查询词典 twisted torus

Every connected, compact Lie groups G contains a maximal torus T. This maximal torus is unique up to conjugation, and every element of G is conjugate to the element of the maximal torus.

每个连通紧李群具有极大环面子群，任二极大环面子群彼此共轭，且连通紧李群中每个元素共轭于极大环面的一个元素。

Next in section 2.3,usingthe finite isolated regular representations in SO(3)character varity of 〓,weobtained a computation formula of SO(3)Donaldson invariants with degree 1 of4—manifold 〓(Theorem 2.3.1).Finally in section 2.4 wediscussed the Donaldson invariants of 4—manifolds with smoothly embedded 2—torus 〓 whose selfintersection is +1,with the help of the single irreducibleSU(2)representation of the principal 〓—bundle over a 2—torus with Eulernumber—1,we got a gluing formula of the Donaldson invariant on the 2—homology represented by 2—torus 〓(Theorem 2.4.1),it is a supplement of P.

最后在§2.4我们讨论了具有自交数为+1的嵌入环面〓的4—流形的Donladson不变量，运用环面上欧拉数为-1的圆丛的单个不可约SU（2）表示给出了Donaldson不变量在环面表示的同调类上的一个粘合公式（定理2.4.1），这一结果补充了P。

The paper discusses the position relationship between the litter circles of torus and the section circle of sphere figured out the intersection of torus and sphere when the central axis of torus and sphere center in XOZ coordinate plane through coordinate transformation.

利用坐标变换使圆环中心轴与球心同在XOZ平面内，讨论了在该平面内圆环截圆与球圆的位置不相交、相切和相交时圆环面和球面的相交情况，并给出了判别圆环面、球面相交情况的流程图以及圆环面和球面相交实例。

We study the recursive structure of the twisted-cube connected network sufficiently, and prove that the twisted-cube connected network is an n regular graph with connectivity n: point out that the twisted-cube connected network is a cube-free network, which is an essential distinction with the hypercube and other variations of the hypercube; prove that the diameter of n dimensional twisted-cube connected network is [ (n+1)/2] , which is almost the half of hypercube's.

首先对其结构的递归性进行充分地研究，证明它是连通度为n的n正则图；指出扭立方体连接网络无立方体子图，这是扭立方体连接网络与超立方体及其其它变种的本质差别；证明了n维扭立方体连接网络的直径为[（n+1）/2]，它几乎是超立方体直径的一半；最后，给出超立方体及其变种的等价定义，并对它们的结构递归性、网络参数和拓扑性质等作了简单的分析、综合和比较。

I sat in the cafe by the cracker factory You were practicing a magic trick And my thoughts got rude, As you talked and chewed On the last of your pick and mix Said your mistaken if your thinking that I haven't been caught cold before As you bit into your strawberry lace And then a flip in your attention in the form of a gobstopper Is all you have left and it was going to waste Your past-times, consisted of the strange And twisted and deranged And I love that little game you had called Crying lightning And how you like to aggravate The ice-cream man on rainy afternoons The next time that I caught my own reflection It was on it's way to meet you Thinking of excuses to postpone You never look like yourself from the side But your profile did not hide The fact you knew I was approaching your throne With folded arms you occupy the bench like toothache Saw them, puff your chest out like you never lost a war And though I try so not to suffer the indignity of a reaction There was no cracks to grasp or gaps to claw And your past-times, consisted of the strange And twisted and deranged And I hate that little game you had called Crying lightning And how you like to aggravate The icky man on rainy afternoons Uninviting But not half as impossible as everyone assumes You are crying lightning Your past-times, consisted of the strange And twisted and deranged And I hate that little game you had called Crying lightning Crying lightning Crying lightning Crying lightning Your past-times, consisted of the strange And twisted and deranged And I hate that little game you had called Crying

我坐在咖啡厅的饼干工厂你练习了魔法把戏和我的想法有粗鲁，当你说话和咀嚼最后你挑选和混合如果你说你的错误思想我一直没感冒了当你咬到你的草莓的花边然后在你的注意力在翻了个大糖球好形式你已经离开，就会浪费你的past-times，组成了奇怪的和扭曲和混乱我爱那小游戏，你打过电话哭闪电您想如何加重男人在雨季的冰淇淋下一次，我抓住了我自己的倒影这是在它的方式来满足你思考的借口拖延你从不看起来像你自己从侧面但你并不隐瞒事实上，你知道我很接近你的宝座上你用双臂占据板凳像牙痛看见他们，像你一样。至终，你的胸扁从来没有输过一场战争虽然我试着不那么受了侮辱没有很好地掌握或空白，爪和你的past-times，组成了奇怪的和扭曲和混乱我讨厌这样的小游戏，你打过电话哭闪电您想如何加重在雨天的下午粪便人并狡滑但是不是每个人都承担一半是不可能的你在哭你的past-times，组成了奇怪的和扭曲和混乱我讨厌这样的小游戏，你打过电话哭闪电哭闪电哭闪电哭闪电你的past-times，组成了奇怪的和扭曲和混乱我讨厌这样的小游戏，你打过电话哭没赏分，你又这么长肯定难找到人答题啊下次记的要+分快给我分吧

We then introduce a conformal invariant quantity which is formulated in terms of the square of the length of the trace free part of the second fundamental form and the mean curvature, and prove that if this quantity is bounded above by that value of the Clifford torus then x is either a totally umbilical sphereor a conformal Clifford torus.

接著我们介绍一个由第二基本型式迹为零部份的张量长度平方与平均曲率形成的保角不变量，并证明此保角不变量的上界若为Clifford环面之值，则x不是全脐球面就是Clifford环面的保角类。

Then it proves a necessary and sufficient condition for anamalgamation of two 3-manifolds with toms boundary with no new incompressible surfaces.Lastly, with the help of the condition and the theorem about the classification of allautomorphisms of a torus, it is proveed that there exists infinitely many 3-manifolds each ofwhich contains no incompressible surfaces besides a torus.

最后，文章给出了以环面作为边界的两个3维流形在作融合积时不产生新的不可压缩曲面的一个充分必要条件，并将这个结果与关于环面到自身的自同胚类的分类的结果相结合，证明了本文的一个核心结论，即存在无穷多个互不同胚的3维流形满足除了一个环面以外不含有其他的不可压缩曲面。

In this design, the dimension M of the memory vector field may be not necessarily equal to the dimension N of the network vector field. This may be the usually case in applications. Designing a network with either static or oscillating behavior, after analysing the dynamical. behavior of its four-dimension subspace, we get 2-torus in the subspace. If we vary the ratio of the imagine parts of the complex conjugate eigenvalues, the periodic motion of all kinds of period ratio on 2-torus are obtained.

设计一个既具有静态平衡点又具有动态振荡的网络，其静态平衡点由多余维叉形分叉得到，动态振荡形式由多余维Hopf分叉得到，通过对其中一个具有振荡行为的四维子空间的进一步分析，可以得到网络在四维子空间中的二环面运动，适当调整约当形中共轭复特征根虚部的比值，可以得到各种周期比的二环面上的周期运动。

According to the helix theories of cylinder,the essential factors of helix with torus are analyzed,and the parametric equation of helix on torus is given based on analytic geometry.

根据圆柱螺旋线理论，分析了形成圆环螺旋线的要素，并运用解析几何方法建立了圆环螺旋线的参数方程。

A deadlock free plane self-adapting routing method in a two-dimensional torus network belongs to the distributing high performance fault tolerance computing technology field, characterized in that each physical passage between nodes are divided into two virtual passages which are both two-way passages and distributed to four virtual sub network of the two-dimensional torus network; the virtual passage distribution strategy avoids the deadlock formed among the sub networks and between the sub networks and has greater self-adapting.

二维torus网络无死锁的自适应路由方法属于分布式高性能容错计算技术领域，其特征在于，把节点之间的每条物理通道被划分为两条虚拟通道，这两条通道均为两向通道，并分配到二维torus网络的四个虚拟子网中，利用虚拟通道分配策略避免了各子网内以及各子网间可能形成的死锁，同时达到更高的自适应性。

The teacher likes the honeymouthed little girl very much.

老师很喜欢这个嘴甜的小姑娘。

Mr. Notker Bien's interests are traveling, spending quality time with the family and long-distance-running.

诺特卡·柏恩先生热爱旅游，长跑，以及和家人一起共度美好时光。