LEADER 01210nam--2200409---450- 001 990001475960203316 005 20051102095137.0 035 $a000147596 035 $aUSA01000147596 035 $a(ALEPH)000147596USA01 035 $a000147596 100 $a20040304d1973----km-y0itay0103----ba 101 0 $aeng 102 $aUS 105 $aa|||||||001yy 200 1 $aDarwin and facial expression$gedited by Paul Ekman 210 $aNew York [etc.]$cAcademic Press$d1973 215 $aXI, 273 p.$cill.$d23 cm 410 0$12001 454 1$12001 461 1$1001-------$12001 600 0 $aDarwin, Charles Robert 676 $a152.42 700 1$aEKMAN,$bPaul$0148574 801 0$aIT$bsalbc$gISBD 912 $a990001475960203316 951 $aII.6. 1016a(VI ps B 530)$b92680 L.M.$cVI ps 951 $aII.6. 1016(VI ps B 553)$b14745 LM$cVI ps 959 $aBK 969 $aUMA 979 $aSIAV1$b10$c20040304$lUSA01$h0955 979 $aPATRY$b90$c20040406$lUSA01$h1743 979 $aCOPAT5$b90$c20051028$lUSA01$h1404 979 $aCOPAT5$b90$c20051028$lUSA01$h1405 979 $aCOPAT5$b90$c20051102$lUSA01$h0951 996 $aDarwin and Facial Expression$9204325 997 $aUNISA LEADER 06936nam 2201513 a 450 001 9910789737103321 005 20200520144314.0 010 $a1-283-37995-3 010 $a9786613379955 010 $a1-4008-4269-7 024 7 $a10.1515/9781400842698 035 $a(CKB)2670000000133884 035 $a(EBL)827806 035 $a(OCoLC)769343169 035 $a(SSID)ssj0000575876 035 $a(PQKBManifestationID)11396459 035 $a(PQKBTitleCode)TC0000575876 035 $a(PQKBWorkID)10553953 035 $a(PQKB)11008932 035 $a(StDuBDS)EDZ0001756336 035 $a(DE-B1597)447361 035 $a(OCoLC)979582934 035 $a(DE-B1597)9781400842698 035 $a(Au-PeEL)EBL827806 035 $a(CaPaEBR)ebr10521870 035 $a(CaONFJC)MIL337995 035 $z(PPN)199244979 035 $a(MiAaPQ)EBC827806 035 $a(PPN)187959625 035 $a(EXLCZ)992670000000133884 100 $a20111017d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFre?chet differentiability of Lipschitz functions and porous sets in Banach spaces$b[electronic resource] /$fJoram Lindenstrauss, David Preiss, Jaroslav Tiser 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$d2012 215 $a1 online resource (436 p.) 225 1 $aAnnals of mathematics studies ;$vno. 179 300 $aDescription based upon print version of record. 311 $a0-691-15355-8 311 $a0-691-15356-6 320 $aIncludes bibliographical references and indexes. 327 $t Frontmatter -- $tContents -- $tChapter One: Introduction -- $tChapter Two: Gâteaux differentiability of Lipschitz functions -- $tChapter Three: Smoothness, convexity, porosity, and separable determination -- $tChapter Four: ?-Fréchet differentiability -- $tChapter Five: ?-null and ?n-null sets -- $tChapter Six: Férchet differentiability except for ?-null sets -- $tChapter Seven: Variational principles -- $tChapter Eight: Smoothness and asymptotic smoothness -- $tChapter Nine: Preliminaries to main results -- $tChapter Ten: Porosity, ?n- and ?-null sets -- $tChapter Eleven: Porosity and ?-Fréchet differentiability -- $tChapter Twelve: Fréchet differentiability of real-valued functions -- $tChapter Thirteen: Fréchet differentiability of vector-valued functions -- $tChapter Fourteen: Unavoidable porous sets and nondifferentiable maps -- $tChapter Fifteen: Asymptotic Fréchet differentiability -- $tChapter Sixteen: Differentiability of Lipschitz maps on Hilbert spaces -- $tBibliography -- $tIndex -- $tIndex of Notation 330 $aThis book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics. 410 0$aAnnals of mathematics studies ;$vno. 179. 606 $aBanach spaces 606 $aCalculus of variations 606 $aFunctional analysis 610 $aAsplund space. 610 $aBanach space. 610 $aBorel sets. 610 $aEuclidean space. 610 $aFrechet differentiability. 610 $aFréchet derivative. 610 $aFréchet differentiability. 610 $aFréchet smooth norm. 610 $aGâteaux derivative. 610 $aGâteaux differentiability. 610 $aHilbert space. 610 $aLipschitz function. 610 $aLipschitz map. 610 $aRadon-Nikodým property. 610 $aasymptotic uniform smoothness. 610 $aasymptotically smooth norm. 610 $aasymptotically smooth space. 610 $abump. 610 $acompleteness. 610 $acone-monotone function. 610 $aconvex function. 610 $adeformation. 610 $aderivative. 610 $adescriptive set theory. 610 $aflat surface. 610 $ahigher dimensional space. 610 $ainfinite dimensional space. 610 $airregular behavior. 610 $airregularity point. 610 $alinear operators. 610 $alow Borel classes. 610 $alower semicontinuity. 610 $amean value estimate. 610 $amodulus. 610 $amultidimensional mean value. 610 $anonlinear functional analysis. 610 $anonseparable space. 610 $anull sets. 610 $aperturbation function. 610 $aperturbation game. 610 $aperturbation. 610 $aporosity. 610 $aporous sets. 610 $aregular behavior. 610 $aregular differentiability. 610 $aregularity parameter. 610 $arenorming. 610 $aseparable determination. 610 $aseparable dual. 610 $aseparable space. 610 $aslice. 610 $asmooth bump. 610 $asubspace. 610 $atensor products. 610 $athree-dimensional space. 610 $atwo-dimensional space. 610 $atwo-player game. 610 $avariational principle. 610 $avariational principles. 610 $a?-null sets. 610 $a?-Fréchet derivative. 610 $a?-Fréchet differentiability. 610 $a?-porous sets. 615 0$aBanach spaces. 615 0$aCalculus of variations. 615 0$aFunctional analysis. 676 $a515/.88 686 $aSI 830$2rvk 700 $aLindenstrauss$b Joram$f1936-$041187 701 $aPreiss$b David$0515729 701 $aTis?er$b Jaroslav$f1957-$0515783 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910789737103321 996 $aFréchet differentiability of Lipschitz functions and porous sets in Banach spaces$9854568 997 $aUNINA LEADER 03068nam 2200541 450 001 9910816370703321 005 20200520144314.0 010 $a1-118-94554-9 010 $a1-118-94555-7 010 $a1-118-94556-5 035 $a(CKB)4330000000007621 035 $a(Au-PeEL)EBL4923293 035 $a(CaPaEBR)ebr11416143 035 $a(MiAaPQ)EBC4923293 035 $a(OCoLC)972640368 035 $a(EXLCZ)994330000000007621 100 $a20170818h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 00$aInsect biodiversity$hVolume 1 $escience and society /$fedited by Dr. Robert G. Foottit, Professor Peter H. Adler 205 $aSecond edition. 210 1$aHoboken, New Jersey :$cWiley Blackwell,$d2017. 210 4$d©2017 215 $a1 online resource (876 pages) $cillustrations (some color), photographs 311 $a1-118-94553-0 320 $aIncludes bibliographical references at the end of each chapters and indexes. 327 $aIntroduction -- The importance of insects -- Insect biodiversity : regional examples -- Insect biodiversity in the nearctic region -- Amazonian rainforests and their richness and abundance of terrestrial arthropods on the edge of extinction : abiotic-biotic players in the critical zone -- Insect biodiversity in the afrotropical region -- Biodiversity of australasian insects -- Insect biodiversity in the palearctic region -- Insect biodiversity : taxon examples -- Biodiversity of aquatic insects -- Biodiversity of diptera -- Biodiversity of heteroptera -- Biodiversity of coleoptera -- Biodiversity of hymenoptera -- Diversity and significance of lepidoptera : a phylogenetic perspective -- Insect biodiversity : tools and approaches -- The science of insect taxonomy : prospects and needs -- Insect species, concepts and practice -- Molecular dimensions of insect taxonomy in the genomics era -- Dna barcodes and insect biodiversity -- Insect biodiversity informatics -- Parasitoid biodiversity and insect pest management -- Taxonomy of crop pests : the aphids -- Adventive (non-native) insects and the consequences for science and society of species that become invasive -- Biodiversity of blood-sucking flies : implications for humanity -- Reconciling ethical and scientific issues for insect conservation -- Taxonomy and management of insect biodiversity -- Insect biodiversity, millions and millions. 606 $aInsects$xVariation 606 $aInsects$xEvolution 606 $aInsects$xEcology 606 $aBiodiversity conservation 615 0$aInsects$xVariation. 615 0$aInsects$xEvolution. 615 0$aInsects$xEcology. 615 0$aBiodiversity conservation. 676 $a595.7 702 $aFoottit$b R$g(Robert G.), 702 $aAdler$b Peter H$g(Peter Holdridge),$f1954- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816370703321 996 $aInsect biodiversity$9778601 997 $aUNINA