Symfony Profiler

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POST	Search
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Und die Autorenbiographie von Jakob Weiss wirft einen neuen Blick auf den bedeutenden Wissenschaftler Richard Weiss.</p>" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 5 "Text" => "<ul><li>Die «Bibel» der Schweizer Bauernhausforschung in bibliophiler Neuauflage. </li><li>Alle Haustypen der Schweiz ausführlich beschrieben und reich bebildert. </li><li>Mit einem Geleitwort von Jean-Pierre Anderegg.</li></ul>" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 13 "Text" => "<p>$$Weiss, Richard\|Richard Weiss$$<br>Richard Weiss (1907–1962) war ein Schweizer Volkskundler und Professor für Volkskunde in Zürich von 1946 bis 1962.<br><br>$$Egli, Hans\|Hans Egli$$<br></p>" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 14 "Text" => "«Weiss‘ Standardwerk ist nicht nur eine ernsthafte Heimatkunde, sondern auch ein zeitloser Kompass für den Umgang mit dem Wandel.»<br>NZZ<br><br>«Das Buch war ein Wurf, es ist eine Entdeckung für uns Nachgeborene. Für die Landschaft Bewanderten, für die in Architektur Engagierten und für die in Planung Verstrickten. Eine kleine Umfrage zeigt: Sie kennen Richard Weiss nicht. Ich sage: «Ändert das.».»<br>Hochparterre<br><br>«Erstmals 1959 veröffentlicht und letztes Jahr vom Haupt-Verlag neu aufgelegt, ist dieses Standardwerk heute wichtiger denn je. Zu schauen, wie unsere Vorfahren gebaut oder das Land bewirtschaftet haben, kann uns helfen, besser zu planen, zu bauen und schliesslich zu leben. Heimatkunde ist nicht nur wichtig mit Bezug auf die Vergangenheit, sondern auch für die Zukunft.»<br>NZZ Bellevue<br><br>«Das neu aufgelegte Standardwerk von Richard Weiss ist auch fast 60 Jahre nach Erscheinen noch lesenswert. 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Chamber Systems 1 Chapter 2. Coxeter Groups 9 Chapter 3. Roots 17 Chapter 4. Reduced Words 27 Chapter 5. Opposites 33 Chapter 6. 2-Interiors 41 Chapter 7. Buildings 47 Chapter 8. Apartments 61 Chapter 9. Spherical Buildings 73 Chapter 10. Extensions of Isometries 81 Chapter 11. The Moufang Property 91 Chapter 12. Root Group Labelings 117 References 131 Index 133" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 14 "Text" => "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 t" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 13 "Text" => "Richard M. Weiss" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 16 "Text" => ""Richard M. Weiss's book is an extremely valuable addition to the literature."---Kenneth S. Brown, Bulletin of the American Mathematical Society" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 10 "Text" => "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. 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(The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as "thick," "residue," "rank," "spherical," etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive rela tive rank £ is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs [101] is that the converse, for £ ::::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three." ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 4 "Text" => "I Preliminary Results.- 1 Introduction.- 2 Some Definitions.- 3 Generalized Polygons.- 4 Moufang Polygons.- 5 Commutator Relations.- 6 Opposite Root Groups.- 7 A Uniqueness Lemma.- 8 A Construction.- II Nine Families of Moufang Polygons.- 9 Alternative Division Rings, I.- 10 Indifferent and Octagonal Sets.- 11 Involutory Sets and Pseudo-Quadratic Forms.- 12 Quadratic Forms of Type E6, E7 and E8, I.- 13 Quadratic Forms of Type E6, E7 and E8, II.- 14 Quadratic Forms of Type F4.- 15 Hexagonal Systems, I.- 16 An Inventory of Moufang Polygons.- 17 Main Results.- III The Classification of Moufang Polygons.- 18 A Bound on n.- 19 Triangles.- 20 Alternative Division Rings, II.- 21 Quadrangles.- 22 Quadrangles of Involution Type.- 23 Quadrangles of Quadratic Form Type.- 24 Quadrangles of Indifferent Type.- 25 Quadrangles of Pseudo-Quadratic Form Type, I.- 26 Quadrangles of Pseudo-Quadratic Form Type, II.- 27 Quadrangles of Type E6, E7 and E8.- 28 Quadrangles of Type F4.- 29 Hexagons.- 30 Hexagonal Systems, II.- 31 Octagons.- 32 Existence.- IV More Results on Moufang Polygons.- 33 BN-Pairs.- 34 Finite Moufang Polygons.- 35 Isotopes.- 36 Isomorphic Hexagonal Systems.- 37 Automorphisms.- 38 Isomorphic Quadrangles.- V Moufang Polygons and Spherical Buildings.- 39 Chamber Systems.- 40 Spherical Buildings.- 41 Classical, Algebraic and Mixed Buildings.- 42 Appendix.- Index of Notation." ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 0 "Text" => "From the reviews:"In this excellently written book, the authors give a full classification for Moufang polygons. … The book is self contained … . the content of the book is accessible for motivated graduate students and researchers from every branch of mathematics. We recommend this book for everybody who is interested in the developments of the modern algebra, geometry or combinatorics." (Gábor P. Nagy, Acta Scientiarum Mathematicarum, Vol. 71, 2005)"The publication of this long-awaited book is a major event for geometry in general, and for the theory of buildings in particular. … The classifications established in this book are splendid achievements of fundamental significance. The whole book is extremely well written, in a clear and concise style … . It is the definitive treatment and a standard reference." (Theo Grundhöfer, Mathematical Reviews, Issue 2003 m)"This book contains the complete classification of all Moufang generalized polygons, including the full proof. … So, in conclusion, the book is a Bible for everyone interested in classification results related to spherical buildings. It is written in a very clear and concise way. It should be in the library of every mathematician as one of the major results in the theory of (Tits) buildings, (combinatorial) incidence geometry and (algebraic) group theory." (Hendrik Van Maldeghem, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2005)" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 14 "Text" => "Gives a complete classification of Moufang polygons, starting from first principles Includes a totally new classification of the spherical buildings of rank 3 at least J. Tits is one of the best and most influential algebraists of the past 50 years R. Weiss is one of the world's leading researchers in the field of combinatorial group theory The book will become a classic in the field" ] ] ] "Prices" => [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaPrices, eurosoft.esMetaCatalog.esMetaData" "$values" => [ [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaPrice, eurosoft.esMetaCatalog.esMetaData" "PriceType" => [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaPriceType, eurosoft.esMetaCatalog.esMetaData" "PriceType" => 4 "IsFixedPrice" => false "PriceTypeDescription" => null ] "Currency_ISO4217" => "CHF" "ValidForCountry_ISO3166_1" => "CH" "Value" => 136.0 "PriceUnit" => 1.0 "PriceName" => null "PriceHint" => "Formel: PREIS+1" "TaxPercent" => 0.0 "TaxType" => 1 "ValidFrom" => "0001-01-01T00:00:00" "ValidTo" => "0001-01-01T00:00:00" "UnitPriceText" => null "PriceParts" => [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaPriceParts, eurosoft.esMetaCatalog.esMetaData" "$values" => [] ] "PriceBoardEntries" => [ 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(The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as "thick," "residue," "rank," "spherical," etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive rela tive rank £ is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs [101] is that the converse, for £ ::::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three." ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 4 "Text" => "I Preliminary Results.- 1 Introduction.- 2 Some Definitions.- 3 Generalized Polygons.- 4 Moufang Polygons.- 5 Commutator Relations.- 6 Opposite Root Groups.- 7 A Uniqueness Lemma.- 8 A Construction.- II Nine Families of Moufang Polygons.- 9 Alternative Division Rings, I.- 10 Indifferent and Octagonal Sets.- 11 Involutory Sets and Pseudo-Quadratic Forms.- 12 Quadratic Forms of Type E6, E7 and E8, I.- 13 Quadratic Forms of Type E6, E7 and E8, II.- 14 Quadratic Forms of Type F4.- 15 Hexagonal Systems, I.- 16 An Inventory of Moufang Polygons.- 17 Main Results.- III The Classification of Moufang Polygons.- 18 A Bound on n.- 19 Triangles.- 20 Alternative Division Rings, II.- 21 Quadrangles.- 22 Quadrangles of Involution Type.- 23 Quadrangles of Quadratic Form Type.- 24 Quadrangles of Indifferent Type.- 25 Quadrangles of Pseudo-Quadratic Form Type, I.- 26 Quadrangles of Pseudo-Quadratic Form Type, II.- 27 Quadrangles of Type E6, E7 and E8.- 28 Quadrangles of Type F4.- 29 Hexagons.- 30 Hexagonal Systems, II.- 31 Octagons.- 32 Existence.- IV More Results on Moufang Polygons.- 33 BN-Pairs.- 34 Finite Moufang Polygons.- 35 Isotopes.- 36 Isomorphic Hexagonal Systems.- 37 Automorphisms.- 38 Isomorphic Quadrangles.- V Moufang Polygons and Spherical Buildings.- 39 Chamber Systems.- 40 Spherical Buildings.- 41 Classical, Algebraic and Mixed Buildings.- 42 Appendix.- Index of Notation." ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 0 "Text" => "From the reviews:"In this excellently written book, the authors give a full classification for Moufang polygons. … The book is self contained … . the content of the book is accessible for motivated graduate students and researchers from every branch of mathematics. We recommend this book for everybody who is interested in the developments of the modern algebra, geometry or combinatorics." (Gábor P. Nagy, Acta Scientiarum Mathematicarum, Vol. 71, 2005)"The publication of this long-awaited book is a major event for geometry in general, and for the theory of buildings in particular. … The classifications established in this book are splendid achievements of fundamental significance. The whole book is extremely well written, in a clear and concise style … . It is the definitive treatment and a standard reference." (Theo Grundhöfer, Mathematical Reviews, Issue 2003 m)"This book contains the complete classification of all Moufang generalized polygons, including the full proof. … So, in conclusion, the book is a Bible for everyone interested in classification results related to spherical buildings. It is written in a very clear and concise way. It should be in the library of every mathematician as one of the major results in the theory of (Tits) buildings, (combinatorial) incidence geometry and (algebraic) group theory." (Hendrik Van Maldeghem, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2005)" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 14 "Text" => "Gives a complete classification of Moufang polygons, starting from first principles Includes a totally new classification of the spherical buildings of rank 3 at least J. Tits is one of the best and most influential algebraists of the past 50 years R. Weiss is one of the world's leading researchers in the field of combinatorial group theory The book will become a classic in the field" ] ] ] "Prices" => [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaPrices, eurosoft.esMetaCatalog.esMetaData" "$values" => [ [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaPrice, eurosoft.esMetaCatalog.esMetaData" "PriceType" => [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaPriceType, eurosoft.esMetaCatalog.esMetaData" "PriceType" => 4 "IsFixedPrice" => false "PriceTypeDescription" => null ] "Currency_ISO4217" => "CHF" "ValidForCountry_ISO3166_1" => "CH" "Value" => 136.0 "PriceUnit" => 1.0 "PriceName" => null "PriceHint" => "Formel: PREIS+1" "TaxPercent" => 0.0 "TaxType" => 1 "ValidFrom" => "0001-01-01T00:00:00" "ValidTo" => "0001-01-01T00:00:00" "UnitPriceText" => null "PriceParts" => [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaPriceParts, eurosoft.esMetaCatalog.esMetaData" "$values" => [] ] "PriceBoardEntries" => [ 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The structures and modes of formation of the self-assembled fibrillar networks (SAFINs) that immobilize the liquid components of the gels are discussed experimentally and theoretically. The spectroscopic, rheological, and structural features of the different classes of low molecular-mass gelators are also presented. Many examples of the application of the principal analytical techniques for investigation of molecular gels (including SANS, SAXS, WAXS, UV-vis absorption, fluorescence and CD spectroscopies, scanning electron, transmission electron and optical microscopies, and molecular modeling) are presented didactically and in-depth, as are several of the theories of the stages of aggregation of individual low molecular-mass gelator molecules leading to SAFINs. Several actual and potential applications of molecular gels in disparate fields (from silicate replication of nanostructures to art conservation) are described. Special emphasis is placed on perspectives for future developments.This book is an invaluable resource for researchers and practitioners either already researching self-assembly and soft matter or new to the area. 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Phase Induced by the Proliferation of Topological Defects.- Applications.- Gels of Liquid Crystals and Ion-Conducting Fluids.- Electron Conducting and Magneto-Sensitive Gels.- Photoresponsive Gels.- Gels of Low Molecular-Mass Organic Gelators as Templates for Transcription.- Responsive Molecular Gels.- Gels as Cleaning Agents in Cultural Heritage Conservation." ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 0 "Text" => "Richard G. Weiss is Professor of Chemistry, Department of Chemistry, Georgetown University, Washington, DC, USA. 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The structures and modes of formation of the self-assembled fibrillar networks (SAFINs) that immobilize the liquid components of the gels are discussed experimentally and theoretically. The spectroscopic, rheological, and structural features of the different classes of low molecular-mass gelators are also presented. Many examples of the application of the principal analytical techniques for investigation of molecular gels (including SANS, SAXS, WAXS, UV-vis absorption, fluorescence and CD spectroscopies, scanning electron, transmission electron and optical microscopies, and molecular modeling) are presented didactically and in-depth, as are several of the theories of the stages of aggregation of individual low molecular-mass gelator molecules leading to SAFINs. Several actual and potential applications of molecular gels in disparate fields (from silicate replication of nanostructures to art conservation) are described. Special emphasis is placed on perspectives for future developments.This book is an invaluable resource for researchers and practitioners either already researching self-assembly and soft matter or new to the area. Those who will find the book useful include chemists, engineers, spectroscopists, physicists, biologists, theoreticians, and materials scientists." ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 4 "Text" => "Materials-Chirality.- Theory.- Theory of Molecular Association and Thermoreversible Gelation.- Growth and Chirality amplification in Helical Supramolecular Polymers.- Self-Assembling Peptide Gels.- Kinetics of Nucleation, Aggregation and Ageing.- Soft Glassy Rheology.- Rheological Chaos in Wormlike Micelles and Nematic Hydrodynamics.- Wetting of Fibers.- Techniques.- Gel Formation: Phase Diagrams Using Tabletop Rheology and Calorimetry.- Direct-Imaging and Freeze-Fracture Cryo-Transmission Electron Microscopy of Molecular Gels.- Molecular Gels and Small-Angle Scattering.- X-Ray Diffraction of Poorly Organized Systems and Molecular Gels.- Optical Spectroscopic Methods as Tools to Investigate Gel Structures.- Circular Dichroism for Studying Gel-Like Phases.- Systems — Organogels.- Low Molecular-Mass Organic Gelators.- Design and Function of Low Molecular-Mass Organic Gelators (LMOGs) Bearing Steroid and Sugar Groups.- Safin Gels with Amphiphilic Molecules.- Systems — Hydrogels.- Advances in Molecular Hydrogels.- Aqueous Gels Made of Chiral Lipid- and Porphyrin-Amphiphiles.- Analyses of Specific Systems.- Rheology of Wormlike Micelles: Equilibrium Properties and Shear Banding Transitions.- Cryo-Tem, X-Ray Diffraction and Modeling of an Organic Hydrogel.- Gelation of a Liquid-Crystalline L? Phase Induced by the Proliferation of Topological Defects.- Applications.- Gels of Liquid Crystals and Ion-Conducting Fluids.- Electron Conducting and Magneto-Sensitive Gels.- Photoresponsive Gels.- Gels of Low Molecular-Mass Organic Gelators as Templates for Transcription.- Responsive Molecular Gels.- Gels as Cleaning Agents in Cultural Heritage Conservation." ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaText, eurosoft.esMetaCatalog.esMetaData" "TextType" => 0 "Text" => "Richard G. Weiss is Professor of Chemistry, Department of Chemistry, Georgetown University, Washington, DC, USA. 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After a first hype, evoked by the fascinating options of this method, clinical studies did not reach the ambitious aims and a phase of disillusion ensued. It became obvious that Gene vaccines displayed a weaker immunogenicity in humans than had been observed in the mouse models. Meanwhile these hurdles have been overcome and gene vaccines undergo a renaissance. The present book gives an update of the “world of naked gene vaccines”, namely DNA and RNA vaccines. Its content ranges from general mechanisms, inherent immunostimulatory properties and the vast potential to modulate immune responses, to recent successful clinical studies and approved veterinary gene vaccines. 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After a first hype, evoked by the fascinating options of this method, clinical studies did not reach the ambitious aims and a phase of disillusion ensued. It became obvious that Gene vaccines displayed a weaker immunogenicity in humans than had been observed in the mouse models. Meanwhile these hurdles have been overcome and gene vaccines undergo a renaissance. The present book gives an update of the “world of naked gene vaccines”, namely DNA and RNA vaccines. Its content ranges from general mechanisms, inherent immunostimulatory properties and the vast potential to modulate immune responses, to recent successful clinical studies and approved veterinary gene vaccines. 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"AdditionalInfo" => null "Content" => "Additive group" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Substructure" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Residue field" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Theorem" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Scientific notation" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Diagram (category theory)" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Purely inseparable extension" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Equivalence class" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Dimension (vector space)" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Algebraic structure" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Composition algebra" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "cardinality" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "special case" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Surjective function" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Algebraic Geometry" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "mathematical induction" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Subring" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Module (mathematics)" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Linear subspace" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Permutation" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "splitting field" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Linear combination" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Biquaternion" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Vector space" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Euclidean Space" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Coset" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Hyperbolic Geometry" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Quaternion algebra" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Unit sphere" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Local field" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Summation" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Dynkin diagram" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Linear space (geometry)" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Algebraically closed field" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Moufang polygon" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Separable extension" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Homomorphism" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Linear Map" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Field extension" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Projective space" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Convex hull" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Finite set" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Galois group" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 "AdditionalInfo" => null "Content" => "Affine transformation" ] [ "$type" => "eurosoft.esMetaCatalog.esMetaData.esMetaProperty, eurosoft.esMetaCatalog.esMetaData" "PropertyType" => 21 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                "Text" => "Spherical buildings are certain combinatorial simplicial complexes intro duced, at first in the language of "incidence geometries," to provide a sys tematic geometric interpretation of the exceptional complex Lie groups. (The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as "thick," "residue," "rank," "spherical," etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive rela tive rank £ is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs [101] is that the converse, for £ ::::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three."
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                "Text" => "I Preliminary Results.- 1 Introduction.- 2 Some Definitions.- 3 Generalized Polygons.- 4 Moufang Polygons.- 5 Commutator Relations.- 6 Opposite Root Groups.- 7 A Uniqueness Lemma.- 8 A Construction.- II Nine Families of Moufang Polygons.- 9 Alternative Division Rings, I.- 10 Indifferent and Octagonal Sets.- 11 Involutory Sets and Pseudo-Quadratic Forms.- 12 Quadratic Forms of Type E6, E7 and E8, I.- 13 Quadratic Forms of Type E6, E7 and E8, II.- 14 Quadratic Forms of Type F4.- 15 Hexagonal Systems, I.- 16 An Inventory of Moufang Polygons.- 17 Main Results.- III The Classification of Moufang Polygons.- 18 A Bound on n.- 19 Triangles.- 20 Alternative Division Rings, II.- 21 Quadrangles.- 22 Quadrangles of Involution Type.- 23 Quadrangles of Quadratic Form Type.- 24 Quadrangles of Indifferent Type.- 25 Quadrangles of Pseudo-Quadratic Form Type, I.- 26 Quadrangles of Pseudo-Quadratic Form Type, II.- 27 Quadrangles of Type E6, E7 and E8.- 28 Quadrangles of Type F4.- 29 Hexagons.- 30 Hexagonal Systems, II.- 31 Octagons.- 32 Existence.- IV More Results on Moufang Polygons.- 33 BN-Pairs.- 34 Finite Moufang Polygons.- 35 Isotopes.- 36 Isomorphic Hexagonal Systems.- 37 Automorphisms.- 38 Isomorphic Quadrangles.- V Moufang Polygons and Spherical Buildings.- 39 Chamber Systems.- 40 Spherical Buildings.- 41 Classical, Algebraic and Mixed Buildings.- 42 Appendix.- Index of Notation."
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                "Text" => "From the reviews:"In this excellently written book, the authors give a full classification for Moufang polygons. … The book is self contained … . the content of the book is accessible for motivated graduate students and researchers from every branch of mathematics. We recommend this book for everybody who is interested in the developments of the modern algebra, geometry or combinatorics." (Gábor P. Nagy, Acta Scientiarum Mathematicarum, Vol. 71, 2005)"The publication of this long-awaited book is a major event for geometry in general, and for the theory of buildings in particular. … The classifications established in this book are splendid achievements of fundamental significance. The whole book is extremely well written, in a clear and concise style … . It is the definitive treatment and a standard reference." (Theo Grundhöfer, Mathematical Reviews, Issue 2003 m)"This book contains the complete classification of all Moufang generalized polygons, including the full proof. … So, in conclusion, the book is a Bible for everyone interested in classification results related to spherical buildings. It is written in a very clear and concise way. It should be in the library of every mathematician as one of the major results in the theory of (Tits) buildings, (combinatorial) incidence geometry and (algebraic) group theory." (Hendrik Van Maldeghem, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2005)"
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                "Text" => "Spherical buildings are certain combinatorial simplicial complexes intro duced, at first in the language of "incidence geometries," to provide a sys tematic geometric interpretation of the exceptional complex Lie groups. (The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as "thick," "residue," "rank," "spherical," etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive rela tive rank £ is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs [101] is that the converse, for £ ::::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three."
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                "Text" => "I Preliminary Results.- 1 Introduction.- 2 Some Definitions.- 3 Generalized Polygons.- 4 Moufang Polygons.- 5 Commutator Relations.- 6 Opposite Root Groups.- 7 A Uniqueness Lemma.- 8 A Construction.- II Nine Families of Moufang Polygons.- 9 Alternative Division Rings, I.- 10 Indifferent and Octagonal Sets.- 11 Involutory Sets and Pseudo-Quadratic Forms.- 12 Quadratic Forms of Type E6, E7 and E8, I.- 13 Quadratic Forms of Type E6, E7 and E8, II.- 14 Quadratic Forms of Type F4.- 15 Hexagonal Systems, I.- 16 An Inventory of Moufang Polygons.- 17 Main Results.- III The Classification of Moufang Polygons.- 18 A Bound on n.- 19 Triangles.- 20 Alternative Division Rings, II.- 21 Quadrangles.- 22 Quadrangles of Involution Type.- 23 Quadrangles of Quadratic Form Type.- 24 Quadrangles of Indifferent Type.- 25 Quadrangles of Pseudo-Quadratic Form Type, I.- 26 Quadrangles of Pseudo-Quadratic Form Type, II.- 27 Quadrangles of Type E6, E7 and E8.- 28 Quadrangles of Type F4.- 29 Hexagons.- 30 Hexagonal Systems, II.- 31 Octagons.- 32 Existence.- IV More Results on Moufang Polygons.- 33 BN-Pairs.- 34 Finite Moufang Polygons.- 35 Isotopes.- 36 Isomorphic Hexagonal Systems.- 37 Automorphisms.- 38 Isomorphic Quadrangles.- V Moufang Polygons and Spherical Buildings.- 39 Chamber Systems.- 40 Spherical Buildings.- 41 Classical, Algebraic and Mixed Buildings.- 42 Appendix.- Index of Notation."
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                "Text" => "From the reviews:"In this excellently written book, the authors give a full classification for Moufang polygons. … The book is self contained … . the content of the book is accessible for motivated graduate students and researchers from every branch of mathematics. We recommend this book for everybody who is interested in the developments of the modern algebra, geometry or combinatorics." (Gábor P. Nagy, Acta Scientiarum Mathematicarum, Vol. 71, 2005)"The publication of this long-awaited book is a major event for geometry in general, and for the theory of buildings in particular. … The classifications established in this book are splendid achievements of fundamental significance. The whole book is extremely well written, in a clear and concise style … . It is the definitive treatment and a standard reference." (Theo Grundhöfer, Mathematical Reviews, Issue 2003 m)"This book contains the complete classification of all Moufang generalized polygons, including the full proof. … So, in conclusion, the book is a Bible for everyone interested in classification results related to spherical buildings. It is written in a very clear and concise way. It should be in the library of every mathematician as one of the major results in the theory of (Tits) buildings, (combinatorial) incidence geometry and (algebraic) group theory." (Hendrik Van Maldeghem, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2005)"
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                "Text" => "Gives a complete classification of Moufang polygons, starting from first principles Includes a totally new classification of the spherical buildings of rank 3 at least J. Tits is one of the best and most influential algebraists of the past 50 years R. Weiss is one of the world's leading researchers in the field of combinatorial group theory The book will become a classic in the field"
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                "Text" => ""Molecular Gels: Materials with Self-Assembled Fibrillar Networks" is a comprehensive treatise on gelators, especially low molecular-mass gelators and the properties of their gels. The structures and modes of formation of the self-assembled fibrillar networks (SAFINs) that immobilize the liquid components of the gels are discussed experimentally and theoretically. The spectroscopic, rheological, and structural features of the different classes of low molecular-mass gelators are also presented. Many examples of the application of the principal analytical techniques for investigation of molecular gels (including SANS, SAXS, WAXS, UV-vis absorption, fluorescence and CD spectroscopies, scanning electron, transmission electron and optical microscopies, and molecular modeling) are presented didactically and in-depth, as are several of the theories of the stages of aggregation of individual low molecular-mass gelator molecules leading to SAFINs. Several actual and potential applications of molecular gels in disparate fields (from silicate replication of nanostructures to art conservation) are described. Special emphasis is placed on perspectives for future developments.This book is an invaluable resource for researchers and practitioners either already researching self-assembly and soft matter or new to the area. Those who will find the book useful include chemists, engineers, spectroscopists, physicists, biologists, theoreticians, and materials scientists."
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