Download or read book The Structure of Spherical Buildings written by Richard M. Weiss and published by Princeton University Press. This book was released on 2020-07-21 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and authoritative introduction to the theory of buildings, a topic of central importance to mathematicians interested in the geometric aspects of group theory. Its detailed presentation makes it suitable for graduate students as well as specialists. Richard Weiss begins with an introduction to Coxeter groups and goes on to present basic properties of arbitrary buildings before specializing to the spherical case. Buildings are described throughout in the language of graph theory. The Structure of Spherical Buildings includes a reworking of the proof of Jacques Tits's Theorem 4.1.2. upon which Tits's classification of thick irreducible spherical buildings of rank at least three is based. In fact, this is the first book to include a proof of this famous result since its original publication. Theorem 4.1.2 is followed by a systematic study of the structure of spherical buildings and their automorphism groups based on the Moufang property. Moufang buildings of rank two were recently classified by Tits and Weiss. The last chapter provides an overview of the classification of spherical buildings, one that reflects these and other important developments.

Download or read book The Structure of Spherical Buildings written by Richard M. Weiss and published by Princeton University Press. This book was released on 2003 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and authoritative introduction to the theory of buildings, a topic of central importance to mathematicians interested in the geometric aspects of group theory. Its detailed presentation makes it suitable for graduate students as well as specialists. Richard Weiss begins with an introduction to Coxeter groups and goes on to present basic properties of arbitrary buildings before specializing to the spherical case. Buildings are described throughout in the language of graph theory. The Structure of Spherical Buildings includes a reworking of the proof of Jacques Tits's Theorem 4.1.2. upon which Tits's classification of thick irreducible spherical buildings of rank at least three is based. In fact, this is the first book to include a proof of this famous result since its original publication. Theorem 4.1.2 is followed by a systematic study of the structure of spherical buildings and their automorphism groups based on the Moufang property. Moufang buildings of rank two were recently classified by Tits and Weiss. The last chapter provides an overview of the classification of spherical buildings, one that reflects these and other important developments.

Download or read book The Structure of Affine Buildings AM 168 written by Richard Mark Weiss and published by Princeton University Press. This book was released on 2009 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions and residues of these buildings.

Download or read book Buildings written by Kenneth S. Brown and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: For years I have heard about buildings and their applications to group theory. I finally decided to try to learn something about the subject by teaching a graduate course on it at Cornell University in Spring 1987. This book is based on the not es from that course. The course started from scratch and proceeded at a leisurely pace. The book therefore does not get very far. Indeed, the definition of the term "building" doesn't even appear until Chapter IV. My hope, however, is that the book gets far enough to enable the reader to tadle the literat ure on buildings, some of which can seem very forbidding. Most of the results in this book are due to J. Tits, who originated the the ory of buildings. The main exceptions are Chapter I (which presents some classical material), Chapter VI (which prcsents joint work of F. Bruhat and Tits), and Chapter VII (which surveys some applications, due to var ious people). It has been a pleasure studying Tits's work; I only hope my exposition does it justice.

Download or read book Buildings and Classical Groups written by Paul B. Garrett and published by CRC Press. This book was released on 1997-04-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Buildings are highly structured, geometric objects, primarily used in the finer study of the groups that act upon them. In Buildings and Classical Groups, the author develops the basic theory of buildings and BN-pairs, with a focus on the results needed to apply it to the representation theory of p-adic groups. In particular, he addresses spherical and affine buildings, and the "spherical building at infinity" attached to an affine building. He also covers in detail many otherwise apocryphal results. Classical matrix groups play a prominent role in this study, not only as vehicles to illustrate general results but as primary objects of interest. The author introduces and completely develops terminology and results relevant to classical groups. He also emphasizes the importance of the reflection, or Coxeter groups and develops from scratch everything about reflection groups needed for this study of buildings. In addressing the more elementary spherical constructions, the background pertaining to classical groups includes basic results about quadratic forms, alternating forms, and hermitian forms on vector spaces, plus a description of parabolic subgroups as stabilizers of flags of subspaces. The text then moves on to a detailed study of the subtler, less commonly treated affine case, where the background concerns p-adic numbers, more general discrete valuation rings, and lattices in vector spaces over ultrametric fields. Buildings and Classical Groups provides essential background material for specialists in several fields, particularly mathematicians interested in automorphic forms, representation theory, p-adic groups, number theory, algebraic groups, and Lie theory. No other available source provides such a complete and detailed treatment.

Download or read book Tits Buildings and the Model Theory of Groups written by Katrin Tent and published by Cambridge University Press. This book was released on 2002-01-03 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.

Download or read book Finiteness Properties of Arithmetic Groups Acting on Twin Buildings written by Stefan Witzel and published by Springer. This book was released on 2014-07-16 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an accessible approach to a special case of the Rank Theorem, the present text considers the exact finiteness properties of S-arithmetic subgroups of split reductive groups in positive characteristic when S contains only two places. While the proof of the general Rank Theorem uses an involved reduction theory due to Harder, by imposing the restrictions that the group is split and that S has only two places, one can instead make use of the theory of twin buildings.

Download or read book Experimental Vibration Analysis for Civil Structures written by Jian Zhang and published by CRC Press. This book was released on 2020-11-04 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experimental Vibration Analysis for Civil Structures: Testing, Sensing, Monitoring, and Control covers a wide range of topics in the areas of vibration testing, instrumentation, and analysis of civil engineering and critical infrastructure. It explains how recent research, development, and applications in experimental vibration analysis of civil engineering structures have progressed significantly due to advancements in the fields of sensor and testing technologies, instrumentation, data acquisition systems, computer technology, computational modeling and simulation of large and complex civil infrastructure systems. The book also examines how cutting-edge artificial intelligence and data analytics can be applied to infrastructure systems. Features: Explains how recent technological developments have resulted in addressing the challenge of designing more resilient infrastructure Examines numerous research studies conducted by leading scholars in the field of infrastructure systems and civil engineering Presents the most emergent fields of civil engineering design, such as data analytics and Artificial Intelligence for the analysis and performance assessment of infrastructure systems and their resilience Emphasizes the importance of an interdisciplinary approach to develop the modeling, analysis, and experimental tools for designing more resilient and intelligent infrastructures Appropriate for practicing engineers and upper-level students, Experimental Vibration Analysis for Civil Structures: Testing, Sensing, Monitoring, and Control serves as a strategic roadmap for further research in the field of vibration testing and instrumentation of infrastructure systems.

Download or read book Lectures on Buildings written by Mark Ronan and published by University of Chicago Press. This book was released on 2009-10-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematics, “buildings” are geometric structures that represent groups of Lie type over an arbitrary field. This concept is critical to physicists and mathematicians working in discrete mathematics, simple groups, and algebraic group theory, to name just a few areas. Almost twenty years after its original publication, Mark Ronan’s Lectures on Buildings remains one of the best introductory texts on the subject. A thorough, concise introduction to mathematical buildings, it contains problem sets and an excellent bibliography that will prove invaluable to students new to the field. Lectures on Buildings will find a grateful audience among those doing research or teaching courses on Lie-type groups, on finite groups, or on discrete groups. “Ronan’s account of the classification of affine buildings [is] both interesting and stimulating, and his book is highly recommended to those who already have some knowledge and enthusiasm for the theory of buildings.”—Bulletin of the London Mathematical Society

Download or read book Advances in Civil Structures written by Li Tian and published by Trans Tech Publications Ltd. This book was released on 2013-08-08 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt: Selected, peer reviewed papers from the 2013 International Conference on Civil, Architecture and Building Materials (3rd CEABM 2013), May 24-26, 2013, Jinan, China

Download or read book Groups and Analysis written by Katrin Tent and published by Cambridge University Press. This book was released on 2008-10-16 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many areas of mathematics were deeply influenced or even founded by Hermann Weyl, including geometric foundations of manifolds and physics, topological groups, Lie groups and representation theory, harmonic analysis and analytic number theory as well as foundations of mathematics. In this volume, leading experts present his lasting influence on current mathematics, often connecting Weyl's theorems with cutting edge research in dynamical systems, invariant theory, and partial differential equations. In a broad and accessible presentation, survey chapters describe the historical development of each area alongside up-to-the-minute results, focussing on the mathematical roots evident within Weyl's work.

Download or read book Global Differential Geometry written by Christian Bär and published by Springer Science & Business Media. This book was released on 2011-12-18 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.

Download or read book Steel and Composite Structures written by Y. C. Wang and published by Routledge. This book was released on 2018-05-08 with total page 1665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over 150 papers representing the most recent international research findings on steel and composite structures. Including steel constructions; buckling and stability; codes; composite; control; fatigue and fracture; fire; impact; joints; maintenance; plates and shells; retrofitting; seismic; space structures; steel; structural analysis; structural components and assemblies; thin-walled structures; vibrations, and wind. A special session is dedicated on codification. A valuable source of information to researchers and practitioners in the field of steel and composite structures.

Download or read book The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra written by Michael Kapovich and published by American Mathematical Soc.. This book was released on 2008 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the Saturation Conjecture for $GL(\ell)$ as a consequence of their solution of the corresponding saturation problem for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.

Download or read book Design of Seismic Isolated Structures written by Farzad Naeim and published by John Wiley & Sons. This book was released on 1999-03-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complete, practical coverage of the evaluation, analysis, and design and code requirements of seismic isolation systems. Based on the concept of reducing seismic demand rather than increasing the earthquake resistance capacity of structures, seismic isolation is a surprisingly simple approach to earthquake protection. However, proper application of this technology within complex seismic design code requirements is both complicated and difficult. Design of Seismic Isolated Structures provides complete, up-to-date coverage of seismic isolation, complete with a systematic development of concepts in theory and practical application supplemented by numerical examples. This book helps design professionals navigate and understand the ideas and procedures involved in the analysis, design, and development of specifications for seismic isolated structures. It also provides a framework for satisfying code requirements while retaining the favorable cost-effective and damage control aspects of this new technology. An indispensable resource for practicing and aspiring engineers and architects, Design of Seismic Isolated Structures includes: * Isolation system components. * Complete coverage of code provisions for seismic isolation. * Mechanical characteristics and modeling of isolators. * Buckling and stability of elastomeric isolators. * Examples of seismic isolation designs. * Specifications for the design, manufacture, and testing of isolation devices.

Download or read book A Sphere in Architecture and Astronomy written by Rune Jakobsen and published by BoD – Books on Demand. This book was released on 2012 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about architecture and astronomy and it combines disciplines from both fields. Astronomic objects can provide inspiration for architecture, and the science of construction and perspective in architecture can describe the processes that take place in the Universe.

Download or read book Homogeneous Spaces Tits Buildings and Isoparametric Hypersurfaces written by Linus Kramer and published by American Mathematical Soc.. This book was released on 2002 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title classifys 1-connected compact homogeneous spaces which have the same rational cohomology as a product of spheres $\mahtbb{S} DEGREES{n_1}\times\mathbb{S} DEGREES{n_2}$, with $3\leq n_1\leq n_2$ and $n_2$ odd. As an application, it classifys compact generalized quadrangles (buildings of type $C_2)$ which admit a point transitive automorphism group, and isoparametric hypersurfaces which admit a transitive isometry group on one f