简介:LetMbeapositivequaternionicKhlermanifoldofdimension4m.Wealreadyshowedthatifthesymmetryrankisgreaterthanorequalto[m/2]+2andthefourthBettinumberb_4isequaltoone,thenMisisometrictoHP~(m).Thegoalofthispaperistoreportthatwecanimprovethelowerboundofthesymmetryrankbyoneforhighereven-dimensionalpositivequaternionicKahlermanifolds.Namely,itisshowninthispaperthatifthesymmetryrankofMwithb_4(M)=1isgreaterthanorequaltom/2+1form≥10,thenMisisometrictoHP~m.OneofthemainstrategiesofthispaperistoapplyamoredelicateargumentofFrankeltypetopositivequaternionicKhlermanifoldswithcertainsymmetryrank.
简介:提出了点集Bézier曲线的概念,给出了点集Bézier曲线的性质及细分算法.按照点集算术的定义,当点集是长方形闭域或圆盘时,点集Bézier曲线就是区间Bézier曲线或圆盘Bézier曲线,因此,点集Bézier曲线是对区间Bézier曲线和圆盘Bézier曲线的推广.
简介:一、填空题(每空3分,共33分)1.当x=时,分式|x|-2x-2的值为零.2.在分式nm中,当时,分式无意义,当时,分式的值为零.3.约分14a5b363ab4c=.4.若a-1a=1,则a2+a-2=.5.若a-bb=23,则ab=.6.当x时,代数式2x-3-1x+2+3x2+1有意义.7.如果1x-3+1=ax-3会产生增根,那么a的值应是.8.若分式x-32x+1的值为负,则x的取值范围为.9.(ba+ab)x=ab-ba-2x (a+b≠0),则x=.10.化简1+11-11+1x=.二、选择题(每小题4分,共32分)1.分式|m+n|m+n的值是( ).(A)1 (B)-1 (C
简介:ThisstudyfocusesontheanisotropicBesov-LionstypespacesBp,θl(Ω;E0,E)associatedwithBanachspacesE0andE.Undercertainconditions,dependingonl=(l1,l2,…,ln)andα=(α1,α2,…,αn),themostregularclassofinterpolationspaceEαbetweenE0andEarefoundsothatthemixeddifferentialoperatorsDαareboundedandcompactfromBp,θl+s(Ω;E0,E)toBp,θs(Ω;Eα).Theseresultsareappliedtoconcretevector-valuedfunctionspacesandtoanisotropicdifferential-operatorequationswithparameterstoobtainconditionsthatguaranteetheuniformBseparabilitywithrespecttotheseparameters.BytheseresultsthemaximalB-regularityforparabolicCauchyproblemisobtained.Theseresultsarealsoappliedtoinfinitesystemsofthequasi-ellipticpartialdifferentialequationsandparabolicCauchyproblemswithparameterstoobtainsufficientconditionsthatensurethesameproperties.
简介:让一,b,k,r是有1一b和r的nonnegative整数2。让G是有$n的顺序n的一张图>\tfrac{{(+b)(r(+b)-2)+ak}}{一}$。在这份报纸,我们首先为部分的所有显示出描述(一,b,k)批评的图。然后使用结果,我们证明G都是部分的(一,b,k)批评如果$\delta(G)\geqslant\tfrac{{(r-1)b^2}}{一}+k$并且$|N_G(x_1)\cupN_G(x_2)\cup\cdots\cupN_G(x_r)|\geqslant\tfrac{{bn+ak}}{{+b}}$为任何独立子集{x1,x2,,xr}在G。而且,这被显示出条件$|N_G(x_1)上的更低的界限\cupN_G(x_2)\cup\cdots\cupN_G(x_r)|\geqslant\tfrac{{bn+ak}}{{+b}}$是在某感觉可能的最好,并且它是Lus的延期以前的结果。
简介:在这篇文章,我们在场有浸透的发生的一个肝炎B流行模型。确定、随机的系统的动态行为被学习。到这个目的,我们首先建立确定的模型的平衡的本地、全球的稳定性条件。由构造合适的随机的Lyapunov功能,第二,为肝炎B的各态历经的静止分发以及扑灭的存在的足够的条件被获得。
简介:让x:Mn是有非零主管弯曲的脐的免费hypersurface。然后,x与Laguerre公制的g被联系,Laguerre张肌\mathbbL\mathbb{L},Laguerre形式C,和一个Laguerre秒基础形成\mathbbB\mathbb{B}它是在Laguerre下面的x的invariants转变组。如果它的Laguerre形式消失,hypersurfacex被称为Laguerreisoparametric并且\mathbbB\mathbb的特征值{B}是不变的。在这份报纸,我们在4分类所有Laguerreisoparametrichypersurfaces。
简介:LetB(E,F)bethesetofallboundedlinearoperatorsfromaBanachspaceEintoanotherBanachspaceF,B+(E,F)thesetofalldoublesplittingoperatorsinB(E,F)andGI(A)thesetofgeneralizedinversesofA2B+(E,F).InthispaperweintroduceanunboundeddomainW(A,A^+)inB(E,F)forA2B+(E,F)andA^+2GI(A),andprovideanecessaryandsufficientconditionforT2W(A,A^+).Thenseveralconditionsequivalenttothefollowingpropertyareproved:B=A^+(IF+(T??A)A^+)??1isthegeneralizedinverseofTwithR(B)=R(A^+)andN(B)=N(A^+),forT2W(A,A^+),whereIFistheidentityonF.Alsoweobtainthesmooth(C¥)diffeomorphismMA(A^+,T)fromW(A,A^+)ontoitselfwiththefixedpointA.LetS=fT2W(A,A^+):R(T)\N(A^+)=f0gg,M(X)=fT2B(E,F):TN(X)R(X)gforX2B(E,F)g,andF=fM(X):8X2B(E,F)g.UsingthediffeomorphismMA(A^+,T)weprovethefollowingtheorem:SisasmoothsubmanifoldinB(E,F)andtangenttoM(X)atanyX2S.ThetheoremexpandsthesmoothintegrabilityofFatAfromalocalneighborhooldatAtotheglobalunboundeddomainW(A,A^+).Itseemstobeusefulfordevelopingglobalanalysisandgeomatricalmethodindifferentialequations.
简介:Inthispaper,forgenerallinearmethodsappliedtostrictlydissipativeinitialvalueprobleminHilbertspaces,weprovethatalgebraicstabilityimpliesB-convergence,whichextendsandimprovestheexistingresultsonRunge-Kuttamethods.Specializingourresultsforthecaseofmulti-stepRunge-Kuttamethods,aseriesofB-convergenceresultsareobtained.
简介:一、填空题(每小题3分,共30分)(1)因式分解的一般步骤是:首先观察能不能,然后考虑应用或法,项数为三项以上时,应当考虑.(2)多项式-5ab+15a2bx-35ab3y的公因式是.(3)18a3+1=(12a+1)( )(4)x2-( )+14=( )2(5)若a2+8ab+2m是一个完全平方式,则m=.(6)(x-4)2x+(4-x)2y=(x-4)2( )(7)分解因式x-y+x2-2xy+y2时,宜分为组,它们是.(8)已知mn=12,则(m+n)2-(m-n)2的值是.(9)2y2+3xy-5x2=(2y )(y )(10)x2-mx+ab=(x+a)(x+b),
简介:引入数值函数关于睇值函数的R-S积分,研究了此类积分的性质及向量值R—S积分存在的几个充分条件,并给出了积分的收敛定理.