简介：Inthispaper,westudyRényi'sproblemandotherrelatedproblemsabouttheadditivefunctionsinshortintervals.Ascorollaries,weimproveIvic'sresults.

简介：ＡＲＯＮＳＯＮ＇ＳＥＳＴＩＭＡＴＥＳＡＮＤＣＯＮＤＩＴＩＯＮＡＬＤＩＦＦＵＳＩＯＮＰＲＯＣＥＳＳＥＳＱＩＡＮＺＨＯＮＧＭＩＮ（钱忠民）ＷＥＩＧＵＯＱＩＡＮＧ（魏国强）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｔａｔｉｓｔｉｃｓ，ＥａｓｔＣｈ...

简介：TheConwaypotentialfunction(CPF)forcoloredlinksisaconvenientversionofthemultivariableAlexander–Conwaypolynomial.WegiveaskeincharacterizationofCPF,muchsimplerthantheonebyMurakami.Inparticular,Conway’s"smoothingofcrossings"isnotintheaxioms.Theproofusesareductionschemeinatwistedgroup-algebraP_nB_n,whereB_nisabraidgroupandP_nisadomainofmulti-variablerationalfractions.Theproofdoesnotusecomputeralgebratools.Aninterestingby-productisacharacterizationoftheAlexander–Conwaypolynomialofknots.

简介：Inthispaper,thecycle’sstructureofembeddedgraphsinsurfacesarestudied.Accordingtothemethodoffundamentalcycles,thesetC(Ccontainsallshortest)isfound.AundirectedgraphGwithnverticeshasatmostO(n5)manyshortestcycles;IftheshortestcycleofGisoddcycle,thenGhasatmostO(n3)manyshortestcycles;IfGhasbeenembeddedinasurfaceSg(Ng,gisaconstant),thenithasatmostO(n3)shortestcycles,moreover,iftheshortestcycleofGisoddcycle,then,GhasatmostO(n2)manyshortestcycles.WecanfindacyclebaseofG,thenumberofoddcyclesofG,thenumberofevencyclesofG,thenumberofcontractiblecyclesofG,thenumberofnon-contractiblecyclesofG,arealldecided.IftheΠ-embeddedgraphGhasΠ-twosidedcycles,then,CcontainsashortestΠ-twosidedcycleofG,thereisapolynomiallyboundedalgorithmthatfindsashortestΠ-twosidedcycleofaΠ-embeddedgraphG,thenewandsimplesolutionsabouttheopenproblemofBojanMoharandCarstenThomassenareobtained.

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简介：Thispaperproposesaformallystrongerset-valuedClaxke'sfixedpointtheorem.Bythis-theoremwecanimproveafixedpointtheoremforweaklyinwardcontractionset-valuedmappingofD.DowingandW.A.Kirk.

简介：Byusingthefundamentalequationsofaxisymmetricshallowshellsofrevolution,thenonlinearbendingofashallowcorrugatedshellwithtaperunderarbitraryloadhasbeeninvestigated.ThenonlinearboundaryvalueproblemofthecorrugatedshellwasreducedtothenonlinearintegralequationsbyusingthemethodofGreen'sfunction.Tosolvetheintegralequations,expansionmethodwasusedtoobtainGreen'sfunction.ThentheintegralequationswerereducedtotheformwithdegeneratecorebyexpandingGreen'sfunctionasseriesofcharacteristicfunction.Therefore,theintegralequationsbecomenonlinearalgebraicequations.Newton'siterativemethodwasutilizedtosolvethenonlinearalgebraicequations.Toguaranteetheconvergenceoftheiterativemethod,deflectionatcenterwastakenascontrolparameter.Correspondingloadswereobtainedbyincreasingdeflectiononebyone.Asanumericalexample,elasticcharacteristicofshallowcorrugatedshellswithsphericaltaperwasstudied.Calculationresultsshowthatcharacteristicofcorrugatedshellschangesremarkably.Thesnappinginstabilitywhichisanalogoustoshallowsphericalshellsoccurswithincreasingloadifthetaperisrelativelylarge.Thesolutionisclosetotheexperimentalresults.

简介：AradialfunctioncanbeexpressedbyitsgeneratorthroughThepositivedefiniteofthefunctionplaysanimportantroteintheradialbasisinterpolation.WecannaturallyuseBochner’sTheoremtocheckifispositivedefinite.Thisrequireshoweveran-dhnensiotialFouriertransformationanditisnotveryeasytocalculate.Furthermoreinalotofcaseswewilluseforspacesofvariousdimensionstoo,thenforeveryfixednweneeddotheFouriertransformationoncetocheckifthefunctionispositivedefiniteinthen-di-mensionalspace.Thecompletelymonotonefunction:,whichisdiscussedin[4]ispositivedefiniteforarbitraryspacedimensions.Withthistechniquetvecanveryeasilycharacterizethepositivedefinite,ofaradialfunctionthroughitsgenerator.Unfortunatelythereisonlyaverysmallsubsetofradialfunctionwhichiscompletelymonotone.Thusthiscriterionexcludedalotofinterestingfunctionssuchascompactlysupportedradialfunction,whcihareveryusefulinapplic

简介：WeconductedtheresearchonthecalculationoftheJordannormalformofamatrixfrom1993to1998.Inthisperiod,weobtainedsometheoreticalresults,alsodevelopedandimplementedaseriesofalgorithmsforthetheoreticalresults.Nowthisresearchiscompletedtosomedegree.TheGolub-Wilkinson’sProblemComputingtheJordandecompositionofamatrix,introducedbyG.H.GolubandJ.

简介：Mardia(1970)definedameasureofmultivariatekurtosisandderiveditsasymptoticdistributionforsamplesfromamultivariatenormalpopulation.SomenewresultsonellipticaldistributionsareusedtoextendMardia’sresultstosamplesfromanellipticaldistribution.Theseresultsprovideamethodfortestinghypothesesonthekurtosisparameterofellipticaldistributions.AnappendixprovidesextensionsofKendallandStuart’s(1977)standarderrorsofbivariatemomentstothethirdandfourthorder.

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简介：AhighlyefficienttotalsynthesisofS-(+)-tylophorinehasbeenaccomplishedinfullyasymmetricfashion.

简介：ExplicitexpressionsofMori-Tanaka’stensorforatransverselyisotropicfiberreinforcedUDcompositearepresented.Closed-formformulaefortheeffectiveelasticpropertiesofthecompositeareobtained.Ina3Dsense,theresultingcompliancetensorofthecompositeissymmetric.Nevertheless,the2DcompliancetensorbasedonadeterioratedMori-Tanaka’stensorisnotsymmetric.Noristhecompliancetensordefineduponadeteriorated2DEshelby’stensor.Thein-planeeffectiveelasticpropertiesgivenbythosethreeapproachesaredifferent.AdetailedcomparisonbetweenthepredictedresultsobtainedfromthoseapproacheswithexperimentaldataavailableforanumberofUDcompositesismade.更多还原

简介：导出了迁移方程的扩散近似方程,说明了它的离散纵标方法在区间内和边界上都有扩散极限,它的解关于一致地收敛于迁移方程的解.其收敛性的证明是依据其渐近扩散展开式,在边界层上得到的误差估计逼近其离散纵标方法的解.

简介：对于圆锥型和棱锥型Hamiltonian的Eikonal型方程，本文给出了一种几何方法，得出其初值问题解的表达式并且说明由此式给出的解为原初值问题的粘性解．首先用一个凸函数序列逼近Eikonal型方程中的Hamiltonian，再由Hopf-Lax公式给出方程序列的粘性解，最后证明了该粘性解序列会收敛到Eikonal方程的粘性解．

简介：用变分方法得到一类非线性差分方程多重周期解的存在性．我们的结果推广了Cai，Yu和Guo[Comput．Math．Appl．，52（2006），1630-1647]的结果，并且这里给出的证明显著地简化了．

简介：复习目标了解有关方程、方程组的概念；能正确、熟练地解一元一次方程、一次方程组和一元二次方程；掌握分式方程的解法并会验根；掌握由一个二元一次方程和一个二元二次方程组成的方程组的解法；掌握一元二次方程根的判别式及应用；能正确列出方程或方程组解应用题．

简介：建立了一维p-laplacian方程(1)的一切解均为非振动的必要条件.所得定理改进了Kusano等在文[4]中的相应结果.