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

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