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1.
平面凸n边形A1A2…An中记μn={[∑1≤i≠j≤n d(Ai,Aj)]/[min 1≤i≠j≤n d(Ai,Aj)]}(d(Ai,Aj)表点Ai与点Aj之间距离),证明了μn的最小值只有当各边长等于min 1≤i≠j≤n d(Ai,Aj)时才能取得,且μn的下确界为15 3√3,下确界取得仅当凸六边形退化为等边三角形。还证明了等边凸六边形当任一对角线长不小于边长时,μn的最大值为12 6√3。  相似文献   

2.
本文在贵刊文[1]的基础上,探讨平面闭折线A(n)关于点P的k号心与它的一级顶点子集V j(1≤j≤n)关于点P的k号心之间的关系.定理1设闭折线A(n)关于P的k号心为Q.闭折线A(n)一级顶点子集V j关于点P的k号心为Q j(1≤j≤n),过点P任作一直线l,且Q、Q j、Aj三点到直线l的有向距离分别为d(Q)、d(Q j)、d(Aj),则d(Q)=d(Q j)+d(A j)/k.证明以任意一点P为原点建立平面直角坐标系xPy,则可设直线l的方程为ax+by=0.设各点的坐标分别为:Ai(xi,y i),Q(x,y),Q j(x'j,y'j)(i=1,2L,n且1≤j≤n),则11niix=k∑=x,y=1k∑in=1yi,'1j1(ni j)ix=k∑=x?x,y'j=…  相似文献   

3.
一种场站设置问题的探讨   总被引:2,自引:0,他引:2  
设n个点A1,A2,…,An∈R^m,记μm=(∑1≤i,j≤n|AiAj|)/mini≠j1≤i,j≤n|AiAj|,求inμn^m的值则是组合几何中的一个困难问题。本文给出infμm 1^、infμn^1的值等,提出几个猜想。  相似文献   

4.
The sequences {Zi,n, l≤i≤n}, n≥l have multi-nomial distribution among i.i.d. random variables {X1,i, i≥1}, {X2,i,u≥l }, …, {Xm,i, i≥1 }. The extreme value distribution Gz(x) of this particular triangular array of i.i.d, random variables Z1,n, Z2Zn,n is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) Gz(x) = r-1∏i=1ФAiαi(x) × Фαr (x);ii) Gz (x) = r-1∏i=1ψAiαi (x) × ψαr (x); iii) Gz (x) = r-1∏i=1 ∧Ai (λix) × A(x), r≥2, 0<α1≤α2≤…≤αr and λi∈ (0,1] for i, l≤i≤r-1 which occur if Fj, …, Fm belong to the same MDA.  相似文献   

5.
本文证明了长方四元数矩阵奇异值的一些不等式:设H为四元数体,A∈H~(n×m),B∈H~(m×k),S=min{n,k},1≤l≤s,则 sum from i=1 to l σ_i(AB)≤sum from i=1 to l σ_i(A)σ_i(B) (ⅰ) sum from i=1 to l σ_s _(i+1)(AB)≥sum from i+j=m+s-l+1 σ_i(A)σ_j(B) (ⅱ) multiply from i=1 to l σ_i(A)σ_(m-i+1) (B)≤multiply from i=1 to l σ_i(AB)≤multiply from i=1 to l σ_i(A)σ_i(B) (ⅲ) 其中,σ_1(A)≥σ_2(A)≥…≥σ_m(A)≥0是A的从大到小的奇异值,当i>m时,σ_1(A)(?)0。不等式(ⅰ),(ⅱ),(ⅲ)包含或加强了文[3]、[4]、[5]的一些基本结果。  相似文献   

6.
设Xn={1,2,…,n},Q(Xn)={A1,A2,…,Ar}为Xn上任意一个划分,令OCT(Xn)={α∈On:Ai,Aj∈Xn,d(Aiα,Ajα)≤d(Ai,Aj)},则OCT(Xn)是一个半群。本文刻划了该半群的Green关系及一些相关的性质。  相似文献   

7.
设M^m∪→R^m+1为紧致凸超曲面,m个主曲率0〈λ1≤λ2≤…≤λm满足:λm〈λ1+λ2+…+λm-1,证明如果:Ф:M→N为稳定的指数调和映射,且|dФ|^2〈1/2λm^2mini{λi(m∑j=1λj-2λi)},则Ф为常值映射。  相似文献   

8.
朱华伟 《中等数学》2007,(8):F0004-F0004
第一天1.给定实数a1,a2,…,an.对每个i(1≤i≤n),定义:di=max{aj|1≤j≤i}-min{aj|i≤j≤n},且令d=max{di|1≤i≤n}.(1)证明:对任意实数x1≤x2≤…≤xn,有max{|xi-ai||1≤i≤n}≥2d.(2)证明:存在实数x1≤x2≤…≤xn,使得式①中的等号成立.(新西兰供题)2.设A、B、C、D、E五点中,四边形ABCD是平行四边形,四边形BCED是圆内接四边形.设l是通过点A的一条直线,l与线段DC交于点F(F是线段DC的内点),且l与直线BC交于点G.若EF=EG=EC,求证:l是∠DAB的平分线.(卢森堡供题)3.在一次数学竞赛活动中,有一些参赛选手是朋友,朋友关系是相互的.如…  相似文献   

9.
假设{Sj}j=0^m-1是由压缩映射Sj(z)=εj+ρj(z-εj),组成的迭代函数系(IFS),0〈Pj〈1,|εj|≤1,且至少有一个εj满足|εj|=1,K是{Sj}j=0^m-1的吸引子,μ是支撑在K上的Hausdofff测度,最近,文献[1]中讨论了自相似测度的柯西变换F(z)=∫k(z-w)^-1dμ(w)在|z|〉1在内的罗朗系数.主要研究G(z)=∫k(λz-w)^-1dμ(w)在|z|〉1/|λ|(|λ|≥1)内的罗朗系数,得到了一些结果.  相似文献   

10.
短论集锦     
《中等数学》2009,(9):16-17
关于一道集合竞赛题的再议 文[1]从一道浙江省数学竞赛题的解答中,引出并推广至求Tk之一般公式.设X为n元集合,A1,A2,…,Am为x的全部子集,Tk定义为Tk=∑1≤i1〈i2〈…〈ik≤m|Ai1∩Ai1∩…∩Aik|,①其中,|A|表示集合A的元素个数.  相似文献   

11.
The communication of people partially is the communication of cultures. Culture has a direct effect on international commercial activities in all aspects. Different conceptions about time, space, equality, law and the like, lead people to deal with things in different ways. So to know cultures of the counterpart is to facil-itate our enterprises so as to have a smooth and successful communication in commercial activity.  相似文献   

12.
风的曲线     
Rosco and I wait for the fishermen to return.I sit at a wooden bench near the store at Mt.Baker Resort and watch the clouds change shape. Rosco has my belt around his neck and an eight foot tow chain hooked to a tree. Dogs must be on a leash. Ducks and rabbits are loose.  相似文献   

13.
Given a graph G,a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and |C|≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as TC (G), is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K (G), is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F={G|K(G) is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus TC (G)/|G|≤1/2 for all G ∈ F.  相似文献   

14.
《海外英语》2007,(5):44-45
It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,  相似文献   

15.
一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/  相似文献   

16.
《海外英语》2007,(5):10-11
Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?  相似文献   

17.
Different nations have different social cultures, and the social culture of every nation is developing with the development of the nation, language is greatly influenced by social culture, which enables language to possess national and historical characteristics. Word is the smallest, independent, meaningful linguistic unit of language. It can well reflect the national and historical characteristics. From synchronic aspect, the social and cultural influence on word meaning is mainly embodied in conceptual and associative meanings of word. The incorrespondence of word meaning is a phenomenon that exists in both conceptual and associative meanings of word among different languages. From diachronic aspect, the development of social culture causes some changes of word meaning to some extent. Therefore, social culture plays a key role in vocabulary learning and mastery of a language.  相似文献   

18.
汉字倒说     
汉字的六书,《说文》对“转注”一类,语焉不详。后世学者提及转注,也仅限于许慎所举出的例字。《汉字例说》一文,作者从转注的角度综合考虑,对部分现代常用字作了分析,跟传统的解释有所不同。希望能抛砖引玉,互相切磋,以推进学术研究。  相似文献   

19.
《海外英语》2007,(4):36
There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.  相似文献   

20.
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