阶

According to normalforms that we obtained,we study universal unfolding for some degenerate bifurcationcases of codimension three and some simple global characterizations.

利用共轭算子法研究了具有幂零线性部分和不具有Z2—对称性的非线性动力系统的2阶规范形、3阶规范和4阶规范形，讨论了几种余维3退化分岔情况下的普适开折问题及其一些全局特性。

We obtain the necessary and sufficient conditions for the commutativity of k~-order slant Toeplitz operators and the compactness of products of such operators, in particular, the commutativity and the essential commutativity of such operators are in accord.

第二章研究了L~2上的k阶斜Toeplitz算子的性质、得到了两个k阶斜Toeplitz算子可交换的充要条件及其乘积和换位子是紧算子的充要条件，特别地，给出了两个k阶斜Toeplitz算子的交换性与本性交换性是一致的。

This method is an improvement of existing methods to construct nearly order elliptic curves using complex multiplication. To get elliptic curves with nearly prime orders, the time complexity of this method is O , but to get elliptic curves with prime orders, the time complexity arises to O .

该算法是现有利用复乘构造近乎素数阶椭圆曲线方法的改进，利用该算法构造近乎素数阶椭圆曲线的时间复杂性为O，同时，该算法可用于构造素数阶椭圆曲线，但时间复杂性上升为O。

In general quantum case the equal-time kinetic hierarchies for the energy moments of the covariant Wigner function were established.

在普遍量子情形下，建立了协变Wigner函数的能量矩的等时动力论链和链的截断方案，得到了与低阶矩相关的物理密度量的输运方程和约束方程，并且证明高阶矩都能通过低阶矩表示。

Let F=LF be a s-closed local formation such that every minimal non-F-groups is solvable. It is proved that 1 If every cyclic subgroup of of order 4 and every minimal subgroup of G are contained in, then G is a F-group. 2 If there exists a normal subgroup N of G such that G/N∈F and every cyclic subgroup of N of order 4 is weakly c-normal in G and every element of N of prime order is contained in Z(superscript f subscript ∞), then G is a F-group.

设F=LF是一个子群闭的局部群系，满足每个极小非F-群是可解群，证明了：1如果G的任意极小子群和任意4阶循环子群都含于Z中，那么G是F-群；2如果存在G的正规子群，使得G/N∈F，且N的任一4阶循环子群在G中弱c-正规，N的任一素数阶元含于Z中，那么G是F-群。

Yet for thickness shear actuators, due to the shear deformation dominates the plate deflection for shear actuation mechanism, the higher order shear theory can provide more accurate evaluation of the shear strain energy of the plate than the first-order o

但对于厚度剪切型激励器而言，由于激励器主要是引起板的剪切变形，而高阶剪切变形理论比一阶剪切变形理论能更好地反映结构的剪切应变能，因此高阶剪切变形理论可以提供板变形的更为精确的解。

The performance of traditional particle filter would be degenerate in alpha stable distribution noise.A new fractional lower order particle filter based on fractional lower order model was presented in this paper,and the detailed operation algorithm was proposed.

在alpha稳定分布噪声下，传统的基于二阶模型的粒子滤波器性能会出现退化，文章提出了一种基于分数低阶模型的分数低阶粒子滤波器，并给出了具体的运算公式。

In the aspect of multivariate modeling, three forms of multivariate GARCHSK model includes vector form, diagonal form and simplify form, are put forward and compared. The famous dimension disaster exists in multivariate GARCHSK model also. Based on Independent Component Analysis, multivariate volatilities of conditional higher moments are estimated through IC-GARCHSK model, which make dynamic relation of higher moment risk between multi-assets to be possible.

鉴于多元 GARCHSK 模型存在严重的"维数灾难"问题，基于独立成分分解技术提出 IC-GARCHSK 模型，给出多元条件高阶矩波动率的估计方法，使得同时度量多个资产高阶矩风险之间动态关系成为可能，为利用组合投资方式分散高阶矩风险的影响奠定了方法论基础。

Fourth precision solution can be derived from two grid sets solution with a second precision central difference scheme by Richardson extrapolation. It reduces the amount of calculation. Uncertainty is determined from the discretization error analysis. A finer grid calculation is made to validate the extrapolation scheme.

对于2阶精度中心差分格式的2套网格数值解，用Richardson外推法可以得到4阶精度的解，其工作量比直接求解4阶离散方程的工作量减少许多；对于计算中的数值不确定度，用该方法分析了离散误差，并用逐次加密网格的方法探讨了外推法的合理性。

In such doing, this dissertation serves as a step stone for papers of its counterparts to come, and, more importantly, it proposes a strategic alternative to the realization of models for image processing. This dissertation consists of three major parts. In the first part, detailed discussions and delicate analyses of academic papers on Cellular Neural Network will be provided in the hope of helping us see the potentiality of Cellular Neural Network in the applications of image processing. I will focus on the aforementioned limitations on hardware compilation as well. In the second part, I will put forth "texture analysis" as one basic model of analysis when we apply Cellular Neural Network to image processing. In this so-called texture analysis, a useful "spatial feature" is especially drawn to help us overcome possible problems of more complicated Cellular Neural Network applications in image processing."Spatial feature" also serves as a well-functioning mechanism for technology of image identification. In the last part of this thesis, I will look into a case study, where Cellular Neural Network is applied to help de-screen document image. Using it as an example, we will see how algorithms of Cellular Neural Network may be of marvelous use in applications in document image processing, since it would reduce a great deal of calculation and computation when applied to software compilation, yet opens up unlimited possibilities for higher-speed hardware compilation of high-level image processing.

这篇论文主要可以分为三大部分：在第一部份里，我们会详细地说明并讨论在过去到现在大部分将分子类神经网路应用於影像处理的相关文献及未来所有可能的发展和技术，另外也将分子类神经网路作一完整的介绍，除此之外，我们也会特别著重於分子类神经网路在影像处理相关应用理论的讨论以及其硬体实现化的考量；在第二部分里，我们提出了一个将分子类神经网路应用於影像辨识处理的基础分析—纹路分析，这是由於纹路分析的复杂性和普遍性会使得分子类神经网路於高阶影像处理的应用不会只局限在单一的影像处理技术，其中我们也提出了一个相当有用的空间特徵，此一特徵不但可以使复杂地高阶影像处理能够应用分子类神经网路，也为影像辨识技术提供了一个很好的辨识机制；在最后一部分里，我们也将文件影像分析做了一个完整的剖析，并以文件影像的去网点为例来说明在实际情况下的分子类神经网路的应用，如此演算法的开发也为文件影像处理提供了更多实际的应用，更考量了文件影像处理若以软体实现时的计算量负荷，而对未来高阶数位影像处理能够以硬体实现来提高处理速度提供了无限的可能。

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。