Peter Gabriel – författare

Der heutige Hochschulunterricht für Mathematiker gründet meist auf Abstraktion und führt vom Allgemeinen zum Speziellen. Die Methode hat Vorteile, sie stärkt das Denkvermögen und meidet lästige Wiederholungen. Doch sie "stellt den Pflug vor die Ochsen", weil Abstraktion auf Spezialfälle baut, die dem Lernenden oft fremd sind. So bleibt der Erfolg den Glücklichen vorbehalten, die den Weg von der Abstraktion zu den Beispielen finden. Dieses Lehrbuch führt von zwei Spezialfällen zur Allgemeinheit und gründet nicht auf Abstraktion. Die Beweise der abstrakten Algebra werden zuerst am konkreten Beispiel der Matrizen vorgeführt. Zur Schärfung der Anschauung wird dann die Begriffswelt der Elementargeometrie durchleuchtet. Die Auseinandersetzung mit dem Lehrstoff der Schule dient der Vorbereitung auf die geometrisch gefärbte Sprache der linearen Algebra, die am Ende des Buches erläutert wird. Dem Text sind Anwendungsbeispiele und zahlreiche historische Kommentare beigefügt.

The monograph aims at a general outline of old and new results on representations of finite-dimensional algebras. In a theory which developed rapidly during the last two decades, the lack of textbooks is the main impediment for novices. Therefore special attention is paid to the foundations, and proofs are included for statements which are elementary, serve comprehension or are scarcely available. In this manner the authors try to lead the reader up to a point where he can find his way through the original literature. The discourse is centered around the fairly complete theory of finitely-represented posets and algebras. The monograph provides many examples and all the needed background on decomposition theorems, quivers, almost split sequences and derived categories. It includes a survey on representations of tame and wild quivers, lists of critical algebras and a proof of the old conjectures of Brauer and Thrall.

From the reviews: "...They (Gabriel and Roiter) are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature..." The Mathematical Gazette, 1993"...The standard of this text is high and will be definitely appreciated by the algebraic community." Monatshefte Mathematik, 1994"..This book is very welcome because it presents some basic material and at the same time it presents some new insights of the theory..." Zentralblatt fur Mathematik, 1996

RFID is a key technology for Europe. Today there is a noticeable shift away from the days of RFID pilot projects, and towards a time where organisations are looking to RFID to drive efficiency and innovation. Although Europe is a leading player in the world of RFID technology, several challenges which are preventing RFID from reaching its full potential need to be addressed.To further the advancement of this technology, coordinated European efforts need to be promoted, specifically in the areas of standardisation, user guidelines, legislation, technology development, and research and development. These themes have been analysed, and clear recommendations have been derived, stating what the different RFID stakeholders can do to support the technology. This book is aimed at decision makers in all fields of society, e.g. in companies, politics, business associations, etc.The publication is a summary of the results of the coordination action CE RFID - "Coordinating European Efforts in the RFID Value Chain" - and is a network of European RFID technology providers, vendors and end users. It aims at promoting the use of RFID technology and supporting further development. The project was funded by the European Commission under the 6th Framework Programme.

The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo­ topic category (IV). This category is, in fact, - according to Chapter VII and a well-known theorem of J. H. C. WHITEHEAD - equivalent to the category of CW-complexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CW-complex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods which have proved efficacious in homo­ logical algebra. Our category is thus the" topological" analogue of the derived category of an abelian category (VERDIER). The algebraic machinery upon which this work is essentially based includes the usual grounding in category theory - summarized in the Dictionary - and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category ,10 Iff of simplicial sets (C.S.S. complexes or semi-simplicial sets in a former terminology).

RFID is a key technology for Europe. Today there is a noticeable shift away from the days of RFID pilot projects, and towards a time where organisations are looking to RFID to drive efficiency and innovation. Although Europe is a leading player in the world of RFID technology, several challenges which are preventing RFID from reaching its full potential need to be addressed.To further the advancement of this technology, coordinated European efforts need to be promoted, specifically in the areas of standardisation, user guidelines, legislation, technology development, and research and development. These themes have been analysed, and clear recommendations have been derived, stating what the different RFID stakeholders can do to support the technology. This book is aimed at decision makers in all fields of society, e.g. in companies, politics, business associations, etc.The publication is a summary of the results of the coordination action CE RFID - "Coordinating European Efforts in the RFID Value Chain" - and is a network of European RFID technology providers, vendors and end users. It aims at promoting the use of RFID technology and supporting further development. The project was funded by the European Commission under the 6th Framework Programme.