简介:Thefollowingpartialdifferentialequationsarestudied:generalizedfifth-orderKdVequation,waterwaveequation,Kupershmidtequation,couplesKdVequation.Theanalyticalsolutionstotheseproblemsviausingvariousansaizesbyintroducingasecond-orderordinarydifferentialequationarefoundout.
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简介:Thefluidized-bedpolymerizationprocesshasbeeninusefordecades.Fromthemanufacturer'sperspectiveitisdesirabletoimprovetechnologywithoutmajormodificationofthereactorsystem.Therefore,inordertomeetthedemandfornewproductsormoreefficientreactoroperation,manufacturersprefertoimprovethecatalystsysteminthemostcosteffectivemanner.Usingpolypropyleneproductionasanexample,somerecentadvancesinfluidized-bedpolymerizationtechnologyarepresented.
简介:Accordingtothebasicideaofdual-complementarity,inasimpleandunifiedwayproposedbytheauthor,somebasicprinciplesindynamictheoryofelasticmaterialswithvoidscanbeestablishedsys-tematically.Inthispaper,animportantintegralrelationintermsofconvolutionsisgiven,whichcanbecon-sideredasthegeneralizedprincipleofvirtualworkinmechanics.Basedonthisrelation,itispossiblenoton-lytoobtaintheprincipleofvirtualworkandthereciprocaltheoremindynamictheoryofelasticmaterialswithvoids,butalsotoderivesystematicallythecomplementaryfunctionalsfortheeight-field,six-field,four-fieldandtwo-fieldsimplifiedGurtin-typevariationalprinciples.Furthermore,withthisapproach,thein-trinsicrelationshipamongvariousprinciplescanbeexplainedclearly.
简介:BytheaidofanideaoftheweightedENOschemes,someweight-typehigh-resolutiondifferenceschemeswithdifferentordersofaccuracyarepresentedinthispaperbyusingsuitableweightsinsteadoftheminmodfunctionsappearinginvariousTVDschemes.Numericalcomparisonsbetweentheweightedschemesandthenon-weightedschemeshavebeendoneforscalarequation,one-dimensionalEulerequations,two-dimensionalNavier-StokesequationsandparabolizedNavier-Stokesequations.
简介:Basedonthegeneralconservationlawsincontinuummechanics,theEulerianandLagrangiandescriptionsofthejumpconditionsofshockwavesin3-dimensionalsolidswerepresentedrespectively.Theimplicationofthejumpconditionsandtheirrelationsbetweeneachother,particularlytherelationbetweenthemassconservationandthedisplacementcontinuity,werediscussed.Meanwhiletheshockwaveresponsecurvesin3-dimensionalsolids,i.e.theHugoniotcurveswereanalysed,whichprovidethefoundationforstudyingthecouplingeffectsofshockwavesin3-dimensionalsolids.
简介:Basedontheclassical(matrixtype)input-outputanalysis,atypeofnonlinear(continuoustype)conditionalLeontiefmodel,input-outputequationwereintroduced,aswellasthreecorrespondingquestions,namely,solvability,continuityandsurjectivity,andsomefixedpointandsurjectivitymethodsinnonlinearanalysiswereusedtodealwiththesequestions.Asaresult,themaintheoremsareobtained,whichprovidesomesufficientcriterionstosolveabovequestionsdescribedbytheboundarypropertiesoftheenterprise'sconsumingoperator.