积分几何与几何概率（英文版）

图书标准信息

• 作者 [阿根廷]路易斯桑塔洛 著
• 出版社 世界图书出版公司
• 出版时间 2009-05
• 版次 1
• ISBN 9787510004933
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 404页
• 正文语种 英语

【内容简介】

Thoughitstitle"IntegralGeometry"mayappearsomewhatunusualinthiscontextitisneverthelessquiteappropriate,forIntegralGeometryisanoutgrowthofwhatintheoldendayswasreferredtoas"geometricprobabil-ities."
Originating,aslegendhasit,withtheBuffonneedleproblem（whichafternearlytwocenturieshaslostlittleofitseleganceandappeal）,geometricprobabilitieshaverunintodifficultiesculminatingintheparadoxesofBertrandwhichthreatenedthefledglingfieldwithbanishmentfromthehomeofMathematics.Inrescuingitfromthisfate,Poincar6madethesuggestionthatthearbitrarinessofdefinitionunderlyingtheparadoxescouldberemovedbytyingcloserthedefinitionofprobabilitywithageometricgroupofwhichitwouldhavetobeaninvariant.

【目录】

EditorsStatement
Foreword
Preface
Chapter1.ConvexSetsinthePlane
1.Introduction
2.EnvelopeofaFamilyofLines
3.MixedAreasofMinkowski
4.SomeSpecialConvexSets
5.SurfaceAreaoftheUnitSphereandVolumeoftheUnitBall
6.NotesandExercises

Chapter2.SetsofPointsandPoissonProcessesinthePlane
1.DensityforSetsofPoints
2.FirstIntegralFormulas
3.SetsofTriplesofPoints
4.HomogeneousPlanarPoissonPointProcesses
5.Notes

Chapter3.SetsofLinesinthePlane
1.DensityforSetsofLines
2.LinesThatIntersectaConvexSetoraCurve
3.LinesThatCutorSeparateTwoConvexSets
4.GeometricApplications
5.NotesandExercises
Chapter4.PairsofPointsandPairsofLines
1.DensityforPairsofPoints
2.IntegralsforthePoweroftheChordsofaConvexSet.
3.DensityforPairsofLines
4.DivisionofthePlanebyRandomLines
5.Notes

Chapter5.SetsofStripsinthePlane
1.DensityforSetsofStrips
2.BuffonsNeedleProblem
3.SetsofPoints,Lines,andStrips
4.SomeMeanValues
5.Notes

Chapter6.TheGroupofMotionsinthePlane：KinematicDensity.
1.TheGroupofMotionsinthePlane
2.TheDifferentialFormson9Jl
3.TheKinematicDensity
4.SetsofSegments
5.ConvexSetsThatIntersectAnotherConvexSet
6.SomeIntegralFormulas
7.AMeanValue;CoverageProblems
8.NotesandExercises

Chapter7.FundamentalFormulasofPoinear~andBlaschke
1.ANewExpressionfortheKinematicDensity
2.Poincar6sFormula
3.TotalCurvatureofaClosedCurveandofaPlaneDomain
4.FundamentalFormulaofBlaschke
5.ThelsoperimetricInequality.
6.HadwigersConditionsforaDomaintoBeAbletoContainAnother
7.Notes

Chapter8.LatticesofFigures
1.DefinitionsandFundamentalFormula
2.LatticesofDomains
3.LatticesofCurves
4.LatticesOfPoints
5.NotesandExercise

Chapter9.DifferentialFormsandLieGroups
1.DifferentialForms
2.PfaffianDifferentialSystems
3.MappingsofDifferentiableManifolds
4.LieGroups;LeftandRightTranslations
5.Left-lnvariantDifferentialForms
6.Maurer-CartanEquations
7.lnvariantVolumeElementsofaGroup：UnimodularGroups
8.NotesandExercises

Chapter10.DensityandMeasureinHomogeneousSpaces
1.Introduction
2.invariantSubgroupsandQuotientGroups
3.OtherConditionsfortheExistenceofaDensityonHomo-geneousSpaces
4.Examples
5.LieTransformationGroups
6.NotesandExercises

Chapter11.TheAffineGroups
1.TheGroupsofAffineTransformations
2.DensitiesforLinearSpaceswithRespecttoSpecialHomo-geneousAffinities
3.DensitiesforLinearSubspaceswithRespecttotheSpecialNonhomogeneousAffineGroup
4.NotesandExercises

Chapter12.TheGroupofMotionsinE,
1.Introduction
2.DensitiesforLinearSpacesinE
3.ADifferentialFormula
4.Densityforr-PlanesaboutaFixedq-Plane
5.AnotherFormoftheDensityforr-Planesin
6.SetsofPairsofLinearSpaces
7.Notes

Chapter13.ConvexSetsin
1.ConvexSetsandQuermassintegrale
2.CauchysFormula
3.ParallelConvexSets;SteinersFormula
4.IntegralFormulasRelatingtotheProjectionsofaConvexSetonLinearSubspaces
5.IntegralsofMeanCurvature
6.IntegralsofMeanCurvatureandQuermassintegrale.
7.IntegralsofMeanCurvatureofaFlattenedConvexBody
8.Notes

Chapter14.LinearSubspaces,ConvexSets,andCompactManifolds
1.Setsofr-PlanesThatIntersectaConvexSet
2.GeometricProbabilities
3.CroftonsFormulasinEn
4.SomeRelationsbetweenDensitiesofLinearSubspaces
5.LinearSubspacesThatIntersectaManifold
6.HypersurfacesandLinearSpaces
7.Notes

Chapter15.TheKinematicDensityinE
1.FormulasonDensities
2.IntegraloftheVolume
3.ADifferentialFormula
4.TheKinematicFundamentalFormula
5.FundamentalFormulaforConvexSets
6.MeanValuesfortheIntegralsofMeanCurvature
7.FundamentalFormulaforCylinders
8.SomeMeanValues
9.LatticesinEn.
10.NotesandExercise

Chapter16.GeometricandStatisticalApplications;Stereology
1.SizeDistributionofParticlesDerivedfromtheSizeDistributionofTheirSections
2.IntersectionwithRandomPlanes
3.IntersectionwithRandomLines
4.Notes

Chapter17.NoneuclideanIntegralGeometry
1.Then-DimensionalNoneuclideanSpace
2.TheGauss-BonnetFormulaforNoneuclideanSpaces
3.KinematicDensityandDensityforr-Planes
4.Setsofr-PlanesThatMeetaFixedBody
5.Notes

Chapter18.CroftonsFormulasandtheKinematicFundamentalFormula
inNoneuclideanSpaces
1.CroftonsFormulas
2.DualFormulasinEllipticSpace
3.TheKinematicFundamentalFormulainNoneuclidean
Spaces
4.SteinersFormulainNoneuclideanSpaces
5.AnIntegralFormulaforConvexBodiesinEllipticSpace
6.Notes
Chapter19.IntegralGeometryandFoliatedSpaces;TrendsinIntegralGeometry
1.FoliatedSpaces
2.SetsofGeodesicsinaRiemannManifold
3.MeasureofTwo-DimensionalSetsofGeodesics
4.Measureof（2n-2）-DimensionalSetsofGeodesics
5.SetsofGeodesicSegments
6.IntegralGeometryonComplexSpaces
7.SymplecticIntegralGeometry
8.TheIntegralGeometryofGelfand
9.Notes
Appendix.DifferentialFormsandExteriorCalculus
1.DifferentialFormsandExteriorProduct
2.TwoApplicationsoftheExteriorProduct
3.ExteriorDifferentiation
4.StokesFormula
5.ComparisonwithVectorCalculusinEuclideanThree-DimensionalSpace
6.DifferentialFormsoverManifolds
BibliographyandReferences
AuthorIndex
SubiectIndex