简介：ThesplittingofpotentialenergylevelsforgroundstateX2ΠgofOx2(x=+1,1)underspin–orbitcoupling(SOC)hasbeencalculatedbyusingthespin–orbit(SO)multi-configurationquasi-degenerateperturbationtheory(SO-MCQDPT).TheirMurrell–Sorbie(M–S)potentialfunctionsaregained,andthenthespectroscopicconstantsforelectronicstates2Π1/2and2Π3/2arederivedfromtheM–Sfunction.TheverticalexcitationenergiesforOx2(x=+1,1)areν[O+12(2Π3/2→X2Π1/2)]=195.652cm1,andν[O12(2Π1/2→X2Π3/2)]=182.568cm1,respectively.Allthespectroscopicdataforelectronicstates2Π1/2and2Π3/2aregivenforthefirsttime.

简介：设P为素数，利用同余及高次丢番图方程的一些结果证明了不定方程组x-1=3py^2，x^2＋x＋1=3z^2仅有正整数解（p，x，y，z）=（7，22，1，13）。

简介：浅谈公式ｘ２＋（ａ＋ｂ）ｘ＋ａｂ＝（ｘ＋ａ）（ｘ＋ｂ）遂宁安居镇中学何旭东十字相乘法是因式分解的一种方法，其灵活性大，难度高。现行义务教材用它分解二次项系数为１和二次项系数不为１的二次三项式，但未提及双十字相乘法。现在我们用公式：ｘ２＋（ａ＋ｂ）ｘ＝...

简介：Inthispaper,westudyseveraliterativemethodsforfindingthemaximal-likesolutionofthematrixequationX+A~*X~(-2)A=I,anddeducesomepropertiesofthemaximal-likesolutionwiththesemethods.

简介：讨论了方程ｘ（ｔ）＝－ｘ＾３（ｔ－１）－ｘ＾３（ｔ－２）周期解的结构。

简介：<正>Foranyintegersa1,a2,a3,a4andcwitha1a2a3a40（modp）,thispapershowsthatthereexistsasolutionX=（x1,x2,x3,x4）∈Z4ofthecongruencea1x12+a2x22+a3x32+a4x42≡c（modp）suchthat‖X‖=max{|x1|,|x2|,|x3|,|x4|}《p1/2logp.

简介：<正>我们通常通过"数形结合"的方法判断过定点的直线与双曲线x2/a2-y2/b2=1能否相切,强调对图形的感知能力。本文拟用严格的代数方法说明定点与双曲线的位置关系对切线条数及切点位置的影响。

简介：设函数f(x)=|α-2x|,α>0,x∈[0,α].设m为大于1的奇数,A_m={x|x/α=h/m,h2~n≡1或2~n≡-1(modm),n∈Z~+).本文研究了f(x)分别包含在区间[0,α]中和集合A_m中的n-周期轨数。所得结果在研究Kaprekar问题中有重要的应用。

简介：使用代数数论和p-adic分析，我们找到了椭圆曲线y^2=x^3＋27x-62上所有的整数点．我们给出了一个全虚四次域的子环上计算基本单位和二次代数数“不相关分解”的方法．

简介：基于定点理论，我们学习存在和非线性的矩阵方程X+A~*X~的最大的Hermitian积极明确的答案的唯一(-2)A=Q，在Q是一个方形的Hermitian积极明确的矩阵和A~的地方*conjugate矩阵A调换。我们也表明一些必要性质并且分析这个答案的敏感。另外，我们关于近似导出可计算出来的错误界限到maximalHermitian非线性的矩阵方程X+A~*X~的积极明确的答案(-2)A=Q。最后，我们进一步概括这些结果到非线性的矩阵方程X+A~*X~(-n)A=Q，在此2是的n≥一个给定的积极整数。

简介：S.M.LozinskiiprovedtheexactconvergencerateatthezeroofLagrangeinterpolationpolynomialsto|x|basedonequidistantnodesin[-1,1].In2000,M.RevergeneralizedS.M.Lozinskii'sresultto|x|α(0≤α≤1).Inthispaperwewillpresenttheexactrateofconvergenceatthepointzerofortheinterpolantsof|x|α(1＜α＜2)..

简介：在不定积分的教学中,我们会碰到形如integralfromn=1（Pn（x）dx）/(（x+Px+q）q?)的积分,如同济二版高等数学

简介：ForquadraticnumberfieldsF=Q(√2pl…pt-1)withprimespj≡1mod8,theauthorsstudytheclassnumberandthenormofthefundamentalunitofF.TheresultsgeneralizenicelywhathasbeenfamiliarforthefieldsQ(√2p)withaprimep≡1mod8,includingdensitystatements.Andtheresultsarestatedintermsofthequadraticformx2+32y2andillustratedintermsofgraphs.

简介：theAlternatingSegmentCrank-Nicolsonschemeforone-dimensionaldiffusionequationhasbeendevelopedin[1],andtheAlternatingBlockCrank-Nicolsonmethodfortwo-dimensionalproblemin[2].Themethodshavetheadvantagesofparallelcomputing,stabilityandgoodaccuracy.Inthispaperforthetwo-dimensionaldiffusionequation,thenetregionisdividedintobands,aspecialkindofblock.ThismethodiscalledthealternatingBandCrank-Nicolsonmethod.

简介：Lithium-aluminum-cobalt-nickeloxideLiAlxCoyNi1xyO2particles,generallyusedascathodeoflithiumbattery,werepreparedbychemicalcoprecipitationfromanaqueoussolutionofLiOH,Al(NO3)3,Co(NO3)2andNi(NO3)2withNH4OH.XRD,SEMandFTIRwereusedtoexaminetheeffectofnickelcontentontheproduct.FTIRpatternsshowedthatincreaseinnickelcontentdecreasedtheabsorptionstrengthofthepeakofspinelstructureoftheproduct,attributedtotheoccupationbynickelinthealuminumsites.Particlesizeandelectricalpropertiesofthelithium-aluminum-cobalt-nickeloxide(abbreviatedasLACNO)particleswerealsodetermined.

简介：SomecharacterizationsoftheconditionalexpectationoperatorsonLebesgue-BochnerspacesL_p(μ,X)aregiven,where1≤p<∞,p≠2.AlsoanexampleisgiventoshowthatthecharacterizationsoftheconditionalexpectationoperatorsonL_p(μ,X)aredifferentfromthatonL_p(μ)_zFinally,arepresentationoftheconstant-preservingcontractiveprojectiononspacesL_p(μ,X)isgotwhen0

简介：X-γradiationbelongtotheionizingradiation.Ionizingradiationsinkstoenergyinorganismbutproduceadisservicetotheorganism.Justasmedicine,thedisserviceoftheradiationtowardsOrganismisdecidedbytoacceptradiationquantify,theradiationquantifywasnameddose.Radiationprotection'sbasicmissionsistowanttoresultthedosetofixquantify.InthissurveythedoseatworkplaceanditssurroundingsenvironmentsofHL-2Adevicewasmeasuredandtheassessmentwasgivenout.

简介：QuantumdynamicscalculationsforthetitlereactionH(2S)+S2(X3-Σg)→SH(X2Π)+S(3P)areperformedbyusingagloballyaccuratedoublemany-bodyexpansionpotentialenergysurface[J.Phys.Chem.A1155274(2011)].TheChebyshevrealwavepacketpropagationmethodisemployedtoobtainthedynamicalinformation,suchasreactionprobability,initialstate-specifiedintegralcrosssection,andthermalrateconstant.Itisfoundnotonlythatthereisareactionthresholdnear0.7eVinbothreactionprobabilitiesandintegralcrosssectioncurves,butalsothatboththeprobabilityandcrosssectionincreasefirstlyandthendecreaseasthecollisionenergyincreases.Theexistenceoftheresonancestructureinboththeprobabilityandcrosssectioncurvesisascribedtothedeeppotentialwell.Thecalculationoftherateconstantrevealsthatthereactionoccurringonthepotentialenergysurfaceoftheground-stateHS2isslowtotakeplace.

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简介：ThespinelLiMn2O4-x(SO4)xcompoundcathodematerialsweresynthesizedbysolid-statereactionofthecalculatedamountsofLiOH·H2O,MnO2andMnSO4.Theresultsoftheelectrochemicaltestdemonstratedthatthesematerialsexhbitedexcellentelectrochemicalproperties.Thehighestreversiblecapacityoftheseseriesofcathodematerialswas-120mAh/g,andafter50cycles,thisreversiblecapacitywasstillaround116mAh/gwithnearly100%reversibleefficiency,whichrevealedthatdopedsulfateioncouldimprovethestructuralstabilityofspinel.