使对称

Firstly, using strategy of introducing associated auxiliary equation to a givenpartial differential equation without admitting Lagrangian, we make the extendedequations possess a variational principle. Based on this, the concepts of extendedconservation law and extended symmetry to given partial differential equationare put forwarded.

首先，我们给出了引入伴随方程扩充原方程的策略，使给定偏微分方程的扩充方程组具有对应泛函，即称为Lagrange系统的方法，以此为基础提出了作为偏微分方程传统守恒律和对称概念的一种推广—偏微分方程扩充对称和扩充守恒律的概念；其次，先给出以得到的Lagrange系统为基础，利用N？

The works in the project just done can be summarized as five respects.(1) A device was designed to fabricate the asymmetrical resonant cavities by a pendant drop. A series ARCs with variable parameters provides a valuable experimental method for investigating the characteristics of ARCs.(2) The relationship between the number of active modes and the shape parameters in an ARC was investigated. The experimental lasing threshold was compared with theoretical result, the good agreement between two shown that it was the decrease of the number of active modes in an ARC that decreased lasing threshold.(3) Dye lasing gain was used to enhance the signals of stimulated Raman scattering of the weak gain Raman modes in a circular cavity made by a pendant drop, the instantaneous SRS spectra of weak gain Raman modes in ethanol was obtained by this new method.(4) The SRS signals of minority compound in a binary chemical complex was obtained by using dye lasing gain method. The detection concentration of minority compound was reduced to an order compared with normal SRS method.(5) A cylindrical circular cavity was formed by a liquid jet, which was used to reduce the pump intensity required for laser induced plasma spectroscopy. The limit of detection of trace element in aqueous sample was greatly decreased by this new method.

我们设计并成功制作了使悬垂液滴连续变形的装置，用此装置可以方便地改变非圆对称谐振腔的几何参数，为ARCs的研究提供了一种有效的实验方法；研究了ARCs中活性模式数和变形参数间的变化规律，激光阈值的数值计算结果和激光辐射的实验结果作了比较，二者吻合的曲线说明ARCs中活性模式数量的减少是受激辐射放大阈值降低的原因；在由单元化合物构成的微型圆对称谐振腔中，首次尝试用"激光增益"增强弱增益拉曼模式的受激拉曼散射信号，获得了乙醇分子中弱增益拉曼模式的瞬态SRS光谱；在由二元混合物构成的微型圆对称谐振腔中，用染料的激光增益增强了少量化合物的SRS信号，把少量化合物的SRS信号探测浓度降低了近一个数量级，在SRS应用于瞬态过程的组份分析方面做了卓有成效的探索；用石英毛细管形成的稳定液拄构成拄形谐振腔，降低了激光诱导等离子体光谱需要的激励能量，有效地降低了水相样品的痕量元素分析极限，为LIPS应用于微量元素的化学分析开拓了一条新的技术路线。

Besides, in the new spectral dynamical framework the calculation amount firstly is decreased to half by properly using the complex conjugate relation of spectral coefficients and the symmetric and anti-symmetric character of spherical function.

另外，新方案中的纬向谱系数计算式，合理利用谱系数的复共轭性质及球函数关于赤道对称或反对称特性，使计算量减半。

Non-symmetric kernel density estimation is first used for life-table graduation in order to solve boundary bais of symmetric kernel used in the standard kernel density estimator,and compare the symmetric kernel graduation with non-symmetric kernel graduation and obtain the satisfied result.

针对以地称核修匀方法存在着边界偏差这种现象，将非对称核密度估计用于生命表数据修匀中，提出了非对称核修匀方法，并与对称核修匀方法进行比较，得到了令人满意的结果，从而使核修匀方法得到了进一步的推广。

In this paper we separate the Hamiltonian into three parts: a spherical symmetry Hamiltonian; a z-component of the angular momentum operator, and a non-spherical symmetric potential as the perturbation operator, and provide a propose method by separating the potential containing squared magnetic field B^2 into two parts spherical symmetric and non-spherical symmetric ones so that the first-order energy correction due to the non-spherical symmetric potential is zero, and the second-order correction due to B^2 can be obtained by a simple variational method.

采用变分法和微扰法相结合的方法，把高强度磁场中氢原子的哈密顿H分为三部分：球对称哈密顿；z分量角动量算符相应部分和非球对称势微扰，并用一种特别规定的分解法将哈密顿H中含磁场平方项的势能分解为球对称与非球对称两部分，且使非球对称部分引起的一级修正能量值为零，并采用一种简便的变分法直接求出B^2对能级的二级修正值。

In order to obtain symmetry and parallel polarized light,the double Wollaston prism is amended. After getting symmetric polarized light at a big splitting beam angle,an ordinary triangular prism is added so that the symmetric light beam can be divided into parallel light beams.

为了获得对称且平行分束的偏振光，对双Wollaston棱镜进行了修正，在获得大分束角的对称偏振光后，配合普通玻璃三棱镜，使对称分束光变成平行分束光，通过改变三棱镜与双Wollaston棱镜间的距离来改变平行光的剪切距离。

In order to obtain symmetry and parallel polarized light, the double Wollaston prism is amended. After getting symmetric polarized light at a big splitting beam angle, an ordinary triangular prism is added so that the symmetric light beam can be divided into parallel light beams. The distance between the triangular prism and the double Wllaston prism is changed so that the distance of the shearing parallel light can be changed.

为了获得对称且平行分束的偏振光，对双wollaston棱镜进行了修正，在获得大分束角的对称偏振光后，配合普通玻璃三棱镜，使对称分束光变成平行分束光，通过改变三棱镜与双wollaston棱镜间的距离来改变平行光的剪切距离。

Problem III Given find such thatProblem IV When Problem I or II or III is consistent, let Se denote the set of its solutions, for given , find , such thatwhere is Frobenius norm, S is Rn×p or a subset of Rn×p satisfying some constraint conditions, such as symmetric, skew-symmetric, centrosymmet-ric, centroskew symmetric, reflexive, antireflexive, bisymmetric or symmetric and antipersymmetric.

问题Ⅳ 设问题Ⅰ或Ⅱ或Ⅲ相容，且其解集合为SE，给定X0∈Rn×p，求X∈SE，使其中‖·‖为Frobenius范数，S为Rn×p或为Rn×p中满足某约束条件的矩阵集合，如对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵、双对称矩阵、对称次反对称矩阵等。

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。

Two kinds of self-made PCF were used, and an effective fusion scheme was adopted to perform the splicing experiments. By combining experiments and numerical calculations, reasonable fusion parameters were set up and the mode fields at each fiber′s end face were rescaled.

基于一种高效的低损耗熔接方案，将理论计算与实验测量相结合，选取合理的熔接参量对光纤端面模场进行重塑，使两光纤端面模场匹配程度大大提高，从而实现了对称结构与非对称结构PCF之间、以及两种非对称结构PCF之间的低损耗、高强度的熔接。

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。