对称

Our main work is as follows: the stable laser mode theory in uniform plasmas is extended to non-uniform plasma cases; the discussion of the sufficient and necessary conditions for laser self-focusing in uniform plasmas is developed to non-uniform plasma cases; a quantitative approach to judge the impact of different plasma density distribution on laser self-focusing is proposed; the evolution properties of asymmetric laser filed in non-uniform and uniform plasmas are discussed and mechanisms that symmetric channel-like plasmas can confine the laser centroid around the plasma channel axes and symmetrize initially asymmetric laser beams are proposed; the formation of solitary standing wave in moderate plasma density is studied by PIC simulations and can be explained by stimulated Raman scattering of laser beams in plasmas.

主要工作为：把均匀等离子体中激光的稳定模理论推广到横向非均匀等离子体情形；把均匀等离子体中激光自聚焦的充分和必要条件的讨论推广到横向非均匀等离子体情形；给出横向密度分布不同的等离子体影响激光自聚焦的定量判据。讨论了初始不对称的激光场在横向非均匀及均匀等离子体中的演化特性，并提出了具有对称腔道结构的等离子体箍缩激光质心和对称化初始不对称激光场的物理机制。用粒子模拟讨论了激光场在等离子体中形成孤立驻波的过程，认为前向受激拉曼散射是发生此现象的可能机制。

The results do indicate that there may be several mechanisms for asymmetric vortical flow.

本文结果表明了大迎角旋转体非对称涡的形成机理可能是多种的，即给定分离线位置不对称或自由涡线的个别线段不对称都能产生非对称涡流。

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。

By using constructive methods and complicated techniques of matrices, necessary and sufficient conditions for the existence of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, skewbisymmetric solution and various interlaced solutions over a finite central algebra Ω to systems of generalized Sylvester matrix equations overΩ are presented.

利用构造方法和复杂的矩阵技巧，研究了有限维中心代数上的多项式环Ω上的广义Sylvester矩阵方程组在Ω上有自共轭解，斜自共轭解，广自共轭解，斜广自共轭解，中心对称解，斜中心对称解，双对称解，斜双对称解及其各种交错解的充要条件。

The concepts in References 1 and 2 are broadened and the properties of the centrosymmetric and skew centrosymmetric matrices are exploited in detail.

推广了文［1，2］的概念，系统地叙述了中心对称和反中心对称矩阵的性质，导出了一类求解系数矩阵为中心对称和反中心对称线性方程组及超定方程组的缩减算法。

By this iterative method ,the solvability of the matrix equation can be judged automatically.When the matrix equation is consistent ,then,for any initial centrosymmetric matrix pair ,a centrosymmetric solution pair can be obtained within finite iteration steps in the absence of roundoff errors, and the least norm centrosymmetric solution pair can be obtained by choosing a special kind of initial centrosymmetric matrix pair.

当矩阵方程相容时，对任意初始的中心对称矩阵对在没有舍入误差的情况下，经过有限步迭代，得到它的一个中心对称解，并且，通过选择一种特殊的中心对称矩阵对，得到它的最小范数中心对称解。

When the matrix equation is consistent, its centrosymmetric solution can be obtained within finite iterative steps in the absence of round off errors for any initial centrosymmetric matrix X1, and its least-norm centrosymmetric solution can be derived by choosing a suitable initial iterative matrix.

当矩阵方程AXB+CXD=F有中心对称解时，在有限的误差范围内，对任意初始中心对称矩阵X1，运用迭代算法，经过有限步可得到矩阵方程的中心对称解；选取合适的初始迭代矩阵，还可以迭代出极小范数中心对称解。

In the fifth chapter, the author first discusses the dissymmetrical forms of their carrying objects.

第五章：首先讨论了&来／去&带宾能力的不对称表现，认为&来／去&带宾能力的不对称主要表现在历时发展过程的不对称和共时带宾能力的不对称两个方面，然后分析了&来／去&语义泛化的过程及原因。

Background : Individuals with hemiparesis frequently shift most of their body weight to uninvolved side, showing a obviously asymmetry of standing posture and weight bearing pattern. Postural asymmetry places the individual with hemiparesis at a greater risk for falls. Asymmetry weight bearing contributes to gait abnormalities.

研究背景：半边麻痹的中风患者时常会把身体的重量放在好边的脚上，让好脚去承载身体大部分的重量，因而产生明显不对称的站立姿势和两脚不对称的重量承载比例，姿势的不对称会致使患者跌倒的危险性更大，重量承载的不对称会致使患者走路时有不正常的步态。

The results showed that the CV performance of PbO〓/PbSO〓 and PbSO〓/Pb powder microelectrode transformed from PbCO〓 under the optimize condition (the positive electrode was activated by asymmetric CV and asymmetric square wave current ways and the negative electrode using asymmetric CV) were better. Their electrode performances were as good as those made from leady oxide product by ball mill under the same conditions.

结果表明，将PbCO〓先制成粉末微电极，在30℃ 1.0mol/L H〓SO4〓溶液中经过化学转化为硫酸铅粉末微电极，以不对称信号活化(对PbO〓/PbSO〓电极，采用不对称循环伏安和不对称方波电流两种方法；对PbSO〓/Pb电极，采用不对称循环伏安法)得到电极的性能最好，正极活性物质的利用率高达89％，负极的达95％。

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。