In The Structure of Affine Buildings, 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. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss's The Structure of Spherical Buildings, The Structure of Affine Buildings is organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss's Moufang Polygons.
This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms.
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.
In The Structure of Affine Buildings, 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. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss's The Structure of Spherical Buildings, The Structure of Affine Buildings is organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss's Moufang Polygons.
Modern Surgical Pathology, 2nd Edition presents today's most complete, current, and practical assistance in evaluating and signing out surgical specimens. Nearly 3,000 high-quality color pathology images provide a crystal-clear basis for comparison to any sample you see under the microscope. Clinical, gross, microscopic, immunohistochemical, and molecular genetic features are integrated as appropriate for all tumors and tumor-like lesions, addressing all of the investigative contexts relevant to formulating an accurate diagnosis. Edited by four leading surgical pathologists - Noel Weidner, MD, Richard J. Cote, MD, Saul Suster, MD and Lawrence M. Weiss, MD - with contributions from more than 70 other experts, Modern Surgical Pathology, 2nd Edition delivers the well-rounded, well-organized, richly illustrated, user-friendly guidance you need to efficiently arrive at confident diagnoses for even the most challenging lesions. Contributions from many leading surgical pathologists give you well-rounded, expert answers to any question that you may face. Clinical, gross, microscopic, immunohistochemical, and molecular genetic features are correlated as appropriate for every type of surgical pathology specimen, addressing all of the investigative contexts relevant to formulating an accurate diagnosis and thereby ensuring a completely accurate surgical report. Nearly 3,000 brand-new, high-quality color pathology images provide a crystal-clear basis for comparison to any specimen you see under the microscope. A completely rewritten section on the female reproductive tract offers many more illustrations of common entities to help you more easily distinguish between tumors and tumor-like lesions. Expanded coverage of non-neoplastic diseases and disorders makes it easier to recognize benign conditions that can mimic malignancy. The latest classification schemes and criteria for malignancy, incorporated throughout, enable you to include the most current gradings in your reports. A new, more consistent organization explores anatomy/histology, gross and microscopic appearance, adjunct techniques, diagnosis, and differential diagnosis for each neoplastic or non-neoplastic lesion, facilitating rapid consultation in the reporting room. An increased number of differential diagnosis and classification tables expedite diagnosis.
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.
This book introduces a new class of non-associative algebras related to certain exceptional algebraic groups and their associated buildings. Richard Weiss develops a theory of these "quadrangular algebras" that opens the first purely algebraic approach to the exceptional Moufang quadrangles. These quadrangles include both those that arise as the spherical buildings associated to groups of type E6, E7, and E8 as well as the exotic quadrangles "of type F4" discovered earlier by Weiss. Based on their relationship to exceptional algebraic groups, quadrangular algebras belong in a series together with alternative and Jordan division algebras. Formally, the notion of a quadrangular algebra is derived from the notion of a pseudo-quadratic space (introduced by Jacques Tits in the study of classical groups) over a quaternion division ring. This book contains the complete classification of quadrangular algebras starting from first principles. It also shows how this classification can be made to yield the classification of exceptional Moufang quadrangles as a consequence. The book closes with a chapter on isotopes and the structure group of a quadrangular algebra. Quadrangular Algebras is intended for graduate students of mathematics as well as specialists in buildings, exceptional algebraic groups, and related algebraic structures including Jordan algebras and the algebraic theory of quadratic forms.
Descent in Buildings begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. The authors then put their algebraic solution into a geometric context by developing a general fixed point theory for groups acting on buildings of arbitrary type, giving necessary and sufficient conditions for the residues fixed by a group to form a kind of subbuilding or "form" of the original building. At the center of this theory is the notion of a Tits index, a combinatorial version of the notion of an index in the relative theory of algebraic groups. These results are combined at the end to show that every exceptional Bruhat-Tits building arises as a form of a "residually pseudo-split" Bruhat-Tits building. The book concludes with a display of the Tits indices associated with each of these exceptional forms. This is the third and final volume of a trilogy that began with Richard Weiss' The Structure of Spherical Buildings and The Structure of Affine Buildings.
The reference JAMA called "an outstanding contribution" and "must reading" is back in a fully revised New Edition! This 2-volume set presents cutting-edge discussions of scientific principles, pathogenesis, pathophys-iology, diagnosis, treatment, and prevention for the full range of tropical infectious diseases. A new bonus CD-ROM, a clinical-focused organization, standardized life-cycle diagrams, and 850 illustrations make vital guidance easy to find and apply
A behind-the-scenes expose of the Time Warner media conglomerate explains how the merger came about, profiles the personalities involved, and provides an eye-opening look at the deals, intrigues, and machinations.
This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division rings, quadratic Jordan division algebras of degree three, pseudo-quadratic forms, BN-pairs and norm splittings of quadratic forms. This book also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appendix, the connection between spherical buildings and algebraic groups is recalled.
This volume covers binary alloys and intermetallic compounds of uranium with transition metals of the Cu, Zn, Sc (including the lanthanides), and Ti groups as well as ternary alloys containing another transition metal as a third component. The compounds UCu5, UAu2, U14Au51, U2Zn17, UZn12, and UCd11 have been shown to be heavy-fermion materials exhibiting unusual behavior as far as the heat capacity and the magnetic and electrical properties at low temperatures are concerned. The alloys of uranium with titanium and zirconium and related ternary alloys are of technological interest. Thus emphasis in this volume is placed on recent scientific as well as technological work.
A look at the crimes of true-life fiends describes the gruesome doings of James Riva, Pete Kurten, Adolfo de Jesus Constanzo, Octavio Flores, Jeffrey Dahmer, and Ted Bundy." --Goodreads.
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