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简介：Thispaperusesgraphicmethodtoanalyzethemechanismofprimenumberformationandtheperiodiccharacteristicsofitsmultipleinnaturalnumbers.TheGoldbach’sconjectureisprovedbytheanalysisdiagrams.

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简介：ThispapergivesatutorialonhowtoproveLyapunovtypecriteriabyoptimalcontrolmethods.Firstly,weconsiderstabilitycriteriaonHill'sequationswithnonnegativepotential.Byoptimalcontrolmethodsdevelopedin1990s,weobtainseveralstabilitycriteriaincludingLyapunov'scriterion,Ne..gauzandLidski'scriterion.Secondly,wepresentstabilitycriteriaonHill'sequationswithsign-changingpotentialinwhichBrog'scriterionandKrein'scriterionareincluded.

简介：Thispaperaimstoinvestigatethehydrodynamicbehaviorofatensionlegplatform(TLP)whenthetendonconnectionanglesarevariedat90°,70°,50°,and30°.ThreedifferenttypesofloadingconditionsareappliedtotheTLP.Conditionsinclude100-yearhurricanestormperiod,regularwavesandnoloading.TheTLPdisplayedmajorresponseinthepitchdegreeoffreedom.Amaximumreductionof14%inpitchrotationisachievedwhen100-yearhurricanestormconditionsareappliedtotheTLP.Thisoccurredin0°loadingsat30°tendonconnectionangleascomparedto90°tendonconnectionangle.Reductioninpitchrotationisalsoachievedintheregularwaveloadings.Amaximumof9%inpitchrotationisachievedduring0°waveloadingat30°tendonconnectionangleascomparedto90°.Whenthetendonconnectionangleisreducedfrom90°to30°,thenaturalfrequencyoftheTLPincreasedbothinpitchandyawdegreesoffreedomby2.55%and2.40%,respectively.

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简介：通过5-甲基-7-甲氧基异黄酮与盐酸羟胺的缩合制得中间产物4-苯基-5-（2-羟基-4-甲氧基-6-甲基苯基）异恶唑,然后经过光异构化反应合成了4-甲氧基-6-甲基-7a-苯基苯并吡喃并[2,3-b]氮丙啶-7-酮,并采用IR,NMR,HRMS和单晶X-衍射分析对其结构进行了表征.单晶X-衍射分析结果表明：标题化合物属于单斜晶系,空间群P2（1）/n.在其晶体结构中,存在着氢键及芳香堆积作用,这些作用将标题化合物分子组装成了三维网络结构.

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简介：In1929,AmericanastronomerHubblefirstdiscoveredthattherecessionalvelocityofagalaxyincreaseswithitsdistancefromtheearth,andthereforeputforwardHubble’slaw.ItisconsideredthefirstobservationalbasisfortheexpansionoftheuniverseandtodayservesasoneofthepiecesofevidencemostoftencitedinsupportoftheBigBangmodel.SincethentheastrophysicscommunityhasbelievedthattheuniverseisinaconstantrateofexpansionuntilSaulPermutter,BrianPaulSchmitandAdamGuyRieesdiscoveredtheacceleratingexpansionoftheuniversethroughobservationofseveraldozendistantsupernovasin1998,whothenwontheNobelPrizeinPhysics2011.Buthumanstillcannotcompletelyexplainthephenomenonthattheuniverseisexpandingatanever-acceleratingrate.Thustheauthorofthispaperstudiedtheoriginandevolutionofgalaxiesagain,andrevealedthestructureofgalaxyandprovedHubble’slaw,thenrevealedthetruthabouttheexpansionoftheuniverseaswellasdarkmatteranddarkenergy.

简介：Head-oncollisionbetweentwohydroelasticsolitarywavespropagatingatthesurfaceofanincompressibleandidealfluidcoveredbyathinicesheetisanalyticallystudiedbymeansofasingularperturbationmethod.TheicesheetisrepresentedbythePlotnikov-TolandmodelwiththehelpofthespecialCosserattheoryofhyperelasticshellsandtheKirchhoff-Loveplatetheory,whichyieldsthenonlinearandconservativeexpressionforthebendingforces.TheshallowwaterassumptionistakenforthefluidmotionwiththeBoussinesqapproximation.TheresultinggoverningequationsaresolvedasymptoticallywiththeaidofthePoincar-Lighthill-Kuomethod,andthesolutionsuptothethirdorderareexplicitlypresented.Itisobservedthatsolitarywavesaftercollisiondonotchangetheirshapesandamplitudes.Thewaveprofileissymmetricbeforecollision,anditbecomes,aftercollision,unsymmetricandtitledbackwardinthedirectionofwavepropagation.Thewaveprofilesignificantlyreducesduetogreaterimpactsofelasticplateandsurfacetension.Agraphicalcomparisonispresentedwithpublishedresults,andthegraphicalcomparisonbetweenlinearandnonlinearelasticplatemodelsisalsoshownasaspecialcaseofourstudy.