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Held during algebraic topology special sessions at the Vietnam Institute for Advanced Studies in Mathematics (VIASM, Hanoi), this set of notes consists of expanded versions of three courses given by G. Ginot, H.-W. Henn and G. Powell. They are all introductory texts and can be used by PhD students and experts in the field.   Among the three contributions, two concern stable homotopy of spheres: Henn focusses on the chromatic point of view, the Morava K(n)-localization and the cohomology of the Morava stabilizer groups. Powell’s chapter is concerned with the derived functors of the destabilization and iterated loop functors and provides a small complex to compute them. Indications are given for the odd prime case.   Providing an introduction to some aspects of string and brane topology, Ginot’s contribution focusses on Hochschild homology and its generalizations. It contains a number of new results and fills a gap in the literature. .

Mathematics. --- Category theory (Mathematics). --- Homological algebra. --- Algebraic topology. --- Algebraic Topology. --- Category Theory, Homological Algebra. --- Homological algebra --- Algebra, Abstract --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Logic, Symbolic and mathematical --- Topology --- Functor theory --- Math --- Science --- Algebra. --- Mathematics --- Mathematical analysis

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Lubrication and lubricants. --- Hydrodynamics. --- Bearings (Machinery). --- Differential equations, Partial. --- Electronic data processing --- Girders. --- Structures, Theory of.

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This book investigates the coordinated power management of multi-tenant data centers that account for a large portion of the data center industry. The authors include discussion of their quick growth and their electricity consumption, which has huge economic and environmental impacts. This book covers the various coordinated management solutions in the existing literature focusing on efficiency, sustainability, and demand response aspects. First, the authors provide a background on the multi-tenant data center covering the stake holders, components, power infrastructure, and energy usage. Then, each power management mechanism is described in terms of motivation, problem formulation, challenges and solution.

Engineering. --- Computer communication systems. --- Data structures (Computer science). --- Electrical engineering. --- Power electronics. --- Communications Engineering, Networks. --- Power Electronics, Electrical Machines and Networks. --- Data Structures. --- Computer Communication Networks. --- Information Systems Applications (incl. Internet). --- Data protection --- Standards. --- Data governance --- Data regulation --- Personal data protection --- Protection, Data --- Electronic data processing --- Telecommunication. --- Production of electric energy or. --- Data structures (Computer scienc. --- Application software. --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Communication systems, Computer --- Computer communication systems --- Data networks, Computer --- ECNs (Electronic communication networks) --- Electronic communication networks --- Networks, Computer --- Teleprocessing networks --- Data transmission systems --- Digital communications --- Electronic systems --- Information networks --- Telecommunication --- Cyberinfrastructure --- Network computers --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science) --- Electronics, Power --- Electric power --- Electronics --- Electric engineering --- Engineering --- Distributed processing