字定理在Heegaard分解方面的一个应用

The word theorem states that x can be denoted as a rotation inserting word of A if x is in the normal closure of A in F(X). As an application of the theorem, in this note a condition that guarantees reducing the genus of Heegaard splitting of 3-manifolds is given. This leads Poincare conjecture to a new formulation.     

组合群试

概率群试的方法针对所提出的方案理论上是相当完美的 .当情况很不明确时 ,独立性的假设也是可以理解的 ,而且具有容易执行的优点 .但如果能够掌握更多的信息 ,例如能够确切知道带菌者的人数 ,组合群试的方法效果更佳 .例如确切知道万名应征者中 ,恰有一名带菌者 ,用概率群试方法 ,ｐ=0 0 0 0 1 ,最佳群试为 1 0 1 -试 ,大约要做2 0 0次化验才能查清谁是带菌者 ;而用组合群试方法只需要 1 4次就够了 .为什么会有这么大的差距呢 ?显然概率群试的方案本身就提得不尽合理 ,一旦群试的结果是阳性 ,就不论组里个人带菌的概率有多大 ,一律逐个进行…     

利用组合群验数学模型分析汽车故障

利用组合群验的理论和方法建立数学模型,依据汽车可靠度对汽车系统定量分析,为确定故障部位,汽车维修,故障分析提供方法.     

利用组合群验方法确认运动员违禁物质

组合群验设计属于非适应性的组合群试,非适应性的组合群试算法可以同时进行所有测试,而且不必考虑各次测试之间的影响,它省时快捷,已被广泛应用于低发生率的实验设计中.利用组合群验方法给出了确认运动员体内含有违禁物质的检测与判定方法.     

组合群验在数控机床可靠性方面的应用

对数控机床子系统或子系统单元定量分析,得到了数控机床串联系统可靠度;利用组合群验数学模型,依据数控机床串联系统模型可靠度评价子系统的可靠性,也可为子系统故障分析提供方法.     

基于非适应性组合群测的多路存取信道模型的构作

在多路存取信道中当前用户的信息传输是计算机通信网络的一个重要内容,基于组合群测理论构作了多路存取信道模型,介绍了它在多路存取信道中当前用户信息传输方面的应用.     

一类二次方程组的一个定理及其运用

定理　在方程组∑ni=1xi=A∑ni=1x2i=B中 ,A、B是实数 ,记Δ=n B-A2 .若 xi∈ R( i=1,2 ,… ,n) ,则Δ≥ 0 ,当且仅当x1 =x2 =… =xn=An时 Δ=0 .证明　 ∑1≤ i相似文献   

E*-酉范畴逆半群的一个表示定理

本文,我们对带零逆半群定义了0-对偶预同态的概念,并且用0-对偶预同态刻画了E*-酉范畴逆半群。     

最大无关组判定定理及其它

本文给出了一个判定最大无关组的充要性定理，同时对用矩阵的行变换求最大无关组这一问题进行了点滴分析并介绍了一个解齐次线性方程组的简便方法。     

完全单半群上的相容组与同余结

对完全0-单半群上的相容组条件进行简化,引入完全单半群上同余结的概念,并给出相容组与同余结的应用.     

A proof of the Gordon Conjecture

A combinatorial proof of the Gordon Conjecture: The sum of two Heegaard splittings is stabilized if and only if one of the two summands is stabilized.     

A note on tunnel number of composite knots

Let K be a knot in a sphere S³. We denote by t(K) the tunnel number of K. For two knots K₁ and K₂, we denote by K₁?K₂ the connected sum of K₁ and K₂. In this paper, we will prove that if one of K₁ and K₂ has high distance while the other has distance at least 3 then t(K₁?K₂)=t(K₁)+t(K₂)+1.     

A formula on Heegaard genus of self-amalgamated 3-manifolds

Let M be an orientable compact irreducible and ∂-irreducible 3-manifold, and suppose ∂M consists of two boundary components F₁ and F₂ with g(F₁)=g(F₂)>1. Let Mf be the closed orientable 3-manifold obtained by identifying F₁ and F₂ via a homeomorphism f:F₁→F₂. With the assumption that M is small or g(M,F₁)=g(M)+g(F₁), we show that if f is sufficiently complicated, then g(Mf)=g(M,∂M)+1.     

A Note on Heegaard Genus of Self-amalgamated 3-Manifold

Let M be a connected orientable compact irreducible 3-manifold. Suppose that αM consists of two homeomorphic surfaces F1 and F2, and both F1 and F2 are compressible in M. Suppose furthermore that g(M, F1) = g(M) + g(F1), where g(M, F1)is the Heegaard genus of M relative to F1. Let Mfbe the closed orientable 3-manifold obtained by identifying F1 and F2 using a homeomorphism f : F1 → F2. The authors show that if f is sufficiently complicated, then g(Mf) = g(M, αM) + 1.     

Heegaard分解的重新分块

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＭｂｅａｃｏｍｐａｃｔ 3 ｍａｎｉｆｏｌｄ .ＩｆｔｈｅｒｅｉｓａｐｒｏｐｅｒｌｙｅｍｂｅｄｄｅｄｃｌｏｓｅｄｓｕｒｆａｃｅＳｉｎＭｗｈｉｃｈｓｅｐａｒａｔｅｓＭｉｎｔｏｔｗｏｃｏｍｐｒｅｓｓｉｏｎｂｏｄｉｅｓＨ1ａｎｄＨ2 ,ｔｈｅｎＭｃａｎｂｅｗｒｉｔｔｅｎａｓＭ =Ｈ1∪ＳＨ2 .ＴｈｉｓｓｔｒｕｃｔｕｒｅｏｎＭｉｓｃａｌｌｅｄａＨｅｅｇａａｒｄｓｐｌｉｔｔｉｎｇｏｆＭａｎｄＳｉｓａｓｐｌｉｔｔｉｎｇｓｕｒｆａｃｅ .Ｈ1∪ＳＨ2 ｉｓｓａｉｄｔｏｂｅｒｅｄｕｃｉｂｌｅ…     

Big Heegaard distance implies finite mapping class group

We show that if M is a closed three manifold with a Heegaard splitting with sufficiently big Heegaard distance then the subgroup of the mapping class group of the Heegaard surface, whose elements extend to both handlebodies is finite. As a corollary, this implies that under the same hypothesis, the mapping class group of M is finite.     

Spanning Annuli in 3—manifolds

Al3-manifOldsandsurfacesconsideredinthisPaperareassumedtobecompactandori-entable,andallconcePtsandnotationsnotdefinedinthepaperareStandardfsee,forexample[2,3j.AcompressionbodyHisconstructedbyadding2-handlestoSXIalongacollectionofpairwisdisjointsimpleclosedcurvesonSX{o},andcaPpingoffanyresulting2-spherebound-arycomponentSwith3-balls,whereSisaconnectedclosedorientablesurface.ThecomponentSX{1}Of8Hisdenoted8 Handthesurface8H-8 H,whichmayormaynotbeconnect-ed,isdenoted8H.If8H=gi,Hisahandleb…     

Some sufficient conditions for tunnel numbers of connected sum of two knots not to go down

In this paper, we show the following result: Let K _i be a knot in a closed orientable 3-manifold M _i such that (M _i ,K _i ) is not homeomorphic to (S ₂ ×S ₁, x ₀ ×S ₁), i = 1, 2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E(K _i ) is less than the difference of one and twice of the tunnel number of K _i . Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive.     

两个压缩体融合为一个压缩体的充分必要条件北大核心CSCD

本文给出了两个压缩体沿紧致连通曲面(带边曲面或闭曲面)融合仍是一个压缩体(有非空负边界)的充分必要条件,还给出了两个3维流形沿着边界上的紧致连通带边曲面融合中的融合曲面为边界不可压缩的一个特征描述,同时还证明了压缩体的每个Heegaard分解是标准的.