LEADER 05140nam 2200865 450 001 9910816776503321 005 20211216205554.0 024 7 $a10.1515/9783110258615 035 $a(CKB)2670000000432708 035 $a(EBL)1121584 035 $a(OCoLC)858762131 035 $a(SSID)ssj0001002014 035 $a(PQKBManifestationID)11555150 035 $a(PQKBTitleCode)TC0001002014 035 $a(PQKBWorkID)10995751 035 $a(PQKB)10236007 035 $a(MiAaPQ)EBC1121584 035 $a(DE-B1597)124070 035 $a(OCoLC)856565338 035 $a(DE-B1597)9783110258615 035 $a(Au-PeEL)EBL1121584 035 $a(CaPaEBR)ebr10786169 035 $a(CaONFJC)MIL807731 035 $a(PPN)18293750X 035 $a(EXLCZ)992670000000432708 100 $a20131008h20132013 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aInverse problems and nonlinear evolution equations $esolutions, Darboux matrices and Weyl-Titchmarsh functions /$fby Alexander Sakhnovich, Lev Sakhnovich, Inna Roitberg 210 1$aBerlin ;$aBoston :$cWalter de Gruyter GmbH & Co., KG,$d[2013] 210 4$d©2013 215 $a1 online resource (356 p.) 225 0 $aDe Gruyter Studies in Mathematics ;$v47 300 $aDescription based upon print version of record. 311 0 $a3-11-025861-7 311 0 $a3-11-025860-9 320 $aIncludes bibliographies and index. 327 $tFront matter --$tPreface --$tNotation --$tContents --$t0 Introduction --$t1 Preliminaries --$t2 Self-adjoint Dirac system: rectangular matrix potentials --$t3 Skew-self-adjoint Dirac system: rectangular matrix potentials --$t4 Linear system auxiliary to the nonlinear optics equation --$t5 Discrete systems --$t6 Integrable nonlinear equations --$t7 General GBDT theorems and explicit solutions of nonlinear equations --$t8 Some further results on inverse problems and generalized Bäcklund-Darboux transformation (GBDT) --$t9 Sliding inverse problems for radial Dirac and Schrödinger equations --$tAppendices --$tA General-type canonical system: pseudospectral and Weyl functions --$tB Mathematical system theory --$tC Krein's system --$tD Operator identities corresponding to inverse problems --$tE Some basic theorems --$tBibliography --$tIndex 330 $aThis book is based on the method of operator identities and related theory of S-nodes, both developed by Lev Sakhnovich. The notion of the transfer matrix function generated by the S-node plays an essential role. The authors present fundamental solutions of various important systems of differential equations using the transfer matrix function, that is, either directly in the form of the transfer matrix function or via the representation in this form of the corresponding Darboux matrix, when Bäcklund-Darboux transformations and explicit solutions are considered. The transfer matrix function representation of the fundamental solution yields solution of an inverse problem, namely, the problem to recover system from its Weyl function. Weyl theories of selfadjoint and skew-selfadjoint Dirac systems, related canonical systems, discrete Dirac systems, system auxiliary to the N-wave equation and a system rationally depending on the spectral parameter are obtained in this way. The results on direct and inverse problems are applied in turn to the study of the initial-boundary value problems for integrable (nonlinear) wave equations via inverse spectral transformation method. Evolution of the Weyl function and solution of the initial-boundary value problem in a semi-strip are derived for many important nonlinear equations. Some uniqueness and global existence results are also proved in detail using evolution formulas. The reading of the book requires only some basic knowledge of linear algebra, calculus and operator theory from the standard university courses. 410 3$aDe Gruyter Studies in Mathematics 606 $aBoundary value problems 606 $aDarboux transformations 606 $aEvolution equations, Nonlinear 606 $aFunctions 606 $aInverse problems (Differential equations) 606 $aMatrices 610 $aApplication. 610 $aDifferential Equation. 610 $aDirect Problem. 610 $aExplicit Solution. 610 $aGlobal Solution. 610 $aInitial-Boundary-Value Problem. 610 $aIntegrable Nonlinear Equation. 610 $aInverse Problem. 615 0$aBoundary value problems. 615 0$aDarboux transformations. 615 0$aEvolution equations, Nonlinear. 615 0$aFunctions. 615 0$aInverse problems (Differential equations) 615 0$aMatrices. 676 $a515.357 676 $a515/.357 700 $aSakhnovich$b Alexander$0740259 701 $aRoitberg$b Inna$01642770 701 $aSakhnovich$b L. A$0348825 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910816776503321 996 $aInverse problems and nonlinear evolution equations$93987651 997 $aUNINA LEADER 04945nam 2200613 450 001 9910823760203321 005 20200520144314.0 010 $a1-5231-0179-2 010 $a1-84995-248-5 035 $a(CKB)3710000000603730 035 $a(EBL)4409785 035 $a(MiAaPQ)EBC4409785 035 $a(Au-PeEL)EBL4409785 035 $a(CaPaEBR)ebr11156423 035 $a(CaONFJC)MIL897605 035 $a(OCoLC)939600614 035 $a(PPN)201701170 035 $a(EXLCZ)993710000000603730 100 $a20160310h20162016 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aSoil and rock description in engineering practice /$fDavid Norbury, consultant, director, David Norbury Limited, Reading, UK, Honorary Professor in Engineering Geology, University of Sussex, UK 205 $aSecond edition. 210 1$aDunbeath, Scotland, UK :$cWhittles Publishing,$d[2016] 210 4$d©2016 215 $a1 online resource (321 p.) 300 $aDescription based upon print version of record. 311 $a1-84995-179-9 320 $aIncludes bibliographical references and index. 327 $aContents; Preface ; Definitions ; 1 Introduction ; 1.1 What are we describing and why?; 1.2 Description compared with classification; 1.3 Communication in description; 1.4 Soil meets rock ; 1.5 Health and Safety in description ; 2 History of Description in Codification ; 2.1 Prior to 1970 ; 2.2 The period 1970-1981; 2.3 The period 1981-1999 and the first BS 5930 ; 2.4 Rock weathering; 2.5 1999 and the second BS 5930 ; 2.6 The period since 1999 ; 2.7 Multiple usage of defined terms; 2.7.1 Clay and silt terminology; 2.7.2 Secondary constituent terms; 2.7.3 Loose and dense 327 $a2.7.4 Compactness of silt2.7.5 Rock strength ; 2.7.6 Rock weathering; 2.7.7 Comparison of descriptive technology ; 3 Systematic Description ; 3.1 Standard word order ; 3.2 Standard word order in US practice ; 3.3 The multiple sentence approach ; 4 Description of Materials ; 4.1 Principal soil and rock types ; 4.2 Size fractions ; 4.3 Description procedure using flow chart; 4.4 Very coarse soils; 4.5 Coarse soils; 4.6 Particle shape ; 4.7 The coarse soil/fine soil boundary ; 4.8 Fine soils ; 4.9 Classification of plasticity of fine soils; 4.10 The soil/rock boundary; 4.11 Rock naming 327 $a4.11.1 General naming of rocks 4.11.2 Description of coal ; 4.11.3 Naming of carbonate sediments ; 4.11.4 Naming of volcaniclastic sediments ; 4.12 Grain size in rocks ; 5 Relative Density and Strength ; 5.1 Relative density in coarse soils; 5.2 Consistency of fine soils; 5.3 Strength: shear or unconfined ; 6 Structure, Fabric and Texture; 6.1 Structure; 6.2 Fabric ; 6.3 Texture ; 7 Colour ; 8 Secondary and Tertiary Fractions ; 8.1 Secondary fractions; 8.1.1 Secondary fractions in very coarse soils; 8.1.2 Very coarse particles as a secondary fraction; 8.1.3 Secondary fractions in coarse soils 327 $a8.1.4 Fine soil as a secondary constituent 8.1.5 Secondary fractions in fine soils; 8.1.6 Multiple secondary fractions; 8.2 Tertiary fractions; 8.3 Description of widely graded soils ; 8.4 Description and classification of particle size grading ; 8.5 Other information ; 9 Geological Unit; 10 Weathering ; 10.1 Weathering of soils; 10.2 Rock weathering; 10.3 Approach 1: description of weathering; 10.4 Approaches 2 and 3: classifications for homogeneous stronger rocks ; 10.5 Approach 4: classification for hetrogeneous weather rocks ; 10.6 Material specific weathering schemes 327 $a10.7 Approach 5: special cases 10.7.1 Chalk ; 10.7.2 Karstic limestone ; 10.7.3 Tropical weathering ; 11 Discontinuity Logging ; 11.1 Types of discontinuity ; 11.2 Discontinuity description ; 11.3 Orientation; 11.4 Spacing ; 11.5 Persistence and termination; 11.6 Surface form ; 11.7 Wall strength; 11.8 Aperture and infilling; 11.9 Seepage ; 11.10 Discontinuity sets ; 12 Discontinuity State Recording ; 12.1 Total core recovery ; 12.2 Solid core recovery ; 12.3 Rock quality designation; 12.4 Fracture spacing ; 13 Low Density Soils; 13.1 Organic soils; 13.1.1 Topsoil; 13.1.2 Peat 327 $a13.2 Volcanic soils or rocks 330 $aThis is a revised and updated version of the highly successful first edition. It continues to provide invaluable practical guidance in carrying out engineering geological logging of soil and rock samples and exposures in the field. 606 $aSoils$vIdentification 606 $aSoil science 606 $aRocks$vIdentification 615 0$aSoils 615 0$aSoil science. 615 0$aRocks 676 $a624.151 700 $aNorbury$b David$01623981 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910823760203321 996 $aSoil and rock description in engineering practice$93958683 997 $aUNINA