零化子

In order to find a stable approximate solution of linear compact operator equation, the article introduces general theories about ill-posed problems, it bases on spectral theory of self-adjiont compact operators and the singular value decomposition for compact operators, avails singular system to give expression of the solution, and explains ill-posedness of compact operator equation roots in the property that the singular values trends to zero. Thereout, it is provided with theoretic support of building up regularization method by inducting regularization filter to weaken or filtrate the influence that the nature of the singular value being very close to zero has on the solutions stability.

为了得到线性紧算子方程稳定的近似解，介绍了不适定问题正则化的一般理论，以自伴紧算子的谱分析与紧算子奇异值分解为理论基础，利用奇异系给出了解的表达式，说明了紧算子方程不适定性的根源在于紧算子的奇异值趋于零的性质，由此通过引入正则化滤子函数来减弱或滤掉奇异值趋于零的性质对解的稳定性的影响，构造正则算子，从而提供了建立正则化方法的理论依据。

In addition, the discrete Euler operator and homotopy operator of order zero are preliminarily studied.

另外，初步研究了离散化的零阶欧拉算子和同伦算子。

Different from the traditional approach of solving GDA by singular value decomposition,the new algorithm utilizes kernel modified Gram-Schmidt orthogonalization algorithm to extract the optimal transformation matrix directly,which can not only effectively hold the most discriminant information in the null space of within-class scatter matrix,but also make the solution more stable in numeric.

与传统用奇异值分解获取目标特征子空间的方式不同，新算法运用核修正格兰-施密特正交化过程直接提取最优投影变换矩阵，不仅有效地地保留了类内散度矩阵最具辨别力的零空间信息，同时使所求解在数值上更稳定。

Finally, it investigate QF-ring with right gpm-injective, and obtain the following theorem:Theorem The following statements are equivalent:(1) R is quasi-Frobeniusean ring:(2) R is right noetherian, left pm-injective ring, right pm-injective ring;(3) R is right noetherian, left pm-injective ring, right GP-injective ring;(4) R is right noetherian, left gpm-injective ring, right gpm-injective ring;(5) R is right noetherian, right gpm-injective ring and each right minimal ideal is right annihilator.

最后用右gpm-内射对QF环进行研究，得到了如下定理：定理下列条件等价：(1) R是quasi-Frobeniusean环；(2) R是右Noether，左pm-内射环，右pm-内射环：(3) R是右Noether，左pm-内射环，右GP-内射环；(4) R是右Noether，左gpm-内射环，右gpm-内射环；(5) R是右Noether，右gpm-内射环且每个极小右理想是右零化子。

This dissertation studies some topics in soliton and integrable system,which mainly include as follows:exact solutions especially travelling wave solu-tions and solitary wave solutions,Painlevēproperty,transformation,similarity reduction,symmetries and their Lie algebra structure,generation ofsoliton hierarchy and their zero curvature representation,Hamiltonian struc-ture,Lax or Liouville integrability,nonlinearization of Lax pairs,applications ofWu's method and symbolic computation.

本文研究内容涉及到孤立子和可积系统的多个方面：精确解特别是行波解和孤波解，Painlevē性质、变换、相似约化、对称及其Lie代数结构、孤子族的生成及其零曲率表示，Hamilton结构，Lax和Liouville可积性、Lax组的非线性化以及吴方法和符号计算在上述研究中的应用。

C.R.Miers has shown that the Lie triple derivation on a vN algebra M with no central abelian summands has the form D +λ, where D is an associative derivation and A is a linear map of M into its center which annihilates brackets of operators.

Miers证明了无交换部分的vN代数M上的三元Lie导子具有D+λ形式，其中D是M上的结合导子，λ是从M到它的中心Z上的线性映射且零化M中的括积。

The exact solutions of the linearized Schwinger-Dyson equation of fermion self-energy are obtained and applied to the problem of chiral symmetry breaking in the theory of four-fermion and gauge interactions.

零温下线性化费密子自能的许温格-戴森方程的严格解被求出并用于四费密子和规范相互作用理论中的手征对称破坏问题。

This invention relates to three-dimensional seismic data processing quality monitoring technology. Selecting time-window and analysis frequency for FFT to obtain frequency-domain conversion result for every channel; taking mean-filter to obtain the statistic excited energy or noise disturbance; plotting all results on plane graph to monitor the 3D excited energy or noise disturbance; taking normalization and autocorrelation to all earthquake channel; summating all autocorrelation statistic result to obtain opposite statistic autocorrelation result; finding out and plotting the zero-crossing of autocorrelation on plane position for monitoring excited wavelet.

本发明涉及一种三维地震资料处理质量监控技术，步骤是：选定时窗和分析频率；对某炮各地震道在时窗内做快速富立叶变换，得到道数据在频率域变换结果；对同炮的所有地震道做频率域中值滤波，得到该炮的统计激发能量或噪声干扰量结果；将所有炮的计算结果绘到各炮点平面图上，监控三维激发能量或噪声干扰；对地震数据某炮的各地震道做归一化自相关；对同炮的所有地震道的自相关统计求和，得到该炮的统计自相关结果；寻找该炮统计自相关的零交叉时，将所有炮的零交叉时绘到各炮点平面位置上，完成激发子波监控。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。