LEADER 03869nam 22004335 450 001 9910300109203321 005 20200701120143.0 010 $a4-431-49822-2 024 7 $a10.1007/978-4-431-49822-3 035 $a(CKB)4100000007110625 035 $a(MiAaPQ)EBC5592862 035 $a(DE-He213)978-4-431-49822-3 035 $a(PPN)232469954 035 $a(EXLCZ)994100000007110625 100 $a20181103d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aComplex Analytic Desingularization /$fby José Manuel Aroca, Heisuke Hironaka, José Luis Vicente 205 $a1st ed. 2018. 210 1$aTokyo :$cSpringer Japan :$cImprint: Springer,$d2018. 215 $a1 online resource (xxix, 330 pages) 311 $a4-431-70218-0 327 $aPrologue -- 1 Complex-Analytic Spaces and Elements -- 2 The Weierstrass Preparation Theorem and Its Consequences -- 3 Maximal Contact -- 4 Groves and Polygroves -- 5 The Induction Process -- Epilogue: Singularities of differential equations -- Bibliography -- Index. 330 $a[From the foreword by B. Teissier] The main ideas of the proof of resolution of singularities of complex-analytic spaces presented here were developed by Heisuke Hironaka in the late 1960s and early 1970s. Since then, a number of proofs, all inspired by Hironaka's general approach, have appeared, the validity of some of them extending beyond the complex analytic case. The proof has now been so streamlined that, although it was seen 50 years ago as one of the most difficult proofs produced by mathematics, it can now be the subject of an advanced university course. Yet, far from being of historical interest only, this long-awaited book will be very rewarding for any mathematician interested in singularity theory. Rather than a proof of a canonical or algorithmic resolution of singularities, what is presented is in fact a masterly study of the infinitely near ?worst? singular points of a complex analytic space obtained by successive ?permissible? blowing ups and of the way to tame them using certain subspaces of the ambient space. This taming proves by an induction on the dimension that there exist finite sequences of permissible blowing ups at the end of which the worst infinitely near points have disappeared, and this is essentially enough to obtain resolution of singularities. Hironaka?s ideas for resolution of singularities appear here in a purified and geometric form, in part because of the need to overcome the globalization problems appearing in complex analytic geometry. In addition, the book contains an elegant presentation of all the prerequisites of complex analytic geometry, including basic definitions and theorems needed to follow the development of ideas and proofs. Its epilogue presents the use of similar ideas in the resolution of singularities of complex analytic foliations. This text will be particularly useful and interesting for readers of the younger generation who wish to understand one of the most fundamental results in algebraic and analytic geometry and invent possible extensions and applications of the methods created to prove it. 606 $aGeometry, Algebraic 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aGeometry, Algebraic. 615 14$aAlgebraic Geometry. 676 $a516.35 700 $aAroca$b José Manuel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0534547 702 $aHironaka$b Heisuke$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVicente$b José Luis$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300109203321 996 $aComplex Analytic Desingularization$91910227 997 $aUNINA LEADER 02631nam 22005775 450 001 9910568280803321 005 20251113210909.0 010 $a981-19-1472-9 024 7 $a10.1007/978-981-19-1472-0 035 $a(MiAaPQ)EBC6976083 035 $a(Au-PeEL)EBL6976083 035 $a(CKB)21957548700041 035 $a(PPN)267814763 035 $a(DE-He213)978-981-19-1472-0 035 $a(EXLCZ)9921957548700041 100 $a20220503d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aUncertain Graph and Network Optimization /$fby Bo Zhang, Jin Peng 205 $a1st ed. 2022. 210 1$aSingapore :$cSpringer Nature Singapore :$cImprint: Springer,$d2022. 215 $a1 online resource (144 pages) 225 1 $aSpringer Uncertainty Research,$x2199-3815 311 08$aPrint version: Zhang, Bo Uncertain Graph and Network Optimization Singapore : Springer,c2022 9789811914713 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Graph and Network -- Uncertainty Theory -- Uncertain Programming -- Uncertain Graph -- Uncertain Network Optimization -- Applications of Uncertain Network Optimization. 330 $aThis first book focuses on uncertain graph and network optimization. It covers three different main contents: uncertain graph, uncertain programming and uncertain network optimization. It also presents applications of uncertain network optimization in a lot of real problems such as transportation problems, dispatching medical supplies problems and location problems. The book is suitable for researchers, engineers, teachers and students in the field of mathematics, information science, computer science, decision science, management science and engineering, artificial intelligence, industrial engineering, economics and operations research. 410 0$aSpringer Uncertainty Research,$x2199-3815 606 $aAutomatic control 606 $aSystem theory 606 $aControl theory 606 $aControl and Systems Theory 606 $aSystems Theory, Control 615 0$aAutomatic control. 615 0$aSystem theory. 615 0$aControl theory. 615 14$aControl and Systems Theory. 615 24$aSystems Theory, Control. 676 $a519.3 700 $aZhang$b Bo$0875254 702 $aPeng$b Jin 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910568280803321 996 $aUncertain graph and network optimization$92987188 997 $aUNINA