LEADER 01328nam0 22003371i 450 001 RML0293796 005 20231121125738.0 010 $a3540003134 100 $a20121121d2005 ||||0itac50 ba 101 | $aeng 102 $ade 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 1 $aStochastic integration and differential equations$fPhilip E. Protter 205 $a2. ed.$bVersion 2.1 210 $aBerlin [etc.] $cSpringer $d2005 215 $aXIII, 419 p.$cill.$d24 cm 225 | $aStochastic modeling and applied probability. - Berlin [etc.] $eSpringer 300 $a3. rist. 410 0$1001RML0332617$12001 $aStochastic modeling and applied probability. - Berlin [etc.] $eSpringer 606 $aMatematica applicata$2FIR$3RMLC088528$9I 676 $a519.2$9$v21 700 1$aProtter$b, Philip E.$3RMLV189674$059510 801 3$aIT$bIT-01$c20121121 850 $aIT-FR0098 899 $aBiblioteca Area Giuridico Economica$bFR0098 912 $aRML0293796 950 0$aBiblioteca Area Giuridico Economica$d 53DIMET 519.2/36$e 53VM 0000634315 VM barcode:9783540003137. - Inventario:111. - Fondo:Sala consultazioneVM$fA $h20070216$i20121204 977 $a 53 996 $aStochastic integration and differential equations$982147 997 $aUNICAS LEADER 03560nam 22006975 450 001 9910144620703321 005 20230617035935.0 010 $a3-540-39399-4 024 7 $a10.1007/b13785 035 $a(CKB)1000000000230799 035 $a(SSID)ssj0000323928 035 $a(PQKBManifestationID)11245091 035 $a(PQKBTitleCode)TC0000323928 035 $a(PQKBWorkID)10305112 035 $a(PQKB)11364110 035 $a(DE-He213)978-3-540-39399-3 035 $a(MiAaPQ)EBC6299080 035 $a(MiAaPQ)EBC5585524 035 $a(Au-PeEL)EBL5585524 035 $a(OCoLC)166469097 035 $a(EXLCZ)991000000000230799 100 $a20150519d2003 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aImproved Bonferroni Inequalities via Abstract Tubes $eInequalities and Identities of Inclusion-Exclusion Type /$fby Klaus Dohmen 205 $a1st ed. 2003. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003. 215 $a1 online resource (X, 122 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1826 300 $aBased on author's habilitation thesis--Humboldt-University. 311 $a3-540-20025-8 320 $aIncludes bibliographical references and indexes. 327 $a1. Introduction and Overview -- 2. Preliminaries -- 3.Bonferroni Inequalities via Abstract Tubes -- 4. Abstract Tubes via Closure and Kernel Operators -- 5. Recursive Schemes -- 6. Reliability Applications -- 7. Combinatorial Applications and Related Topics -- Bibliography -- Index. 330 $aThis introduction to the recent theory of abstract tubes describes the framework for establishing improved inclusion-exclusion identities and Bonferroni inequalities, which are provably at least as sharp as their classical counterparts while involving fewer terms. All necessary definitions from graph theory, lattice theory and topology are provided. The role of closure and kernel operators is emphasized, and examples are provided throughout to demonstrate the applicability of this new theory. Applications are given to system and network reliability, reliability covering problems and chromatic graph theory. Topics also covered include Zeilberger's abstract lace expansion, matroid polynomials and Möbius functions. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1826 606 $aCombinatorial analysis 606 $aAlgebra 606 $aOrdered algebraic structures 606 $aProbabilities 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aOrder, Lattices, Ordered Algebraic Structures$3https://scigraph.springernature.com/ontologies/product-market-codes/M11124 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aCombinatorial analysis. 615 0$aAlgebra. 615 0$aOrdered algebraic structures. 615 0$aProbabilities. 615 14$aCombinatorics. 615 24$aOrder, Lattices, Ordered Algebraic Structures. 615 24$aProbability Theory and Stochastic Processes. 676 $a512.97 700 $aDohmen$b Klaus$4aut$4http://id.loc.gov/vocabulary/relators/aut$0149982 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910144620703321 996 $aImproved Bonferroni inequalities via abstract tubes$9168037 997 $aUNINA