对称的

For example, Keyfitz made the classification of the bifurcations in one state variable, without symmetry up to codimension 7; Golubitsky and Schaeffer obtained the classification of the bifurcation problems in one state variable with Z_2 symmetry, in one parameter up to codimension 3; Golubitsky and Roberts studied the classification of degenerate Hopf bifurcation in two state variables with dihedron D_4 symmetry, in one parameter up to topological codimension 2; Melbourne obtained the classification of bifurcations in three state variables with octahedral symmetry, in one parameter, up to

需要指出的是以上研究均没有考虑分歧参数的对称性，Futer，Sitta和Stewart的工作虽然考虑了分歧参数的对称性，但仅限于分歧参数与状态变量具有相同的对称性，他们得到了状态变量与分歧参数均关于二面体群D_4对称，拓扑余维数不大于1的分歧问题的分类。高守平和李养成则讨论状态变量和分歧参数均具有对称性且对称性可以不同的分歧问题，并给出了状态(来源：A770707BC论文网www.abclunwen.com)变量关于二面体群D_4对称，分歧参数关于S~1对称，拓扑余维不超过1的分歧问题的分类。本文第一章讨论两个状态变量关于二面体群D_3对称，两个分歧参数关于O(2)对称的分歧问题，给出了该类分歧问题在非退化条件q(0)≠0下所有情形的分类与相应的识别条来源：AdadaBC论文网www.abclunwen.com

Thus LES is proved to be suitable to simulate the flow and temperature fields of large scale vortices with complex geometric boundaries. LES cooperated with the second order full extension ETG finite element method is applied to simulate the forced convection heat transfer around two square cylinders arranged side by side. While the boundary conditions are symmetrical, the time history and power spectrums of drag coefficient, lift coefficient, averaged Nusselt number at the wall, and the streamwise velocity and temperature on the symmetrical points are calculated. The results show that the power spectrums are all almost symmetrical.

应用大涡模拟与二阶全展开ETG有限元离散格式相结合的方法对间距比为1.5的条件下横掠并列双方柱强制对流换热问题进行了数值模拟，通过边界条件对称时，对并列双方柱对称点上的速度和温度以及方柱的阻力系数、升力系数和壁面平均Nu数进行的时域分析和频域分析，得到了在对称边界条件下并列双方柱对称点上的速度和温度以及方柱的阻力系数、升力系数和壁面平均Nu数的功率谱均基本对称的结论。

First, the typhoon flow field is decomposed into two parts: the maximum asymmetric vortex and irrotational environmental flow field. Then the maximum asymmetric vortex is also decomposed into two parts: the maximum symmetric vortex and β-gyres. Finally, typhoon Pearl(2006) is simulated by WRF model(weather research and forcasting model), and flow fields at various times at 500hPa...

首先，将台风的流场分解成最大的、不对称的涡旋流场和无旋流场；然后将不对称的涡旋流场分解成最大的对称涡旋和不对称的β涡旋对；最后，利用WRF(weather research and forcasting)模式(V2.1.2)模拟了200601号珍珠台风，并对各时次的500hPa风场用该方法进行分解，结果表明：该方法对台风的运动机理研究和实际的台风路径预测提供了有价值的信息。

The conclusion of this article contains:(1) The climatology symmetric index and antisymmetric index which represent the uniform system of ocean and atmosphere is defined according to the unique kinetic character of the large-scale fluid. The symmetric mode, a state mode, and antisymmetric mode, a propagate westward mode, of ocean and atmosphere are distinguished clearly from each other. Also, the primary part which determines the symmetric mode emerges from non-divergenct wind and the dominant part which contributes to the antisymmetric mode mostly is irrotational wind. The article also compares the disparity of the climatology distribution of SST and sea surface wind field between 1948-1975 and 1976-2005. The SST of both the tropical Indian Ocean and the tropical Pacific after 80's is warm than before 80's .

主要结论如下：(1)热带太平洋气候平均态所包含的海-气相互作用的资料分析根据海洋和大气的运动特性，定义了表征海洋大气系统的对称模态和反对称模态指数，通过两个指数对热带太平洋和印度洋关于赤道对称和反对称的两个模态进行区分，发现关于赤道反对称的海-气耦合模态主要包含了大气散度分量和海洋SST的相互作用；关于赤道对称的海-气耦合模态主要包含了大气旋度分量和海洋SST的相互作用，并从资料估算了该耦合模态向西传播的速度。

According to GBEM,a fullysymmetric Galerkin multi-zone boundary element methodisproposed in this paper.Based on regarding the coefficient matrix as thesum of a symmetric part and a non-symmetric one,this problem is solvedby adopting a proper assembly.Following this treatment,GBEM will beextended for a wide scope.

针对这一问题，(1)本文在单域伽辽金边界元的基础上，采用先生成各子域的方程，将系数矩阵表达为对称部分与非对称部分之和，通过恰当的集成方式，消除非对称部分的方法，提出了一种完全对称的伽辽金边界元子域法，拓宽了伽辽金边界元法的使用范围。

得 (1 2r ) A 1 + A2 = 0 由条件得 4π(1 )A1 + 2A2 = P P (1 2) A1 =, A2 = P 2π 2π由及二式的联立求解,得 42 Substitute the obtained A1 and A2 into the forgoing representations, we get (1 +)P rz (1 2)r ur = R2 R + z 2πER (1 +)P z2 ω= 2(1 )+ 2 2πER R P (1 2)R 3r 2 z σr = 3 2 2πR R + z R (1 2)P z R σθ= 2 R R + z 2πR 3Pz3 3Pr z 2 σ z = 5 ,τ zr =τ rz = 2πR 2πR5 43 将得出的A1及A2回代,得(1 +)P rz (1 2)r ur = R2 R + z 2πER (1 +)P z2 ω= 2(1 )+ 2 2πER R P (1 2)R 3r 2 z σr = 3 2 2πR R + z R (1 2)P z R σθ= 2 R R + z 2πR 3Pz3 3Pr z 2 σ z = 5 ,τ zr =τ rz = 2πR 2πR5 44 §8-4 Spherically Symmetric Problem For Space Among spatial problems, if the elasticity body's geometric shape,restraint condition and any external factors are symmetrical in a certain point (any plane which passes this point is all symmetrical one),then all stresses,strains and displacements are symmetrical in this point.

§8-4 空间球对称问题在空间问题中，如果弹性体的几何形状，约束情况以及所受的外来因素，都对称于某一点(通过这一点的任意平面都是对称面)，则所有的应力，形变和位移也对称于这一点。这种问题称为空间球对称问题。

At the second place, feasibility of edge detection based on orthogonal wavelet is discussed in the article. Its theoretical key of edge detection based on orthogonal wavelet that approximate symmetrical or antisymmetrical orthogonal real wavelet can be constructed though Haar wavelet is the only symmetrical or antisymmetrical orthogonal real wavelet.

随后本文讨论了正交小波基用于边缘检测的可行性：虽然除了Haar小波外再也找不到对称或反对称的正交实小波，但是可以构造出近似对称或反对称的正交实小波，这就是正交小波用于边缘检测的理论关键。

A plasma electron density profile in the HT-6M tokamak is obtained when an asymmetric Abel-inversion which depends on plasma shifts is applied to the signals of multichord interferometric measurement.

一种常用的非对称Abel变换是分离变量法，它的基本思想是把测量信号分成对称元和非对称的权函数，对称部分采用标准的Abel变换，变换的结果乘上非对称的权函数。

There are three forms of symmetry in virus capsids: icosahedral , helical and complex forms.

壳粒排列的方式使病毒的结构呈几何对称，病毒衣壳有三种对称形式：二十面体立体对称、螺旋对称、复合对称，螺旋结构呈杆状，而二十面体由对称的亚单位组成近似的球状，非对称的衣壳是较复杂的形式，往往与细菌病毒有关。

We also simulate the environment of photon experiment, and calculate the effect by use of fourfold symmetry torsion pendulum, we find that the double frequency effect caused by gravitational gradient is reduced a magnitude when we buildup the symmetry of measurement system.

我们还对二重对称扭秤的光子实验数据进行了分析，结果发现二倍频的效应为10~(-12)Nm 的量级，通过计算分析我们发现扭秤周围环境的不对称所引入的引力梯度效应是不容忽视的，因此针对喻家山人防山洞的具体情况，我们对光子实验的实际环境进行了模拟计算，理论分析结果表明对于二重对称的扭秤而言，环境不对称的影响引起的力矩效应为5.4940×10~(-10) Nm，对于四重对称的扭秤来说，效应为1.8668×10~(-11)Nm，可以看到随着扭秤对称性的增加，引力梯度的效应减小了一个数量级。

Methods: Five patients with parkinsonism or dystonia were assigned to general anesthesia using an modified endotracheal tube.

本实验依照人体实验之相关规定进行，五位患有帕金森氏症或肌张力异常的病人接受神经立体定位手术。

If you can benefit from this book, it is our honour.

如果您能从本书获益，这将是我们的荣幸。