LEADER 01326nam1 22002893i 450 001 CAG0041670 005 20170908093240.0 100 $a20170628d1870 ||||0itac50 ba 101 | $aita 102 $ait 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 1 $aCatalogo metodico degli animali riportati dalle escursioni nelle provincie meridionali, in Sicilia e in Sardegna negli anni 1868-1869 dal cav. prof. A. Targioni Tozzetti$fcompilata ed annotata dal dottor Antonio Carruccio 210 $aMilano$cCoi tipi di Giuseppe Bernardoni 215 $av.$d22 cm 463 1$1001CAG0041672$12001 $a˜1: Parte 1. ÂœVertebrati$fcompilata ed annotata dal dottor Antonio Carruccio$v1 606 $aFAUNA$xItalia Meridionale$xDescrizione$2FIR$3NAPC026704$9I 700 1$aCarruccio$b, Antonio$3UFIV072609$4070$0317229 702 1$aTargioni Tozzetti$b, Adolfo$3SBLV042840 801 3$aIT$bIT-NA0079$c20170628 850 $aIT-NA0079 912 $aCAG0041670 950 1$aBiblioteca Nazionale Vittorio Emanuele III$bv. 1$cv. 1$d BNMISC. Busta B 153.36 967 $m1 977 $a BN 996 $aCatalogo metodico degli animali riportati dalle escursioni nelle provincie meridionali, in Sicilia e in Sardegna negli anni 1868-1869 dal cav. prof. A. Targioni Tozzetti$91483103 997 $aUNISANNIO LEADER 05566nam 22007215 450 001 9910483493103321 005 20251113175604.0 010 $a3-030-69863-7 024 7 $a10.1007/978-3-030-69863-8 035 $a(CKB)4100000011807201 035 $a(MiAaPQ)EBC6524990 035 $a(Au-PeEL)EBL6524990 035 $a(OCoLC)1243263853 035 $a(PPN)254718949 035 $a(DE-He213)978-3-030-69863-8 035 $a(EXLCZ)994100000011807201 100 $a20210322d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLaplacian Growth on Branched Riemann Surfaces /$fby Björn Gustafsson, Yu-Lin Lin 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (163 pages) $cillustrations 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2287 311 08$a3-030-69862-9 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- 1 Introduction -- 1.1 General Background -- 1.2 Loss of Univalence, Several Scenarios -- 1.3 On the Construction of a Branched Riemann Surface -- 1.4 Moment Coordinates and the String Equation -- 1.5 Outlooks to Physics -- 1.6 Acknowledgements -- 2 The Polubarinova-Galin and Lo?wner-Kufarev Equations -- 2.1 Basic Set Up in the Univalent Case -- 2.2 Dynamics and Subordination -- 2.3 The Polubarinova-Galin Versus the Lo?wner-Kufarev Equation -- 3 Weak Solutions and Balayage -- 3.1 Weak Formulation of the Polubarinova-Galin Equation -- 3.2 Weak Solutions in Terms of Balayage -- 3.3 Inverse Balayage -- 3.4 More General Laplacian Evolutions -- 3.5 Regularity of the Boundary via the Exponential Transform -- 3.6 The Resultant and the Elimination Function -- 4 Weak and Strong Solutions on Riemann Surfaces -- 4.1 Laplacian Growth on Manifolds -- 4.2 Examples -- 4.3 The Riemann Surface Solution Pulled Back to the Unit Disk -- 4.4 Compatibility Between Balayage and Covering Maps -- 5 Global Simply Connected Weak Solutions -- 5.1 Statement of Result, and Two Lemmas -- 5.2 Statement of Conjecture, and Partial Proofs -- 5.3 Discussion -- 6 General Structure of Rational Solutions -- 6.1 Introduction -- 6.2 Direct Approach -- 6.3 Approach via Quadrature Identities -- 7 Examples -- 7.1 Examples: Several Evolutions of a Cardioid -- 7.1.1 The Univalent Solution -- 7.1.2 A Non-univalent Solution of the Polubarinova-Galin Equation -- 7.1.3 A Non-univalent Solution of the Lo?wner-Kufarev Equation -- 7.1.4 A Solution for the Suction Case -- 7.2 Injection Versus Suction in a Riemann Surface Setting -- 8 Moment Coordinates and the String Equation -- 8.1 The Polubarinova-Galin Equation as a String Equation -- 8.2 The String Equation for Univalent Conformal Maps -- 8.3 Intuition and Physical Interpretation in the Non-univalent Case. 327 $a8.4 An Example -- 8.4.1 General Case -- 8.4.2 First Subcase -- 8.4.3 Second Subcase -- 8.5 Moment Evolutions in Terms of Poisson Brackets -- 9 Hamiltonian Descriptions of General Laplacian Evolutions -- 9.1 Lie Derivatives and Interior Multiplication -- 9.2 Laplacian Evolutions -- 9.3 Schwarz Potentials and Generating Functions -- 9.4 Multitime Hamiltonians -- 10 The String Equation for Some Rational Functions -- 10.1 The String Equation on Quadrature Riemann Surfaces -- 10.2 The String Equation for Polynomials -- 10.3 Evolution of a Third Degree Polynomial with RealCoefficients -- 10.4 An Example by Ullemar -- Glossary -- References -- Index. 330 $aThis book studies solutions of the Polubarinova?Galin and Löwner?Kufarev equations, which describe the evolution of a viscous fluid (Hele-Shaw) blob, after the time when these solutions have lost their physical meaning due to loss of univalence of the mapping function involved. When the mapping function is no longer locally univalent interesting phase transitions take place, leading to structural changes in the data of the solution, for example new zeros and poles in the case of rational maps. This topic intersects with several areas, including mathematical physics, potential theory and complex analysis. The text will be valuable to researchers and doctoral students interested in fluid dynamics, integrable systems, and conformal field theory. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2287 606 $aFunctions of complex variables 606 $aDifferential equations 606 $aPotential theory (Mathematics) 606 $aMathematical physics 606 $aSoft condensed matter 606 $aFunctions of a Complex Variable 606 $aDifferential Equations 606 $aPotential Theory 606 $aMathematical Methods in Physics 606 $aFluids 615 0$aFunctions of complex variables. 615 0$aDifferential equations. 615 0$aPotential theory (Mathematics). 615 0$aMathematical physics. 615 0$aSoft condensed matter. 615 14$aFunctions of a Complex Variable. 615 24$aDifferential Equations. 615 24$aPotential Theory. 615 24$aMathematical Methods in Physics. 615 24$aFluids. 676 $a532.053 700 $aGustafsson$b Bjo?rn$f1947-$0853049 702 $aLin$b Yu-Lin 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483493103321 996 $aLaplacian growth on branched Riemann surfaces$91904861 997 $aUNINA