LEADER 01095nam a2200289 i 4500 001 991001993959707536 008 130315s2011 it ab b 000 0 ita d 020 $a9788850653959 035 $ab14103898-39ule_inst 040 $aDi.S.Te.B.A.$beng 082 0 $a593.4$222 245 00$aPorifera 1:$bCalcarea, Demospongiae (partim), Hexactinellida, Homoscleromorpha /$ca cura di Maurizio Pansini, Renata Manconi, Roberto Pronzato 260 3 $aBologna :$bCalderini,$c2011 300 $axi, 554 p. :$bill. ;$c25 cm 490 1 $aFauna d'Italia ;$v46 504 $aIncludes bibliographical references (p. 463-529) 546 $aText in English 650 0$aSponges$vClassification 700 1 $aPronzato, Roberta 700 1 $aPansini, Maurizio 700 1 $aManconi, Renata 907 $a.b14103898$b07-08-20$c15-03-13 912 $a991001993959707536 945 $aLE003 591 FAU01.01 46 (2011) RAM$g1$i2003000073652$lle003$op$pE48.00$q-$rl$s- $t0$u2$v1$w2$x0$y.i15493659$z26-03-13 996 $aPorifera 1$9264867 997 $aUNISALENTO 998 $ale003$b15-03-13$cm$da $e-$fita$git $h0$i0 LEADER 03157nam 2200637Ia 450 001 9910780301503321 005 20230607214439.0 010 $a1-281-86970-8 010 $a9786611869700 010 $a981-238-491-X 035 $a(CKB)111087028338014 035 $a(EBL)183742 035 $a(OCoLC)475900343 035 $a(SSID)ssj0000190753 035 $a(PQKBManifestationID)11156712 035 $a(PQKBTitleCode)TC0000190753 035 $a(PQKBWorkID)10180726 035 $a(PQKB)11633254 035 $a(WSP)00004741 035 $a(Au-PeEL)EBL183742 035 $a(CaPaEBR)ebr10255610 035 $a(CaONFJC)MIL186970 035 $a(MiAaPQ)EBC183742 035 $a(EXLCZ)99111087028338014 100 $a20010713d2001 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLeast action principle of crystal formation of dense packing type and the proof of Kepler's conjecture$b[electronic resource] /$fHsiang, Wu-Yi 210 $aSingapore ;$aRiver Edge, NJ $cWorld Scientific$d2001 215 $a1 online resource (425 p.) 225 1 $aNankai tracts in mathematics 300 $aDescription based upon print version of record. 311 $a981-02-4670-6 320 $aIncludes bibliographical references. 327 $aContents; Foreword; Acknowledgment; List of Symbols; Chapter 1 Introduction; Chapter 2 The Basics of Euclidean and Spherical Geometries and a New Proof of the Problem of Thirteen Spheres; Chapter 3 Circle Packings and Sphere Packings; Chapter 4 Geometry of Local Cells and Specific Volume Estimation Techniques for Local Cells; Chapter 5 Estimates of Total Buckling Height; Chapter 6 The Proof of the Dodecahedron Conjecture; Chapter 7 Geometry of Type I Configurations and Local Extensions; Chapter 8 The Proof of Main Theorem I; Chapter 9 Retrospects and Prospects; References; Index 330 $aThe dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of mono-atomic elements with weak covalent bonds, which achieves the optimal ""known density"" of p/v18. In 1611, Johannes Kepler had already ""conjectured"" that p/v18 should be the optimal ""density"" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that p/v18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of 410 0$aNankai tracts in mathematics 606 $aKepler's conjecture 606 $aSphere packings 606 $aCrystallography, Mathematical 615 0$aKepler's conjecture. 615 0$aSphere packings. 615 0$aCrystallography, Mathematical. 676 $a511/.6 676 $a516 700 $aHsiang$b Wu Yi$f1937-$047829 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780301503321 996 $aLeast action principle of crystal formation of dense packing type and the proof of Kepler's conjecture$93671495 997 $aUNINA