对称

Exploiting this property, we derived several necessary constraints on the number of symmetric/antisymmetric filters, which help to design multiwavelets with the desired symmetric property.

为此首先系统的调查了对应于两种类型对称性的m带紧支撑正交多小波的对称性质，即用滤波器和多相矩阵刻画了多小波系统的对称特征，并由此得到正交多小波系统中对称反对称元数目的约束条件，这对于后来对称多小波的设计是非常重要。

The general form of solution for the non symmetric matrix A is given, the expression of optimal approximation solution is presented, and an algorithm for solving the problem is described. The total least squares problem with symmetric and bisymmetry constraints is discussed respectively. A sufficient condition for existence of solution is derived by use of the theory of matrix Ricaati equation. The general form of solution is given if the problem has a solution, and the expression of optimal approximation solution is presented. Some numerical examples are given.

对矩阵A是非对称情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，并给出了其解的表达式，描述了求解问题的算法；讨论了带对称和双对称约束的总体最小二乘问题，利用Ricaati矩阵方程的理论得到了解存在的一个充分条件，分别对对称矩阵和双对称矩阵两种情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，给出了其解的表达式，提出了求解这些问题的算法，并给出了数值例子。

The conditional symmetry instability is the intermediate process between the stable and instable states of the atmosphere. The evolution of the atmosphere from the stable to unstable state or from unstable to stable state comes through two stages. The convective-symmetric instability circulation is related with the state and type of the instability. When the conditional instability lies in the lower level and conditional symmetric instability in the upper level, the circulation will have vertical updrafts in the lower level and slantwise updrafts in the upper level. The release of conditional symmetric instability gives rise to a mesoscale rain belt.

结果表明：条件对称不稳定是大气稳定状态和条件不稳定状态之间的中间纽带，大气由稳定向不稳定或者由不稳定向稳定的演变均通过条件对称不稳定来实现；对流对称不稳定环流的形成与不稳定层的配置有关，当低层为条件不稳定而高层叠加深厚的条件对称不稳定时，对流对称不稳定环流低层出现垂直上升气流，高层出现范围较广的倾斜上升气流，对称不稳定能量释放产生中尺度云带。

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

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。

Selfconjugate matrix, skewselfconjugate matrix, perselfconjugate matrix, skewperselfconjugate matrix, centrosymmetric matrix, skewcentrosymmetric matrix, bisymmetric matrix, and skewbisymmetric matrix over a ring with an involutorial antiautomorphism are defined. Significant criteria for matrices to be bisymmetric and skewbisymmetric are obtained.

在具有对合反自同构的环上定义了自共轭矩阵，斜自共轭矩阵，广自共轭矩阵，斜广自共轭矩阵，中心对称矩阵，斜中心对称矩阵，双对称矩阵和斜双对称矩阵，建立了双对称矩阵和斜双对称矩阵的重要判定定理。

An algorithm for constructing a class of symmetric-antisymmetric orthogonal refinable functions with multiplicity 2r is presented.

给出一类重数为2r的正交对称-反对称多小波的构造算法，即对任给长度为2N的对称-反对称正交多小波，通过本文所给的构造算法可以得到长度为2N+1的对称和反对称多小波。

In this paper, the inertial theorem of real symmetric matrix has been proved by three methods in three aspects: the relationship between real symmetric matrix and real quadratic form, the relationship between real symmetric matrix and symmetric bilinear function of real linear space.

从实对称矩阵与实二次型的联系、实对称矩阵与实线性空间的对称双线性函数的联系以及将实对称矩阵作为研究主体这三个角度，介绍实对称矩阵的惯性定理的三种证明，以期加深对实对称矩阵的惯性定理的理解。

Its main part provides a detailed exploration of all the symmetries: symmetry of settings, symmetry of the...

论文的主要部分详细地解析了其结构上各部分的对称：背景的对称、家族的对称、叙述者的对称、人物的对称、情节的对称、以及结局的对称。

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。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。