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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.

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.

X 1 O S R Cher lecteur, J'entre bien tard dans la sphere etroite des ecrivains au double alphabet, moi qui, il y a plus de quarante ans deja, avais accueilli sur mes terres un general epris de mathematiques. JI m'avait parle de ses projets grandioses en promettant d'ailleurs de m'envoyer ses ouvrages de geometrie. Je suis entiche de geometrie et c'est d'elle dontje voudrais vous parler, oh! certes pas de toute la geometrie, mais de celle que fait l'artisan qui taille, burine, amene, gauchit, peaufine les formes. Mon interet pour le probleme dont je veux vous entretenir ici, je le dois a un ami ebeniste. En effet comme je rendais un jour visite il cet ami, je le trouvai dans son atelier affaire a un tour. Il se retourna bientot, puis, rayonnant, me tendit une sorte de toupie et me dit: «Monsieur Besse, vous qui calculez les formes avec vos grimoires, que pensez-vous de ceci?)) Je le regardai interloque. Il poursuivit: «Regardez! Si vous prenez ce collier de laine et si vous le maintenez fermement avec un doigt place n'importe ou sur la toupie, eh bien! la toupie passera toujours juste en son interieur, sans laisser le moindre espace.)) Je rentrai chez moi, fort etonne, car sa toupie etait loin d'etre une boule. Je me mis alors au travail ...

Mueller-beck, H., Ed.: Die Archäologischen Und Anthropologischen Ergebnisse Der Kohl-larsen-expeditionen in Nord-tanzania, 1933-1939. , 1983, 131 P.figuras, 830 Gr. Encuadernacion Original. Nuevo. (epa) 830 Gr.

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.

A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

Meisterwerke Aus Der Zeit Des Barocks U Der Bach / Euffonia Duo Wien - CD 4014513029171

Drawn from the Foreword: (...) On the other hand, since much of the material in this volume seems suitable for inclusion in elementary courses, it may not be superfluous to point out that it is almost entirely self-contained. Even the basic facts about trigonometric functions are treated ab initio in Ch. II, according to Eisenstein's method. It would have been both logical and convenient to treat the gamma -function similarly in Ch. VII; for the sake of brevity, this has not been done, and a knowledge of some elementary properties of T(s) has been assumed. One further prerequisite in Part II is Dirichlet's theorem on Fourier series, together with the method of Poisson summation which is only a special case of that theorem; in the case under consideration (essentially no more than the transformation formula for the theta-function) this presupposes the calculation of some classical integrals. (...) As to the final chapter, it concerns applications to number theory (...).

A new and complete treatment of semi-abelian degenerations of abelian varieties, and their application to the construction of arithmetic compactifications of Siegel moduli space, with most of the results being published for the first time. Highlights of the book include a classification of semi-abelian schemes, construction of the toroidal and the minimal compactification over the integers, heights for abelian varieties over number fields, and Eichler integrals in several variables, together with a new approach to Siegel modular forms. A valuable source of reference for researchers and graduate students interested in algebraic geometry, Shimura varieties or diophantine geometry.

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.

The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali- zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea- sure spaces. The category. Some of the flavor of the theory can be perceived in finite- dimensional linear algebra. Matrices are sometimes considered to be an un- natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something.

The book gives an account of handle theory in a piecewise-linear setting and could be the basis of a first year postgraduate lecture or reading course.

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.

Aus Der Bibliotheque Andreas Dorau - LP 4047179824514

127 pages. Light wear only to dust jacket.

Unread book in perfect condition.

Die Geburt der Tragödie (1872) is one of the most important philosophical texts of the modern period. Nietzsche describes how Greek tragedy was born out of the encounter between the Dionysian and the Apollonian and represents a culture in which a balance between the two was achieved. The Dionysian plunged Greek culture into chaos and despair but also paved the way for the regenerative power of Apollonian clarity and rationality. It is this model that Nietzsche employs to understand both the decline of modern culture and the possible rebirth of this culture. In genuine tragic art, the Dionysian and Apollonian elements are completely entwined. In the music of Richard Wagner, to whom the work is dedicated, Nietzsche sees a redemptive power that can overcome the intellectual dichtonomy between the Dionysian and the Apollonian that characterises modern society.

Publisher ID: BA5172 Urtext / Critical Edition

Ausreichend/Acceptable: Exemplar mit vollständigem Text und sämtlichen Abbildungen oder Karten. Schmutztitel oder Vorsatz können fehlen. Einband bzw. Schutzumschlag weisen unter Umständen starke Gebrauchsspuren auf. / Describes a book or dust jacket that has the complete text pages (including those with maps or plates) but may lack endpapers, half-title, etc. (which must be noted). Binding, dust jacket (if any), etc may also be worn.

Zust: Gutes Exemplar. Mit original Schutzumschlag. 378 Seiten, Deutsch 1000g