Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applica.
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Serie: U-Line Baugruppentyp: Erweiterte Steuereinheit Bereich: TeSys Leistung: 0,09 kW Steuerspannung: 24 V dc Strombereich: 0,15 → 0,6 A Für den Einsatz mit einer Basisstation mit der relevanten Kapazität. Erweiterte Steuerungseinheiten, 3 Phasen, Klasse 10. Erforderlich für jedes Basisstationsmodul, wird in den Sockel gesteckt. Auswahl von Steuerspannung, Motorleistung und Klasse. Bietet Schutz für Motoren vor Überlastung, Kurzschluss, Phasenausfall und Phasenasymmetrie. Testschalter.
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Learn to design and create video games using the Java programming language and the LibGDX software library. Working through the examples in this book, you will create 12 game prototypes in a variety of popular genres, from collection-based and shoot-em-up arcade games to side-scrolling platformers and sword-fighting adventure games. With the flexibility provided by LibGDX, specialized genres such as card games, rhythm games, and visual novels are also covered in this book. Major updates in this edition include chapters covering advanced topics such as alternative sources of user input, procedural content generation, and advanced graphics. Appendices containing examples for game design documentation and a complete JavaDoc style listing of the extension classes developed in the book have also been added. What You Will Learn: Create 12 complete video game projects Master advanced Java progr.
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