gymnasiums in den Jahren 1985 und 1986 ihren Höhepunkt erreicht haben. Diese Phase war gekennzeichnet durch vielfältige Aktivitäten, die sich im Effekt gegenseitig verstärk­ ten. Einige seien genannt: - Die informationstechnologische Bildung war zum Spitzenthema der bildungspolitischen Diskussion geworden. Kaum eine schulische oder erziehungswissenschaftliche Tagung verging, auf der nicht Lehrer, Eltern, Wissenschaftler oder Bildungspolitiker auf die besondere Herausforderung der Schulen durch die neuen Informa­ tionstechnologien hinwiesen.

A digital copy of "Ergebnisse der Namenforschung im deutsch-slawischen Ber?hrungsgebiet" by Ernst Eichler. Download is immediately available upon purchase!

Die von Karl Menger und seinen Mitarbeitern (darunter Kurt Gödel) herausgegebenen "Ergebnisse eines Mathematischen Kolloquiums" zählen zu den wichtigsten Quellenwerken der Wissenschafts- und Geistesgeschichte der Zwischenkriegszeit, mit bahnbrechenden Beiträgen von Menger, Gödel, Tarski, Wald, John von Neumann und vielen anderen. In diesem Band liegt der Inhalt erstmals gesammelt vor. Der Nobelpreisträger Gerard Debreu schrieb die Einleitung, die Kommentare wurden vom Logiker und Gödel-Biographen John Dawson jr., dem Topologen Ryszard Engelking und dem Wirtschaftstheoretiker Werner Hildenbrand verfasst. Außerdem enthält der Band einen biographischen Aufsatz über Karl Menger sowie einen von Menger verfassten Überblick über die wichtigsten topologischen und geometrischen Arbeiten des Kolloquiums.

A digital copy of "Ergebnisse Der Hygiene Bakteriologie Immunitatsforschung Und Experiment" by Weichardt. Download is immediately available upon purchase!

This text treats the Korteweg-de Vries (KdV) equation with periodic boundary conditions. This equation models waves in homogeneous, weakly nonlinear and weakly dispersive media in general. For the first time, these important results are comprehensively covered in book form, authored by internationally renowned experts in the field.

Die von Karl Menger und seinen Mitarbeitern (darunter Kurt Gödel) herausgegebenen "Ergebnisse eines Mathematischen Kolloquiums" zählen zu den wichtigsten Quellenwerken der Wissenschafts- und Geistesgeschichte der Zwischenkriegszeit, mit bahnbrechenden Beiträgen von Menger, Gödel, Tarski, Wald, John von Neumann und vielen anderen. In diesem Band liegt der Inhalt erstmals gesammelt vor. Der Nobelpreisträger Gerard Debreu schrieb die Einleitung, die Kommentare wurden vom Logiker und Gödel-Biographen John Dawson jr., dem Topologen Ryszard Engelking und dem Wirtschaftstheoretiker Werner Hildenbrand verfasst. Außerdem enthält der Band einen biographischen Aufsatz über Karl Menger sowie einen von Menger verfassten Überblick über die wichtigsten topologischen und geometrischen Arbeiten des Kolloquiums.

A digital copy of "Paradoxe Ergebnisse von Mehrheitsentscheidungen" by Wolfgang Gerß. Download is immediately available upon purchase!

In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepen­ ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, auto­ matic controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call" qualitative theory of differential equations". The purpose of the present volume is to present many of the view­ points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications.

This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con­ temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc­ tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.

IV, 258 pp. Sprache: Englisch Gewicht in Gramm: 400 8vo. Softcover, no dust jacket, copy from an official library with library signs and stamps / signatures, binding and paper browned, edges bumped, all in all fine.

This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan. It includes a fully updated bibliography of work in this area.

A digital copy of "Atlas der unerw?nschten Ergebnisse in der Chirurgie von Lippen-Kiefer-Gaumenspalten" by . Download is immediately available upon purchase!

A digital copy of "Ergebnisse Phanologischer Beobachtungen Im Deutschen Reich Im Jahre 193" by Unknown. Download is immediately available upon purchase!

A digital copy of "Ergebnisse Der Coaching-forschung" by Boning. Download is immediately available upon purchase!

384 S., 214 graph. Darst., 24 x 17 cm, gebunden Dieses markante Buch deutscher und amerikanischer Autoren setzt sich sowohl mit den traditionellen als auch den neuen Ansätzen des Operanten Lernens auseinander und bietet zahlreiche Informationen, die im deutschen Sprachraum bisher nur schwer zugänglich Sprache: Deutsch