算子的本性相似

对作用于一复可分无穷维Hilbet空间(？)上的两个有界线性算子T,S,它 们本性相似和π(T),π(S)(T,S在Calkin代数中的象)相似是否等价？这是有趣的问 题.本文引入一个算子类ES((？)),并证明了对ES((？))中的算子,上面提到的两种相 似性是等价的. 此外,还证明了ES((？))在B((?))中按照算子范数拓扑稠密.     

Totally real minimal 2-spheres in quaternionic projective space

Let HPn be the quaternionic projective space with constant quaternionic sectional curvature 4. Then locally there exists a tripe {I, J, K} of complex structures on HPn satisfying U = -JI = K,JK = -KJ = /, KI = -IK = J. A surface M(？) HPn is called totally real, if at each point p ∈M the tangent plane TPM is perpendicular to I(TPM), J(TPM) and K(TPM). It is known that any surface M(？)RPn(？) HPn is totally real, where RPn (?) HPn is the standard embedding of real projective space in HPn induced by the inclusion R in H, and that there are totally real surfaces in HPn which don't come from this way. In this paper we show that any totally real minimal 2-sphere in HPn is isometric to a full minimal 2-sphere in Rp2m (？) RPn(？) HPn with 2m≤n. As a consequence we show that the Veronese sequences in KP2m (m≥1) are the only totally real minimal 2-spheres with constant curvature in the quaternionic projective space.     

有心二次曲线的直径式方程

我们知道：若A(x1,y1)和B(x2,y2)为圆的直径两端点,则圆c的直径式方程为(x-x1)(x-x2) (y-y1)(y-y2)=0.由此我们是否可自然地提出如下一个问题：若AB为椭圆或双曲线的直径,即线段AB为过有心二次曲线的中心的弦,那么曲线的直径式方程是否存在？又是什么形式？     

Convergence of cascade algorithm for individual initial function and arbitrary refinement masks

The cascade algorithm plays an important role in computer graphics and wavelet analysis. For any initial function φn, a cascade sequence (φn)n∞=1 constructed by the iteration φn=Cnφn-1=1,2.. where Cαis defined by g∈Lp(R) In this paper, we characterize the convergence of a cascade sequence in terms of a sequence of functions and in terms of joint spectral radius. As a consequence, it is proved that any convergent cascade sequence has a convergence rate of geometry, i.e., ||φ 1-φn||Lp(R)=O((？)n)for some (？)∈(0.1i). The condition of sum rules for the mask is not required. Finally, an example is presented to illustrate our theory.     

Total Dominating Set Games

1 DefinitionsIn this paper we discuss cooperative cost games that arise from total domination problems on graphs. A cooperative cost game (Г) = (N,c) consists of a player set N = {1,2,…,n} and a characteristic function c : 2N→R, where for each subset S(？)N, c(S) represents the cost incurred by the coalition of players in S. The central problem in cooperative game is     

非汉字符号~*-覆盖正则半群的构造(Ⅰ)

本文刻画了■*-覆盖正则半群的结构,得到了弱覆盖正则半群和覆盖正则半 群的分类.作为其主要结论的应用, 我们还得到了(？)-覆盖完全正则半群, 弱覆盖完 全正则半群和覆盖完全正则半群的结构刻画.     

非汉字符号~*-覆盖正则半群的构造(Ⅰ)

本文刻画了■*-覆盖正则半群的结构,得到了弱覆盖正则半群和覆盖正则半 群的分类.作为其主要结论的应用, 我们还得到了(？)-覆盖完全正则半群, 弱覆盖完 全正则半群和覆盖完全正则半群的结构刻画.     

判定P_n(Γ)的Hilbert基的一个充要

设Γ是一作用在R^n上的紧李群，P_n(Γ)是Γ不变的多项式芽构成的环. Hilbert-Weyl定理证明了对于P_n(Γ)总存在一组由Γ不变的齐次多项式芽组成的Hilbert基. 然而，如何从Γ不变的齐次多项式芽中选出一组Hilbert基？如何判定Γ不变的齐次多项式芽的一个有限集就是P_n(Γ)的一组Hilbert基？该文借助于Noether环和不变积分的某些基本性质以及奇点理论的有关定理，证明了判定P_n(Γ)的Hilbert基的一个充要条件. 这对某些P_n(Γ)提供了计算一组Hilbert基的新途径.     

1个简单不等式及其应用

命题若 x∈R,y>0, 则x/y(x-y)≥x-y (*) 证明 x/y(x-y)≥x-y(？)x(x-y)≥y(x -y)(y>0)(?)x2-xy≥xy-y2(?)x2-2xy+y2≥0(?)(x-y)2≥0,而此式显然成立,故(*)式成立,从证明过程易知等号成立的条件是x=y. 下面我们来看这个命题的一点应用. 例1 对任意实数a>1,b>1有不等式:     

这样的直线有多少条?

不少报刊可能都刊载过这样的问题:过空间任意一点且与两已知直线成等角的直线有多少条?这个问题解决后,现在问:过空间任意一点且与两已知平面成等角的直钱又有多少条?本文对此问题作一探讨. 问题 已知P为空间任意一点,二面角α-l-β的大小为θ,则过点P且与α、β成等角(?)的直线m有几条? 解析 由已知,θ∈[0,π],(？)∈[0,π/2],1.若θ=0或π,不难得到(1)当(？)=π/2时,     

关于有理Lp逼近的非唯一性

设（？），是次数不超n(n≥0)的全体实代数多项式的集合，令     

精彩无限，尽在智力快车

1．请问哪里的佛像最少？A．南半球B．北半球C．赤道.2．3个人3天用3桶水,9个人9天用几桶水？A．3桶B．9桶C．27桶.3．什么动物的牙齿最好？A．狼B．老虎C．老鼠.4．读完北京大学需要多久？A．一秒钟B．4年C．一辈子.5．关羽为什么比张飞死得早？A．身体虚弱B．奋战沙场C．红颜薄命。     

2022年北京高考压轴题解法探究

<正>1真题呈现已知Q:a₁,a₂,……,a_k为有穷整数数列．给定正整数m,若对于任意的n∈{1,2,……,m},Q中存在a_i,a_i+1,……,a_i+j(j≥0),使得a_i+a_i+1+……+a_i+j=n,则称Q为m-连续可表数列．(1)判断Q:2,1,4是否为5-连续可表数列？是否为6-连续可表数列？说明理由．(2)若Q:a₁,a₂,……,a_k为8-连续可表数列,求证：k的最小值为4.a₁,a₂,a₃……     

数学基础知识学习方法系列

1.学会善待失误同学们在数学学习过程中,难免会出现各种各样的失误.面对失误,是弃之不顾,还是理性思考？采取何种态度,将直接影响到学习数学的成效.正确的做法是,在数学学习中,要善待失误!善待失误,体现在对失误要有一种追问反思的态度,即善于思考发现失误究竟误在何处？为何失误？如何避误？能回答好这三个问题,你就能把＂善待失误...     

POSITIVE SOLUTIONS OF FOURTH-ORDER TWO-POINT BOUNDARY VALUE PROBLEMS

1IntroductionInthispaper,weconsidertheexistenceofpositivesolutionsoftheequationwithoneofthefollowingsetsofboundaryvalueconditionsWhenthefunctionf(x,y)p)inequation(l.1)isoftheformf(x,y,p)Hy,theboundaryvalueproblem(l.1)-(1.2)describesthedeformationsofanelasticbeambothofwhoseendssimplysupportedat0and1,andtheboundaryvalueproblem(1.l)-(l.3)describesanelasticbeamwithoneofitsendsimplysupportedandtheotherendclampedbyslidingclamps.In[11,Aftabizadehshowedtheexistenceofasolutionto(l.l)-(l.2)undertherest…     

关于虚二次域Tame核计算的一个注记

本文给出了一种计算数域Tame核的方法.应用到虚二次域上,证明了当 Nv>8δD6时,(？)t／:K2S'F／K2SF→k*是双射。     

Whc 168的一个结果的改进

Whc 168：一堆书放入n个抽屉(允许有空抽屉)，为了使任意两个抽屉里书的数目之差不同，问至少要有多少本书？     

An Oscillation Criterion for Second Order Superlinear Differential Equations

61.IntroductionConsiderthesecondordersuperlinearequationx'(t) p(t)X'(t) q(t)1x(t)l"sgnx(t)=o,t>to,(1)wherea>l,pandq:[t,'co)-R=(-co,oo)arecontinuous.Weconsideronlysuchsolutionsxofequation(l)whichexistonsomeinterval[t.,oo),t.>t,>o.Asolutionofequation(l)issaidtobeoscillatoryifithasarbitrarilylargezerosandotherwise,itissaidtobenonoscillatory.Equation(l)iscalledoscillatoryifallofitssolutionsareoscilllatory.Forthespecialcasewherep(t)=Oli.e.,forthedifferentialequationx'(t) q(t)lx(t)l"sgnx(t)=o,a>1-…     

THE SECOND EXPONENT SET OF PRIMITIVE DIGRAPHS

51.IntroductionandNotationsLetD=(V,E)beadigraphandL(D)denotethesetofcyclelengthsofD.ForuEVandintegeri21,letfo(u):={vEVIthereedestsadirectedwalkoflengthifromutov}.WedelveRo(u):={u}.Letu,vEV.IfN (v)=N (v)andN--(v)=N--(v),thenwecanvacopyofu.LotDbeaprimitivedigraphand7(D)denotetheexponentofD.In1950,H.WielandtI61foundthat7(D)5(n--1)' 1andshowedthatthereisapiquedigraphthatattainsthisbound.In1964,A.L.DulmageandN.S.Mendelsohn[2]ObservedthattherearegapsintheexponentsetEd={ry(D)IDEPD.}…     

贝卡语录

1.数学课上,老师提问：“谁能出一道关于时间的题目？”话音刚落,贝卡举手回答：“老师,什么时候放学？”