简介：<正>ThispaperprovidesapolyhedraltheoryongraphsfromwhichthecriteriaofWhit-neyandMacLanefortheplanarityofgraphsareunified,andabriefproofoftheGausscrossingconjectureisobtained.

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简介：Inthenormal-modetheoryofMorse,itgivesaseriesofnormalmodesasthesolutionofforcedvibrationinaroom.Butactuallythereisalwaysthedirectradiationbesidesthenormalmodeswhichrepresentthereverbrantsoundfieldonly.Thereasonisthatthenormalmodeswereassumedonlyinthesource,andnaturallynormalmodesonlyareobtainedinthesolution.Atheoryofdoublesourceisproposed,thatthesoundsourceisboththesourceofthedirectradiationasifinfreespacebeforetheboundarysurfaceswerereachedbythedirectradiation,andafterthefirstreflectionfromtheboundarysurfaces,thesourceofthereflectedwavelets,randomlydistributedbothinspaceanintimeontheboundarysurfacesthatbuildupthenormalmodesafterfurtherreflections.Thewaveequationisformedaccordingly,andthesolutionofthewaveequation,thesoundfieldinaroom,containsexplicitlyboththedirectradiationandthereverberantsoundformedofnormalmodes.Theapproximatemeansquaresoundpressureisfoundtobethedircetsounddeterminedbythesoundpowerofthesource,andreverberantsounddeterminedbythesoundpowerreducedbyafactorofπ/2,differentslightlyfromtheresultobtainedfromenergyconsideration,ifthesourceispuretone.Thereisessentiallynodifferenceforasourceofbandnoise.

简介：Anewformofdamagetheoryofmaterialsisproposed,thatisvalidforthecaseofnonconservativestresses.Thepartialentropy,strainandmicrostructureparametersaretakenasthestatevariables.Withoutassumingthefreeenergytobeastatefunction,thebasicgoverningequationsarederived.Accordingtothebalanceofreleasedanddissipatedenergy,thegeneralformofdamageevolutionequationisobtained.Further,assumingtheexistenceofindependentdamagemechanisms,thenormalityofdamageevolutionequationisproven.Thegeneralizeddamagevariablesaredis-cussed.Finally,someexamplesaregiventoshowtheapplicationsofthetheory.

简介：Inthispaper,weproposetheconceptofcohomologicaloperator.Concretely,wesuggestthecohomologicaldifferentialoperator,correlativecohomologicaldifferentialoperatorandextensivecohomologicaldifferentialoperatorandbringcovariantderivativeintotheextensivecohomologicaldifferentialoperator,WeconstructonetypeofnonlineardifferentialequationsbyextensivecohomologicaldifferentialoperatorandcomparetheobtainedresaleswiththeYang-Millsequation.

简介：Inthispaper,severalusuallyusedpolynomialinterpolationmethodsareexplainedinviewofvectorbasisanddimensioninlinearalgebratheory.Usingtransitionmatrixes,generalconversionformulabetweenthebasisfunctionsetsofthesepolynomialinterpolationmethodsaregiven.Anexamplealsoshowstheeffectivenessoftheresults.

简介：InthispapersomeequivalencedefinitionsaregivenfornativespaceswhichwereintroducedbyMadychandNelsonandhavebecomeinfluentialinthetheoryofradialbasisfunctions.Theabstractelementsinnativespacesareinterpreted.Moreover,WeinrichandIske'stheoriesareunified.

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简介：我们计算在光滑的度量标准的情况下在FJRW理论定义的真实Cauchy-Riemann操作员的索引。为圆柱的度量标准，我们在加权的Sobolev空格学习在Witten地图和重量的线性化的操作符的索引之间的关系。

简介：在光线的基础功能的理论，数学家们把光线的基础功能的translates的线性联合用作interpolants。这些线性联合的集合是一个normed向量空格。这个空格能被完成并且变得一个Hilbert空格，叫了本国的空间，它在最后十年是很重要的。本国的空格然后包含不是光线的基础函数的线性联合的一些抽象元素。这些抽象元素的意思充分不被知道。这份报纸为这些元素论述一些解释。本国的空格被嵌进一些著名空格。例如，Sobolev空间被显示是一个本国的空格。因为许多微分方程在Sobolev空间有答案，我们能因此接近由光线的基础功能的线性联合的答案。而且，嵌进本国的空间L2()的著名问题被作者也解决。

简介：首先，使用关系(2.3)，(2.4)，并且(2.5)，我们定义复杂克利福德代数学和Witt基础。第二，我们利用Witt基础在对珍视的函数起作用的Kaehlermanifolds上定义操作符。另外，在上面的操作员之间的关系和Hodge-Laplace操作员被说服。然后，为珍视的功能的Borel-Pompeiu公式通过设计一个矩阵迪拉克操作员被导出并且2

简介：Inthispaper,theauthorfirstgivesaconjugacy-classversionofCaminahypothesesandthenapplystheCaminagrouptheorytodiscussingtwoclassesoffinitegroups.

简介：Inthispaper,anonlocaltheoryoffractureforbrittlematerialshasbeensystematicallydevel-oped,whichiscomposedofthenonlocalelasticstressfieldsofGriffithcracksofmode-Ⅰ,ⅡandⅢ,theasymptoticformsofthestressfieldsattheneighborhoodofthecracktips,andthemaximumtensilestresscriterionforbrittlefracture.Asanapplicationofthetheory,thefracturecriteriaofcracksofmode-Ⅰ,Ⅱ,ⅢandmixedmodeⅠ-Ⅱ,Ⅰ-Ⅲaregivenindetailandcomparedwithsomeexperimentaldataandthetheoreticalresultsofminimumstrainenergydensityfactor.

简介：LetXdenoteacomplexanalyticmanifold,andletAut(X)denotethespaceofinvertiblemapsofagerm(X,a)toagerm(X,b);thisspaceisobviouslyagroupoid;roughlyspeaking,a'Liegroupoid'isasubgroupoidofAut(X)definedbyasystemofpartialdifferentialequations.ToafoliationwithsingularitiesonXoneattachessuchagroupoid,e.g.thesmallestonewhoseLiealgebracontainsthevectorfieldstangenttothefoliation.Itiscalled'theGaloisgroupoidofthefoliation'.Someexamplesareconsidered,forinstancefoliationsofcodimensionone,andfoliationsdefinedbylineardifferentialequations;inthislastcaseonerecuperatestheusualdifferentialGaloisgroup.

简介：这篇论文的主要目的是学习弱Hopf代数学的扭动的理论；给一个等价在之间(编织)在原版上的弱Hopf双性人模块的monoidal范畴；扭曲的弱Hopf代数学将从Oeckl(2000)概括结果。

简介：AimsandScope:NumericalMathematics:Theory,MethodsandApplications(NM-TMA)publisheshigh-qualityoriginalresearchpapersontheconstruction,analysisandapplicationofnumericalmethodsforsolvingscientificproblems.Importantresearchandexpositorypapersdevotedtothenumericalsolutionofmathematicalproblemsarisinginallareasofscience

简介：Onthebasisofthemedicalandmechanicalanalysisandexplanationsinthispaperthevisco-elasticsimplysupportedbeammodelisproposedtotreatthedisplacementwaveofthebloodvessels.Therelationshipsbetweenthedisplacementwaveandbloodvesselelasticityaswellastheviscousdissipationofthebloodandbloodvesselareobtained.ThecorrespondingrelationsofsuchkindsofpulsesinthetraditionalChinesemedicineassmoothpulse,surfacepulseanddeeppulsetothedisplacementwavesofbloodvesselsarealsofound.Thecomputationalresultsareingoodagreementwiththoseacquiredintheexperimentswithultrasonicwave.

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