简介：在现在的纸，我们学习几个复杂变量的分析函数的多项式近似。几个复杂变量的分析功能的概括类型的描述以近似和插值错误被获得了。

简介：Thecurrentcalibrationfunctionusedincalculatingthemagnitudeofnaturalearthquakeswithin5kmisaconstant;afactthatcausesseveralseriousdifficultiesforthecalculationofthemagnitudeofsmallandshallow-focusearthquakes.Accordingtotheattenuationlawofexplosionsandthepropagationtheoryofelasticwaves,thecalibrationfunctioniscalculatedfornearfieldquakesfrom0kmto5km.Magnitudesoftwoaftershocksequencesarecalculated.Themagnitudesofmostexplosionearthquakesaresmall,rangingmainlyfrommagnitude0.5to1.0.TheM-tchartoftheexplosiveaftershocksiscompletelydifferentfromthatofstrongearthquakeaftershocks.Itnotonlyshowspositivecolumnarlinesindicatinglargemagnitudesbutalsoshortnegativecolumnarlinesindicatingsmallmagnitudes.

简介：Alargeclassoflinearstructuralfunctions(LSF)satisfyingtheconditionofcorrelationalimmunityoforderoneareconstructedbystudyingthelinearstructuralBooleanfunctions.Withthesenewfoundedfunctions,theknownenumerationboundsofcorrelation-immunefunctionsoforderonearegreatlyimproved.Infact,thebest,uptonow,lowerboundisfound.

简介：ForRiemannianmanifoldswithameasure,westudythegradientestimatesforpositivesmoothf-harmonicfunctionswhenthe∞-Bakry-EmeryRiccitensorandRiccitensorareboundedfrombelow,generalizingtheclassicalonesofYau(i.e.,whenfisconstant).

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

简介：Manynonlinearquantumopticalphysicsphenomenaneedmoreaccuratewavefunctionsandcorrespondingenergyorquasienergylevelstoaccountfor.AnanalyticexpressionofwavefunctionswithcorrespondingenergylevelsforanatomicelectroninteractingwithaphotonfieldispresentedasanexactsolutiontotheSchrSdinger-likeequationinvolvedwithbothatomicCoulombinteractionandelectron-photoninteraction.Thesolutionisanaturalgeneralizationofthequantum-fieldVolkovstatesforanotherwisefreeelectroninteractingwithaphotonfield.ThesolutionshowsthatanN-levelatominlightformstationarystateswithoutextraenergysplittinginadditiontotheFloquetmechanism.Thetreatmentdevelopedherewithcomputingcodescanbeconvenientlytransferredtoquantumopticsinclassical-fieldversionasresearchtoolstobenefitthewholephysicscommunity.

简介：让π和π′是GLm(ℚ)和GLm′的自形的无法缩减的尖代表(ℚ),分别地，并且L(s，π×)Rankin-SelbergL功能被纳入π和π′。没有假定概括Ramanujan，推测(GRC)，作者为L给概括素数定理(s，π×)什么时候π≅π′。结果在2007概括刘和汝的相应结果。

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简介：Inthispaper,westudyaspecialclassoffractalinterpolationfunctions,andgivetheirHaar-waveletexpansions.Onthebasisoftheexpansions,weinvestigatetheH(o|¨)ldersmoothnessofsuchfunctionsandtheirlogicalderivativesoforderα.

简介：Theobjectofthispaperistostudythenon-tangentialincreasingpropertiesofpositiveharmonicfunctionuinLipschitzdomainbymeansofMartinrepresentationtheory,Anecessaryandsufficientconditionofthecontrolofgrowthofunearanyfixedboundarypointisobtained.Itisshownthatthenon-tangentialincreasingdegreeofunearaboundarypointisexactlythelocaldegreeofitsrepresentationmeasurewithrespecttotheharmonicmeasure.Someexanlplesaregiven.

简介：Inthispaper,basedonastochasticmode!forinputsandweights,andinviewofthedisturbanceofcorrelativeandlargeinputandweighterrors,ageneralalgorithmtoobtaintheoutputerrorcharacteristicsofaclassofmultilayeredperceptronswiththresholdfunctionsisproposedbyusingstatisticalapproach.Furthermore,theformulatocalculatetherobustnessofthenetworksisalsogiven.Theresultofcomputersimulationindicatesthecorrectnessofthealgorithm.

简介：Inthisstudy,anewmethodologybasedontheHadamardmatrixisproposedtoconstructquantumBooleanfunctionsfsuchthatf=I2n-2P2n,whereI2nisanidentitymatrixoforder2nandP2nisaprojectivematrixwiththesameorderasI2n.TheenumerationofthisclassofquantumBooleanfunctionsisalsopresented.

简介：LetMbead×dexpansivematrix,andFL2(Ω)beareducingsubspaceofL2(Rd).ThispapercharacterizesboundedmeasurablesetsinRdwhicharethesupportsofFouriertransformsofM-refinableframefunctions.Asapplications,wederivethecharacterizationofboundedmeasurablesetsasthesupportsofFouriertransformsofFMRA(W-typeFMRA)framescalingfunctionsandMRA(W-typeMRA)scalingfunctionsforFL2(Ω),respectively.Someexamplesarealsoprovided.

简介：Anexplicitfull-fieldexpressionoftheGreen’sfunctionsforanisotropicpiezoeleetricbimateri-alswithaslippinginterfaceisderived.Whentheelectro-elasticsingularityreducestoapraydislocationindisplacementandelectricpotential,interactionenergy,betweenthedislocationandthebimaterialsisobtainedexplicitlywhilethegeneralizedforceonthedisloeationisgiveninarealformwhiehisalsovalidfordegener-atematerials.Theinvestigationdemonstratesthatthehoundaryconditionsatlheslippinginterfacebetweentwopiezoelectricmaterialswillexertaprominentinfluenceonthemobilityofthedislocation.

简介：LetEbeacompacts-setsofR^n,TheauthorsdefineanorthonormalsystemФoffunctionsonEandobtainthat,foranyf(x)∈L^l(E1H^8),theFourierseriesoff1withrespecttoФ,isequaltof(x)atH^8-a.e-x∈E.Moreover,foranyf∈L^p(E,H^8)(p≥1),thepartialsumsoftheFourierseries,withrespecttoФ,offconvergestofinL^P-norm.

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简介：ThecontentsofbiogenicelementsinChinamarginalseasedimentsarerelatedtotheirgrainsizes,rivertransport,etal.Ingeneral,thefinerthegrainsizeis,thehigherthecontentsoforganicmatterandOC,N,Pare,thelowerthecontentsofSandSiare.ThebiogeochemicalenvironmentsofsedimentsarerelatedtoEh,pH,temperaturecontentofOC,Fe3+/Fe2+radio,waterdynamicscondition,grainsizeofsediment,Ssysteminsedimentinterstitialwaters,etal.,andtheyinfluencetheearlydiagenesesandcycleofbiogenicelementsinsediments.InmostregionsofChinamarginalsea,thefluxdirectionsofS2-,HS-,3-NH4+H4SiO4,PO4,acrossthesediment-waterinterfacearefromsedimenttotheoverlyingseawater,thefluxdirectionsofSO42-,HCO3-,NO3-,NO2-acrossthesediment-waterinterfacearefromtheoverlyingseawatertosediment.Theirrigationoflivingthingsisimportantinthecycleofthebiogenicelementsacrosssediment-waterinterfaces.

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简介：TheauthorsprovethespaceofharmonicfunctionswithpolynomialgrowthofafixedrateonacompletenoncompactRiemannianmanifoldwithasymptoticallynonnegativecurvatureisfinitedimensional.