05333nam 22007095 450 99646648530331620200707032832.03-540-44646-X10.1007/b100262(CKB)1000000000231538(SSID)ssj0000327520(PQKBManifestationID)11268708(PQKBTitleCode)TC0000327520(PQKBWorkID)10301750(PQKB)11322681(DE-He213)978-3-540-44646-0(MiAaPQ)EBC3087322(PPN)155177389(EXLCZ)99100000000023153820121227d2004 u| 0engurnn|008mamaatxtccrThe Valuative Tree[electronic resource] /by Charles Favre, Mattias Jonsson1st ed. 2004.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2004.1 online resource (XVI, 244 p.) Lecture Notes in Mathematics,0075-8434 ;1853Bibliographic Level Mode of Issuance: Monograph3-540-22984-1 Includes bibliographical references and index.1 Generalities -- 1.1 Setup -- 1.2 Valuations -- 1.3 Krull Valuations -- 1.4 Plane Curves -- 1.5 Examples of Valuations -- 1.6 Valuations Versus Krull Valuations -- 1.7 Sequences of Blowups and Krull Valuations -- 2 MacLane’s Method -- 2.1 Sequences of Key Polynomials -- 2.2 Classification -- 2.3 Graded Rings and Numerical Invariants -- 2.4 From Valuations to SKP’s -- 2.5 A Computation -- 3 Tree Structures -- 3.1 Trees -- 3.2 Nonmetric Tree Structure on V -- 3.3 Parameterization of V by Skewness -- 3.4 Multiplicities -- 3.5 Approximating Sequences -- 3.6 Thinness -- 3.7 Value Semigroups and Approximating Sequences -- 3.8 Balls of Curves -- 3.9 The Relative Tree Structure -- 4 Valuations Through Puiseux Series -- 4.1 Puiseux Series and Valuations -- 4.2 Tree Structure -- 4.3 Galois Action -- 4.4 A Tale of Two Trees -- 4.5 The Berkovich Projective Line -- 4.6 The Bruhat-Tits Metric -- 4.7 Dictionary -- 5 Topologies -- 5.1 The Weak Topology -- 5.2 The Strong Topology on V -- 5.3 The Strong Topology on Vqm -- 5.4 Thin Topologies -- 5.5 The Zariski Topology -- 5.6 The Hausdorff-Zariski Topology -- 5.7 Comparison of Topologies -- 6 The Universal Dual Graph -- 6.1 Nonmetric Tree Structure -- 6.2 Infinitely Near Points -- 6.3 Parameterization and Multiplicity -- 6.4 The Isomorphism -- 6.5 Proof of the Isomorphism -- 6.6 Applications -- 6.7 The Dual Graph of the Minimal Desingularization -- 6.8 The Relative Tree Structure -- 7 Tree Measures -- 7.1 Outline -- 7.2 More on the Weak Topology -- 7.3 Borel Measures -- 7.4 Functions of Bounded Variation -- 7.5 Representation Theorem I -- 7.6 Complex Tree Potentials -- 7.7 Representation Theorem II -- 7.8 Atomic Measures -- 7.9 Positive Tree Potentials -- 7.10 Weak Topologies and Compactness -- 7.11 Restrictions to Subtrees -- 7.12 Inner Products -- 8 Applications of the Tree Analysis -- 8.1 Zariski’s Theory of Complete Ideals -- 8.2 The Voûte étoilée -- A Infinitely Singular Valuations -- A.1 Characterizations -- A.2 Constructions -- B The Tangent Space at a Divisorial Valuation -- C Classification -- D Combinatorics of Plane Curve Singularities -- D.1 Zariski’s Terminology for Plane Curve Singularities -- D.2 The Eggers Tree -- E.1 Completeness -- E.2 The Residue Field -- References.This volume is devoted to a beautiful object, called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions. Its intricate yet manageable structure can be analyzed by both algebraic and geometric means. Many types of singularities, including those of curves, ideals, and plurisubharmonic functions, can be encoded in terms of positive measures on the valuative tree. The construction of these measures uses a natural tree Laplace operator of independent interest.Lecture Notes in Mathematics,0075-8434 ;1853Discrete mathematicsAlgebraic geometryCommutative algebraCommutative ringsTopologyDiscrete Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M29000Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Commutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28000Discrete mathematics.Algebraic geometry.Commutative algebra.Commutative rings.Topology.Discrete Mathematics.Algebraic Geometry.Commutative Rings and Algebras.Topology.510 s511/.52Favre Charlesauthttp://id.loc.gov/vocabulary/relators/aut478896Jonsson Mattiasauthttp://id.loc.gov/vocabulary/relators/autBOOK996466485303316The Valuative Tree2530052UNISA03256nam 2200457 450 991083081200332120210203211824.03-527-82643-23-527-82642-43-527-82644-0(CKB)4100000010871109(MiAaPQ)EBC6237448(OCoLC)1163513058(EXLCZ)99410000001087110920201017d2020 uy 0engurcn#---|||||txtrdacontentcrdamediacrrdacarrierCopper catalysis in organic synthesis /edited by Gopinathan Anilkumar, Salim SaranyaWeinheim, Germany :Wiley-VCH,[2020]©20201 online resource (506 pages)Includes bibliographical references and index.Copper Catalysis / Salim Saranya, Gopinathan Anilkumar -- Cu-Catalyst in Reactions Involving Pyridinium and Indolizinium Moieties / Bianca Furdui, Andrea V Dediu, Rodica M Dinica -- Copper-Catalyzed Cross-Coupling Reactions of Organoboron Compounds / Jan Nekvinda, Webster L Santos -- Cu-Catalyzed Homocoupling Reactions / Ganesh C Nandi, Sundaresan Ravindra, Cholakkaparambil Irfana Jesin, Parameswaran Sasikumar, Kokkuvayil V Radhakrishnan -- Cu-Catalyzed Organic Reactions in Aqueous Media / Noel Nebra, Joaquín García-Álvarez -- Cu-Catalyzed Organic Reactions in Deep Eutectic Solvents (DESs) / Noel Nebra, Joaquín García-Álvarez -- Microwave-Assisted Cu-Catalyzed Organic Reactions / Bogdan Štefane, Helena Brodnik-Žugelj, Uroš Grošelj, Jurij Svete, Franc Požgan -- Cu-Catalyzed Asymmetric Synthesis / Hidetoshi Noda, Naoya Kumagai, Masakatsu Shibasaki -- Cu-Catalyzed Click Reactions / Rajagopal Ramkumar, Pazhamalai Anbarasan -- Cu-Catalyzed Multicomponent Reactions / Thachapully D Suja, Rajeev S Menon -- Copper-Catalyzed Aminations / Nissy Ann Harry, Rajenahally V Jagadeesh -- Cu-Catalyzed Carbonylation Reactions / Parameswaran Sasikumar, Thoppe S Priyadarshini, Sanjay Varma, Ganesh C Nandi, Kokkuvayil V Radhakrishnan -- Ligand-Free, Cu-Catalyzed Reactions / Muhammad F Jamali, Sanoop P Chandrasekharan, Kishor Mohanan -- Copper-Catalyzed Decarboxylative Coupling / Firas El-Hage, Jola Pospech -- Copper-Catalyzed C-H Activation / Xun-Xiang Guo -- Aerobic Cu-Catalyzed Organic Reactions / Ahmad A Almasalma, Esteban Mejia -- Copper-Catalyzed Trifluoromethylation Reactions / Dzmitry G Kananovich -- Cu-Catalyzed Reactions for Carbon-Heteroatom Bond Formations / Govindasamy Sekar, Subramani Sangeetha, Anuradha Nandy, Rajib Saha -- Cu-Assisted Cyanation Reactions / Sumanta Garai, Ganesh A Thakur -- Application of Cu-Mediated Reactions in the Synthesis of Natural Products / Anas Ansari, Ramesh Ramapanicker.Organic compoundsSynthesisCopper catalystsOrganic compoundsSynthesis.Copper catalysts.546.652595Anilkumar GopinathanSaranya SalimMiAaPQMiAaPQMiAaPQCaOWtUBOOK9910830812003321Copper catalysis in organic synthesis3940446UNINA