Mirrors and Reflections is a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups.Key features: - Many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory - A large number of exercises at various levels of difficulty - Some Euclidean geometry is included along with the theory of convex polyhedra - Few prerequisites are necessary beyond linear algebra and the basic notions of group theory.The exposition is directed at advanced undergraduates and first-year graduate students.

Mirrors and Reflections: The Geometry of Finite and Affine Reflection Groups

Science & Math

Alexandre V. Borovik, UMIST

Anna S. Borovik, UMIST

Mathematics

Birkhauser Verlag AG

Herzog & de Meuron are one of the world s leading contemporary architectural offices. Landmark buildings such as the copper-clad Signal Box in Basel, the Goetz Collection Gallery in Munich, Student Housing for the University of Burgundy in Dijon, as well as master plans, urban studies and settlement designs for Basel, Sils and Dijon are among the 32 documented projects in Volume 2, covering the years 1989 to 1991.

Herzog and De Meuron: 1989-1991

Gerhard Mack

Unpublished Philosophical Essays

Kurt Gödel

Francisco A. Rodriguez-Consuegra

Kurt Gd̲el

This book systematically presents recent fundamental results on greedy approximation with respect to bases.
Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and does not require a broad background in the field.

Sparse Approximation With Bases

Vladimir Temlyakov

Top Swiss architects create a new urban topography for Switzerland.

Switzerland - An Urban Portrait: Introduction Vol. 1

Diener, Roger

This essential and comprehensive Mies monograph focuses in its analysis on Mies' design intentions: it reconstructs the buildings in their original state, examines them from the present day perspective and rediscovers the inspiring architecture of a great modern master. The book presents eighty of Mies' works in chronological order.

Mies van der Rohe - The Built Work

Krohn, Carsten

The MIT based SENSEable City Lab under Carlo Ratti is one of the research centers that deal with the flow of people and goods, but also of refuse that moves around the world. Experience with large-scale infrastructure projects suggest that more complex and above all flexible answers must be sought to questions of transportation or disposal. This edition, edited by Dietmar Offenhuber and Carlo Ratti, shows how Big Data change reality and, hence, the way we deal with the city. It discusses the impact of real-time data on architecture and urban planning, using examples developed in the SENSEable City Lab. They demonstrate how the Lab interprets digital data as material that can be used for the formulation of a different urban future. It also looks at the negative aspects of the city-related data acquisition and control. The authors address issues with which urban planning disciplines will work intensively in the future: questions that not only radically and critically review, but also change fundamentally, the existing tasks and how the professions view their own roles.

Decoding the City: Urbanism in the Age of Big Data

Arts & Photography

Dietmar Offenhuber

Carlo Ratti

Architecture

Architects and engineers are engaging more and more with the issue of movement in architecture: How can we control and reduce the energy requirement of buildings? How can we expand the range of possible uses? And how can we represent, accommodate, and control dynamic movements in buildings?

MOVE: Architecture in Motion - Dynamic Components and Elements

Unknown, Author

Mies van der Rohe. Continuing the Chicago School of Architecture (Exploration, 3)

Blaser, Werner

Business & Money

This study has two declared aims: it presents the theoretical basis for a provably ideal comparative process for relaxing flows (ICP) and jus tifies its application to jet and, in particular, rocket engines. This will be treated in two parts. Part I offers a status quo report on current calculation methods, and compiles and explains briefly the most important data on selected pro minent rocket engines. Starting from the phenomenology of the dynamical and physico-chemical conversion processes in the fuel-oxidizer fluid mixture and in the burned gases, the ideal thermodynamic comparative process is then derived - as a defined sequential change of states in the system. In order to render this comparative process readily under standable, it is first applied to an appropriate model gas using alge braic equations for all relevant parameters. This model gas undergoes energy conversion processes without forfeiting the simplicity of pre sentation typical of classical gas dynamics. Above all, examination of this model offers proof that it is generally impermissible to use, as is done in practice, the familiar isentropic equation for flow changes of state continuously propagated in flow tube theory. Elementary calculations immediately indicate essential attributes which are also typical for relaxing, multicomponent, one-phase systems, such as the significant 'pressure drop phenomenon' or the establishment of the steady mass flow rate as an 'eigenvalue' of the comparative pro cess. Their relevance to the RE theory is stressed.

Thermofluiddynamics of Optimized Rocket Propulsions: Extended Lewis Code Fundamentals

Dieter Straub

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