对称地

We develop his ideas by finding some algebraic invariants under the adjoint actions of the group in addition to the Killing form and give a rigorous proof of the optimality of the one-parameter systems for the symmetry group of the given equations.

本文系统地研究了1+2维非线性发展方程的对称代数，证明了该方程容许一个七维李点对称群，利用Olver提出的方法，详细地建构了1+2维非线性发展方程的一维最优系统，在此基础上我们发展了他的方法，发现了除Killing型之外的其它六个在群伴随作用下的代数不变量，利用这些不变量证明了该最优系统的最优性。

In this paper,on the basis of the exact solutions for the antiplane and plane symmetric cases,the exact solution of the plane anti-symmetric case has been obtained.

在反平面及平面对称情形的精确解的基础上严格地求出了平面界面横向裂纹反对称问题的精确解。

We have obtained the following main significant results:(1) A master constraint operator for LQG is constructed, which is shown to be self-adjoint in the diffeomorphism invariant Hilbert space. Thus it lays a foundation for the master contraint programme in LQG;(2) The Immirzi parameter ambiguity in LQG is fixed by introducing supersymmetry, which leads to the conclusion that in the case where matter fields are coupled LQG might prefer supersymmetry in low energy;(3) The current accelerating expansion of our universe is successfully explained in the context of 5-dimensional Brans-Dicke theory, which gives a natural strategy to solve the dark energy problem.

重要成果包括：(1)构造出圈量子引力的Master约束算符，并证明了其自伴性，从而为应用Master约束方法解决量子动力学的难题奠定了基础；(2)通过引入超对称合理地固定了Immirzi参数，得出了在与物质场耦合的低能情况下圈量子引力可能偏爱超对称的结论；(3)用五维Brans-Dicke理论成功地解释了当今宇宙的加速膨胀，从而给出了一个自然解决暗能量问题的方案。

The reliability theory is combined with the fuzzy optimization technique, the theories and methods on the symmetrical fuzzy reliability optimization design, the asymmetric fuzzy reliability optimization design and the multi-objective fuzzy reliability optimization design are presented respectively, and then the correspondence direct model solutions, the iterative solutions, the corrected algorithm for iteration method, the level cuts solutions and the searching solutions with limited boundary for the asymmetric fuzzy reliability design are presented respectively.

将可靠性理论与模糊优化技术有机地结合起来，提出了结构对称模糊可靠性优化设计、非对称模糊可靠性优化设计和多目标模糊可靠性优化设计理论与方法，并分别给出了模型的直接解法、迭代解法、迭代求解的改进算法和非对称模糊可靠性优化设计模型的水平截集法和限界搜索法。

However, because of the positive sequence of fundamental frequency, there are still some shortages for wavelet transform in the use of harmonic measurement of three-phase dissymmetrical system. A new approach of harmonic measurement based on Period-interleaving of MALLAT arithmetic for dissymmetrical system is put forward. Analysis and experiment based on TMS320LF2407 Digital Signal Processor are made. And the result of experiment reveals that the proposed method based on Period-interleaving is valid in the use of harmonic measurement of three-phase dissymmetrical system.

但是，目前小波变换在三相不对称系统的谐波检测中存在着无法分离基波正序信号的不足，本文就此提出了一种用于三相不对称系统的基于周期交错的小波MALLAT多分辨率分解的测量方法，详细介绍了该算法的原理、流程及计算公式，同时以TMS320LF2407数字信号处理器为核心建立了实验系统对该算法进行了实验，实验结果证明该周期交错－小波变换算法可以有效地检测出三相不对称系统中的有害电流。

Since Leptokurtosis, skewness and fat-tail are always used to depict market risk, this paper introduces the improved Laplace distribution to risk management of stock portfolio. Empirical results show, improved Laplace distribution and asymmetric Laplace distribution are similar for estimating Leptokurtosis, while improved Laplace distribution is better for estimating skewness.In order to analyze the correlation between return distribution and volatility, the thesis uses ARCH-M Models to simulate the return series of China's Stock Market and developed markets ao as to discover the relation between investment return and time-varying risk.

对尖峰、厚尾、偏态的刻画有助于正确估计市场风险，本文将改进型Laplace分布引入到股票组合的风险管理中，实证结果发现，改进型Laplace分布和非对称Laplace分布对尖峰、厚尾的刻画效果接近；而非对称Laplace分布对负偏性考察不足，改进型Laplace分布的拟合结果能够准确地反映股指收益的负偏态，这也正是改进型Laplace分布相对于传统的非对称Laplace分布的优势所在。

In the present paper, the Properties of the symmetric difference of the sets are systematically researched, the essence of the symmetric difference of the several sets is revealed in terms of disjoint resolution of the set, the formula of the measure calculation with respect to the symmetric difference of the several sets is given.

本文深入地对集合的对称差进行讨论，研究了它的性质，通过集合的不交分解揭示了若干个集合的对称差的本质，给出了关于集合的对称差的测度计算公式。徐州师范大学！徐州；221009；中国矿业大学北京校区！北京；100083

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。

For any initial generalized bisymmetric matrix $X_1$, when $AXB=C$ is consistent, we can obtain the generalized bisymmetric solution of the matrix equation AXB=C within finite iterative steps by the iteration method in the absence of roundoff errors; Moreover, the least-norm solution $X^*$ can be obtained by choosing a special kind of initial generalized bisymmetric matrix.

在不考虑机器误差的情况下，当矩阵方程AXB=C相容时，对任意广义双对称X_1，矩阵方程AXB=C的解可以经过有限步迭代得到；特别地，通过选择特殊地初始广义双对称矩阵极小范数解X^*。

A few spiro ligands have been successfully synthesized and applied in asymmetric catalysis .

手性螺环配体的合成及其在不对称催化反应中的应用是不对称合成和催化研究中重要的研究领域之一，一些手性螺环配体被合成出来并成功地应用于不对称催化反应中。

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。