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简介：ThepurposeofthispaperistogivearelativelyelementaryanddirectproofoftheDeltaInequality,whichplaysaveryimportantroleinthestudyoftheextremalproblemofquasiconformalmappings.

简介：Theproblemofdecisionmakinginanimpreciseenvironmenthasfoundparamountimportanceinrecentyears.Inthispaper,wedefinevaguesoftrelationandsimilaritymeasureofvaguesoftsets.Usingthesedefinitions,somenovelmethodsofobjectrecognitionfromanimprecisemultiobserverdatahasbeenpresented.Moreover,weintroducethenotionofgeneralizedvaguesoftsetsandstudysomeofitsproperties.Thesimilaritymeasureofgeneralizedvaguesoftsetsisalsopresentedandanapplicationofthismeasureindecisionmakingproblemshasbeenshown.

简介：Thispaperusesgraphicmethodtoanalyzethemechanismofprimenumberformationandtheperiodiccharacteristicsofitsmultipleinnaturalnumbers.TheGoldbach’sconjectureisprovedbytheanalysisdiagrams.

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简介：Inthispaperusinganargumentfrom[1],weproveoneoftheprobabilisticversionofHardy'sinequality.

简介：AconstructiveproofisgivenfortheinversionformulaforzonalfunctionsonSL(2,R).AconcretelyconstructedsequenceofzonalfunctionsareprovedtosatisfytheinversionformulaobtaAnedbyHarish-Chandraforcompactsupportedinfinitelydifferentiablezonalfunctfons.Makinguseofthepropertyofthissequencesomehowsimilartothatofapproximationkernels,theauthorndeducethattheinversionformulaistrueforcontinuouszonalfunctiotmon8L(2,R)somecondition.Theclassicalresultcanbeviewedasacorollaryoftheresultshere.

简介：Inthispaperwe’llproveafundameutalpropertyofthevectorspacebymeansoftheex-tensionfield,i.e.thenumbersoftheelementsofabasisofthevectorspaceVoverthefieldFequaltothedimensions(V:F).

简介：TheonlywayTerabytesofdatacanbeprocessedandanalyzedinareasonabletimeisbyusingparallelprocessingarchitectures.TheParalleROOTFacility,PROOF,isssystemfortheparallelinteractiveanalysisofsuchdatasetsonclustersofheterogeneouscomputers.EarlyprototypeshaveconfirmedthevalidityofthebasicPROOFarchitectureHowever,someimportantworkstillhastobedonebeforePROOFcanbeusedasaproductionfacility.Thebasicarchitectureandtheplanneddevelopmentsaredescribedinthispaper.

简介：软弹性的效果，即，到各向同性地变硬的elasticviscoplastic固体的缩进上的收益力量和塑料压缩的可能性的幼仔模量的比率的相对小的价值被调查。计算为完美地粘住的缩进被执行僵硬锋利的indenter进为缩进建模的柱体一半空间。材料被有限紧张elasticviscoplastic描绘允许的组成的关系塑料以及有弹性的压缩的可能性。软弹性和塑料压缩的可能性显著地减少名字的缩进坚硬的比率产出力量。一种线性关系在名字的缩进坚硬和幼仔模量的比率的对数之间被发现产出力量，但是与一个不同系数与在以前的研究报导比。名字的缩进坚硬为塑料泊松比率的价值相当慢慢地从塑料不可压缩性然后减少为小偏差很快减少不到0.25。为软弹性和塑料压缩的可能性，为缩进坚硬的更低的价值的主要原因与在在在indenter下面的材料的静水力学的压力水平的减小有关。

简介：TheconceptofsoftmatterwasfirstintroducedbyP.G.deGennesinhisacceptancespeechfortheNobelPhysicsPrizein1991.Inmechanicscommunity,however,peopleusuallypreferusingsoftmaterialinsteadofsoftmattertodescribethematerialwhoseenergyassociatedwiththermalmotioniscomparativetotheinteractionenergy.Unlikeintheconventionalcondensedmatter,entropyplaysanimportantandevendeterminativeroleinsoftmaterials.Thisparticularcharacteristicofsoftmaterialgivesbirthtoverycomplexandkaleidoscopicsystems,suchasliquidcrystals,polymers,colloids,granularmaterials,andbiologicalsystems.Softmaterialshavemanyvagariousproperties,includingstrongreactiontoweakstimulus,nonlinearresponse,self-assembly,tonameafew,whichfullyembodythecomplexitiesandparticularitiesinmulti-scalecompositions,structuresandinteractions.Theluxuriantmulti-disciplinenatureandwideapplicationsofsoftmaterialshavesuccessfullyintriguedbothscientistsandengineersworldwide.

简介：在这篇文章，我们在用原来被介绍在的相互作用Morawetz估计为Hartree方程散布的精力上给一个简单证明[5]。

简介：SupposethatDisadivisionringinwhichthereisdefinedananti-automorphismα→(?)isinvolutorial,RisaleftvectorspaceoverD.Usingthegivenanti-automorphismα→(?),itiseasytoturnRintoarightvectorspaceoverDbysetingx(?)=ax.Bilinearformg(x,y)connectingtheleftvectorspaceRandtherightvectorspaceRisaHermitianscalar.

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简介：Nano-particlecaptureisakeyprocessinfltration,separation,andbiomedicalapplications.Hereweexploredthemechanismsofsoftparticlecaptureusingnanofbernetworks.Weidentifedpossiblestatesofthecaptureprocess,whicharedefnedbytheirstructuralandmaterialparameters.Byperformingnumericalanalysis,weprovidedaphasediagramintheparametricspaceofthenetworkstructureandinterfacialadhesion.Theworkprovidesaconceptualmodelforrationaldesignofsyntheticmaterialsinrelatedapplicationsthatfocusontheprotectionagainstorremovalofvirus,aswellasothersoftparticles.

简介：Thispaperaimsatdevelopingastochastic-elasticmodelofasoftelasticbodyadheringonawavysurfaceviaapatchofmolecularbonds.Theelasticdeformationofthesystemismodeledbyusingcontinuumcontactmechanics,whilethestochasticbehaviorofadhesivebondsismodeledbyusingBell'stypeofexponentialbondassociation/dissociationrates.Itisfoundthatforsufficientlysmalladhesionpatchsizeorstressconcentrationindex,theadhesionstrengthisinsensitivetothewavelengthbutdecreaseswiththeamplitudeofsurfaceundulation,andthatforlargeadhesionpatchsizeorstressconcentrationindex,thereexistoptimalvaluesofthesurfacewavelengthandamplitudeformaximumadhesionstrength.

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简介：ThefollowingtheoremisprovedTheorem1.Letqbeapolynomialofdegreen（qPn）withndistinctzeroeslyingintheinterval[-1,1]and△’q={-1}∪{τi:q’（τi）=0,i=1,n-1}∪{1}.IfpolynomialpPnsatisfiestheinequalitythenforeachk=1,nandanyx[-1,1]itsk-thderivativesatisfiestheinequality丨pk（x）丨≤max{丨q（k）（x）丨,丨1/k（x2-1）qk+1（x）+xq（k）（x）丨}.ThisestimateleadstotheMarkovinequalityforthehigherorderderivativesofpolynomialsifwesetq=Tn,whereTnisChebyshevpolynomialleastdeviatedfromzero.SomeotherresultsareestablishedwhichgivesevidencetotheconjecturethatundertheconditionsofTheorem1theinequality‖p（k）‖≤‖qk‖holds.

简介：Anoverviewoftheprogressonpulse-preserving,coherent,nonlinearfiber-basedsupercontinuumgenerationispresented.Thecontextencompassesvariouswavelengthrangesandpumpsources,startingwithsilicaphotoniccrystalfiberspumpedwith1.0μmfemtosecondlasersuptochalcogenidestep-indexandmicrostructuredfiberspumpedfromopticalparametricamplifierstunedtomid-infraredwavelengths.Inparticular,silicaandsilicatebasedall-normaldispersion(ANDi)photoniccrystalfibershavebeendemonstratedforpumpingwithfemtosecondlasersoperatingat1.56μmwiththerecordedspectracovering0.9–2.3μm.Thismatchesamplificationbandsofrobustfiberamplifiersandfemtosecondlasers.Thereviewthereforefocusesspecificallyonthiswavelengthrange,discussingglassandnonlinearfiberdesigns,experimentalresultsonsupercontinuumgenerationuptothefundamentallimitofoxideglassfibertransmissionaround2.8μm,andvariouslimitationsofsupercontinuumbandwidthandcoherence.Specifically,theroleofnonlinearresponseagainsttheroleofdispersionprofileshapeisanalyzedfortwodifferentsoftglassANDifiberspumpedatmorethan2.0μm.Aspatio-temporalinteractionofthefundamentalfibermodewithmodespropagatinginthephotoniclatticeofthediscussedANDifibersisshowntohavepositiveeffectsonthecoherenceofthesupercontinuumatpumppulsedurationsof400fs.Finally,thedesignanddevelopmentofgraded-index,nanostructuredcoreopticalfibersarediscussed.Insuchstructuresthearbitraryshapingofthecorerefractiveindexprofilecouldsignificantlyimprovetheengineeringflexibilityofdispersionandeffectivemodeareacharacteristics,andwouldbeaninterestingplatformtofurtherstudytheintermodalinteractionmechanismsandtheirimpactonsupercontinuumcoherenceforsubpicosecondlaserpumpedsetups.