增长和扩散现象的数学模式和应用

　　Permutation groups arguably form the oldest part of group theory. Their study dates back to the early years of the nineteenth century and， indeed， for a long time groups were always understood to be permutation groups. Although， of course， this is no longer true， permutation groups continue to play an important role in modern group theory through the ubiquity of group actions and the concrete representations which permutation groups provide for abstract groups. Today， both finite and infinite permutation groups are lively topics of research.本书为英文版！

暂缺《增长和扩散现象的数学模式和应用》作者简介

1Introduction
2SomeBasicFrameworks
2.1ExponentialFunction
2.1.1TheExponentialFunctionandItsProperties
2.1.2DoublingTimes
2.1.3AnIllustration:PopulationoftheUnitedStates
2.1.4ExponentialFunctionwithMigration
2.1.5PowerLawExponentialFunction
2.1.6AnIllustration:PopulationoftheWorld
2.1.7CombinationsofExponentialFunctions
2.1.8SolutionsandPropertiesoftheEquations
2.1.9AnIllustration:OxygenDistributioninaRiver
2.2LogisticDistribution
2.2.1TheDifferentialEquationandItsSolution
2.2.2PropertiesoftheLogisticDistribution
2.2.3AnIllustration:TechnologySubstitution
2.2.4AnIllustration:DiffusionofImprovedPastureTechnologyinUruguay
2.2.5AnIllustration:GrowthofPrimeMoverHorsepowerintheU.S.
2.3ConfinedExponentialDistribution
2.3.1ScopeofApplicationsoftheDistribution
2.3.2TheDifferentialEquationwithConstantCoefficients
2.3.3TheDifferentialEquationwithVariableCoefficients
2.3.4VariableTransferCoefficient
2.3.5VariableEquilibriumValue
2.3.6AnIllustration:OxygenTransferAcrossaWaterSurface
2.3.7AnIllustration:BiochemicalOxygenDemand
2.3.8AnIllustration:GrowthofHumans
2.3.9AnIllustration:PublicInterestinaNewsEvent
2.4CombinationoftheLogisticDistributionandtheConfinedExponentialDistribution
2.4.1ComparisonoftheTwoDistributions
2.4.2PhenomenainIndustrialTechnologyTransfer
2.4.3PhenomenainSocialInnovationDiffusion
2.4.4PhenomenainChemicalReactionKinetics
2.4.5PhenomenainthePsychologyofLearning
2.4.6TheDifferentialEquation,ItsSolutionandProperties
2.4.7AnIllustration:AdoptionofaTornadoWarningDevice
2.4.8CombinationoftheExponentialFunctionandtheConfinedExponentialDistribution
2.4.9AnIllustration:PopulationofCalifornia
2.5NormalProbabilityDistribution
2.5.1TheNormalProbabilityFunctionandItsFeatures
2.5.2RelationshipBetweentheNormalProbabilityFunctionandtheErrorFunction
2.5.3ApproximateExpressionsfortheNormalFunctionandItsInverse
2.5.4ComparisonoftheLogisticandNormalProbabilityDistributions
2.5.5AnIllustration:AdoptionofHerbicidesbyMexicanBarleyFarmers
2.6PowerLawLogisticDistribution
2.6.1TheDifferentialEquationandItsFeatures
2.6.2TheGrowthCurveandItsProperties
2.6.3TheRichardsFunction
2.6.4AnIllustration:SaleofDevelopmentProperty
2.6.5AnIllustration:GrowthofPineTreesinNewZealand
2.6.6AnIllustration:AdoptionofHybridCornintheUnitedStates
2.7LogisticGrowthwithMigration
2.7.1ImmigrationandEmigration
2.7.2LogisticGrowthwithConstantStocking
2.7.3LogisticGrowthwithConstantHarvesting
2.7.4LogisticGrowthwithVariableHarvesting
2.7.5AnIllustration:FishHarvesting
2.7.6AnIllustration:TheSandhillCrane
2.8EpidemicsandTechnologyTransfer
2.8.1SimpleandGeneralEpidemics
2.8.2TheDifferentialEquationsandPhasePlaneDisplay
2.8.3SolutionstotheDifferentialEquations
2.8.4LogarithmicFormoftheSolutions
2.8.5ATechnologyTransferAnalogy
2.8.6AnIllustration:BombayPlagueof1905-1906
2.9SomeModificationsoftheLogisticDistribution
2.9.1UseofTaylorSeries
2.9.2FirstOrderDifferentialEquations
2.9.3AnIllustration:GrowthofWaterFleasandTrees
2.9.4AnIllustration:SaleofDevelopmentPropertyRevisited
2.9.5SecondOrderDifferentialEquations
2.9.6AnIllustration:Multiplier-AcceleratorModelofaNationalEconomy
3SomeAdditionalFrameworks
3.1GompertzDistribution
3.1.1TheGompertzDistributionandItsFeatures
3.1.2AnIllustration:GrowthofPlantLeaves
3.1.3AnIllustration:DynamicsofTumorGrowth
3.2WeibullDistribution
3.2.1TheWeibullDistributionandItsFeatures
3.2.2AnIllustration:SubstitutionofDieselandElectricLocomotivesforSteamLocomotives
intheUnitedStates
3.3AGeneralizedDistribution
3.3.1CumulativeandDensityDistributionFunctions
3.3.2AGeneralizedSymmetricalFunction
3.3.3ExtremeMaximumValueDistribution
3.3.4ExtremeMinimumValueDistribution
3.3.5AnIllustration:DoseResponseAnalysisofBeetleMortalityData
3.4HyperlogisticDistribution
3.4.1TheDifferentialEquationandSomeExamples
3.4.2SolutiontotheDifferentialEquation
3.4.3SomePropertiesoftheHyperlogisticEquation
3.4.4NumericalExamplesoftheHyperlogisticEquation
3.4.5AnIllustration:AdoptionofaTornadoWarningDeviceRevisited
3.4.6CoalitionandModifiedCoalitionGrowthModels
3.4.7AnIllustration:PopulationoftheWorld
3.4.8AnIllustration:GrowthofthePublicDebtoftheUnitedStates
3.5VariousOtherDistributions
3.5.1ComparisonofDistributionFunctions
3.5.2Arctangent-ExponentialDistribution
3.5.3PearsonTypeVIIDistribution
3.5.4ArctangentDistribution
3.5.5GammaDistribution
3.5.6GeneralizedGammaDistribution
3.5.7AnIllustration:GenerationTimesofCells
3.5.8AnIllustration:PopulationofGreatBritain
4PhenomenawithVariableGrowthCoefficients
4.1LinearlyVariableGrowthCoefficient
4.1.1TheGrowthCurveandItsProperties
4.1.2AnIllustration:GrowthandDeclineofU.S.SailingVessels
4.2HyperbolicallyVariableGrowthCoefficient
4.2.1TheGrowthCurveandItsProperties
4.2.2RelationshiptoPowerLawExponentialGrowth
4.2.3AnIllustration:PopulationoftheGreatPlainsStates
4.3ExponentiallyVariableGrowthCoefficient
4.3.1ExtremeMaximumValueDistribution
4.3.2ExtremeMinimumValueDistribution
4.3.3AnIllustration:SurvivalofRats
4.4SinusoidallyVariableGrowthCoefficient
4.4.1SomeExamplesofOscillatoryPhenomena
4.4.2SimpleHarmonicGrowthCoefficient
4.4.3ExponentiallyDecreasingGrowthCoefficient:TypeI
4.4.4AnIllustration:GrowthofaSpeciesofLandSnails
4.4.5ExponentiallyDecreasingGrowthCoefficient:TypeII
4.4.6AnIllustration:GrowthofCellPopulations
4.4.7SinusoidallyVariableGrowthCoefficientinaPowerLawExponentialEquation
4.4.8AnIllustration:NumberofPatentsIssuedforInventions
5PhenomenawithVariableCarryingCapacities
5.1ExponentiallyVariableCarryingCapacity
5.1.1TheGrowthCurveandItsProperties
5.1.2AnIllustration:FarmPopulationoftheUnitedStates
5.2LogisticallyVariableCarryingCapacity
5.2.1SomePreviousStudies
5.2.2TheGrowthCurveandItsProperties
5.2.3RelativeValuesofGrowthParameters
5.2.4AnIllustration:EnrollmentsinUniversitiesintheUnitedStates
5.3LinearlyVariableCarryingCapacity
5.3.1TheGrowthCurveandItsProperties
5.3.2AnIllustration:HorsesandMulesonU.S.Farms
5.3.3AnIllustration:SteamLocomotivesonU.S.Railroads
5.4HyperbolicallyVariableCarryingCapacity
5.4.1LinearlyChangingCrowdingCoefficient
5.4.2TheGrowthCurvesandItsProperties
5.4.3AnIllustration:GrowthRatesofWheatPlantComponents
5.5SinusoidallyVariableCarryingCapacity
5.5.1CyclicVariationsinGrowthandTransferPhenomena
5.5.2TheGrowthCurveandItsProperties
5.5.3PhasePlaneDisplay
5.5.4ExponentiallyChangingCarryingCapacity
5.5.5AnIllustration:RailwayMileageintheUnitedStates
5.6PowerLawLogisticwithaPowerLawLogisticallyVariableCarryingCapacity
5.6.1ThePowerLawLogistic
5.6.2TheDifferentialEquationandItsSolution
5.6.3AnIllustration:PopulationoftheUnitedStates
6PhenomenawithTimeDelays
6.0.1Introduction
6.0.2TypesandFeaturesofDelayEquations
6.1DiscreteTimeDelayintheExponentialEquation
6.1.1TheDelayDifferentialEquationandItsSolution
6.1.2RootsoftheCharacteristicEquation
6.1.3BehavioroftheSolutions
6.1.4AnIllustration:Tinbergen'sShipbuildingCycle
6.2DiscreteTimeDelayintheLogisticEquation
6.2.1IntroductiontotheDelayDifferentialEquation
6.2.2SolutiontotheDiscreteDelayLogisticFunction
6.2.3NumericalExample
6.2.4AnIllustration:Nicholson'sBlowflies
6.3DistributedTimeDelay:DelayIntegralintheCrowdingTerm
6.3.1TheIntegro-differentialEquation
6.3.2SolutiontotheIntegro-differentialEquation
6.3.3AnIllustration:GrowthandDeclineofthePopulationsofNortheastandEastNorthCentralAmericanCities
6.4DistributedTimeDelay:DelayIntegralinaPollutionTerm
6.4.1TheIntegro-differentialEquationandItsSolution
6.4.2AnApproximateSech-squaredSolution
6.4.3NumericalExamples
6.4.4AnIllustration:GrowthandSelf-ContaminationofBacteria
7PhenomenawithSpatialDiffusion
77.0.1Introduction
7.0.2TheDiffusionEquation
7.1DiffusionfromInstantaneousSources
7.1.1PlaneSource,LineSourceandPointSource
7.1.2RectilinearDiffusionwithConvection
7.1.3AnIllustration:DispersioninPipelines
7.1.4RadialDiffusionwithExponentialGrowth
7.1.5AnIllustration:BiologicalDispersion
7.2DiffusionfromContinuousSource
7.2.1RectilinearDiffusionwithConstantBoundaryCondition
7.2.2AnIllustration:BacterialMotility
7.2.3RectilinearDiffusionwithVariableBoundaryCondition
7.2.4AnIllustration:TemperatureDistributionintheSoil
7.2.5RadialDiffusion
7.2.6AnIllustration:UnsteadyFluidFlowinanAquifer
7.2.7RectilinearDiffusionwithConvection
7.3DiffusionwithReactioninaFiniteRegion
7.3.1DimensionalAnalysis
7.3.2ExponentialGrowthinaFiniteRegion
7.3.3PowerLawExponentialGrowthinaFiniteRegion
7.3.4LogisticGrowthinaFiniteRegion
7.3.5AnIllustration:ZoneofRegulatedFishing
7.4DiffusionwithConvectionandReaction
7.4.1TheDifferentialEquationandItsSolution
7.4.2ExponentialGrowthwithConvectionandDiffusion
7.4.3ExponentialDecaywithConvectionandDiffusion
7.4.4ConvectionandDiffusionwithInterphaseTransfer
7.4.5AnIllustration:ChemicalSoluteRemovalbyAdsorption
7.5DiffusionwithConfinedExponentialGrowth
7.5.1RectilinearDiffusion
7.5.2AnIllustration:HeatTransferfromaRiver
7.5.3RadialDiffusion
7.5.4AnIllustration:PopulationinCities
7.5.5Temporal-SpatialDiffusion
7.5.6AnIllustration:PopulationofLondon
7.6DiffusionwithLogisticGrowth
7.6.1TravelingWaveSolutions
7.6.2APowerLawTravelingWaveSolution
7.6.3AnIllustration:DiffusionofTractorUtilization
7.6.4AnIllustration:AdoptionofHybridCornRevisited
8Conclusion
References
AuthorIndex
SubjectIndex