阶数

In the first part,two methods calculating the coefficients of nilpotentclass normal forms are proposed.one is the iteration search method based onrepresentation theory of Li-algebra,and another is a new matrixrepresentation method based on the adjoint operator concepts,both are ableto be used to analyse the normal form problems with high orders and largedimensions efficiently.

在第一部分工作中，对于幂零类规范形的系数计算，分别提出了基于李代数表示论的迭代搜索的理论和方法以及基于共轭算子概念的新的矩阵表示的理论和方法，从而有效地解决了维数和阶数较高时的计算问题。

A new method of finding the points on an elliptic curve by Maple is supplied; Maple is applied to the addition operation, the scalar product operation and the method of seeking the order of a basic point on the elliptic curve are proposed; the applications of Maple on ECC including encryption and decryption are supplied.

利用Maple编程求出椭圆曲线上有理点，用Maple实现椭圆曲线上两点的加法、点的数乘运算及求某个基点阶数的算法，利用Maple实现椭圆曲线密码体制的加密及解密。相比C语言，Maple语言更接近于平时说话的语法。同时，Maple语言可以方便地转化成C语言。

By using the modal superposition method for the dynamic responses calculation of the linear oscillation system, a judging indictor in the energy norm form is given to determine the number of dominant modes on mode truncation .

针对用模态叠加法计算结构线性振动系统的响应，作模态截断的截尾模态阶数的取值，给出了能量范数形式的判断指标。

Since the modes of foundation are dense,by taking the criterion of energy response as mode truncation index,the energy norm and criterion are established to calculate the mode truncated order of dynamic compaction response.

由于地基模态密集，提出以能量响应信息的收敛作为模态截断的判断指标，建立能量范数和能量判据，计算强夯动力响应的模态截断阶数。

In Chapter 4, A detailed comparison between the realization of Cholesky decomposition and OR method is given, a systolic/wavefront array made of general purpose DSP is used to realize the adaptive beamforming at a moderate speed, and a wavefront array to extract the adaptive weights which is necessary in some applications is designed. In Chapter 5, the author proposed a new structure to realize the space time adaptive processing. First 1~q using the FFr and the truncating infinite sequence and sone optimizing method, a much simpler architecture can be acquired in realizing the three portion of channel processing: quadrature sampling, pulse compression and adaptive equalization.

第五章研究并提出了用全通用DSP模块设计空时二维自适应信号处理机的新方案，首先用快速付立叶变换和对长序列截断处理的重叠保留法以大大减少的运算量完成了处理机通道处理部分的正交插值、脉压、自适应均衡三个功能块的长阶数线性卷积运算，接着对自适应波束形成提出了多种实现方案，分析了多种方案下的运算量和设备要求，指出在不同通道数、不同数据吞吐率、不同自适应要求时这几种方案有不同的可行度和实现难度，并针对实际要求确定了一种运算田N、的实现方案，对自适应波束合成部分的大量贝玉以良元组咸肋冈络结拘和处凰闺和羽凶挝娠昨了优化设计以威少设备复杂性，构成了设备量大夕父伯小、们g团回高、辜于生回阴田闩引愧快的空时二维自适囱戏升引毗四机。

Specifically, there are three kinds:(1) constant variation method to track two-body problem the root number of variables to establish perturbed equation;(2) coordinate perturbation method in order to track objects in real position and the location of an intermediate orbit perturbation differential equation as a variable to establish;(3) transformation theory, through a series of canonical transformation to reduce the order of the equations of motion to make it a more simple form.

具体做法有三种：（1）常数变异法，以二体问题轨道根数为变量建立摄动方程；（2）坐标摄动法，以天体在实际轨道上的位置与某一中间轨道上的位置差作为变量建立摄动方程；（3）变换理论，通过一系列正则变换，降低运动方程的阶数，使其具有更简单的形式。

In this paper we introduce a search algorithm of computer, and the arithmetic can get a magic square of squares with high rank in a short time.

本文提供了一种计算机搜索算法，该算法能够在比较短的时间内获得阶数较大的平方数幻方。

Section two elaborates the structure of a simple model on static yield curve of zero-coupon bond. According to the difference of constitution principle, the dissertation divides the numerous static models into direct ones and indirect ones. On the basis of setting forth the different constitution thoughts of two methods, it compares the merits, shortcomings, and the application scopes of the two methods. Spline model is the most common indirect method, and is the study emphasis of this section, especially its three key approaches that are defining the rank of function, the subinterval number to be divided, and knot of each subinterval, which are fully elaborated in the dissertation.

第二节阐述了现行静态零息票债券收益率曲线简单模型的构造，根据构造原理的不同，论文把众多静态模型划分为直接法和间接法两大类，在简述两种方法各自不同的构造思想的基础上，对两种方法的优缺点及适应范围进行了比较；分段样条函数模型作为最常用的间接法，是本节研究的重点，尤其是对它的三个关键环节：确定函数的阶数、确定所分的段数、确定各段的分解点，论文更是给予了充分的论述。

The effects of theFresnel number, spherical aberration coefficients and the beam orders on the beamquality were discussed in detail.

详细讨论了透镜系统的菲涅尔数、透镜球差系数以及光束阶数等参数对光束质量的影响。

An efficient Sphere Decoding algorithm is proposed for uncoded Multi-Input Multi-Output systems with a large number of antennas and higher modulation constellations. This method utilizes a channel-based group detection strategy.

摘要该文针对无编码的多输入多输出无线通信系统中的最大似然检测接收机在发端天线数较多、调制阶数较高时计算复杂度过高的问题，提出了一种低复杂度的球形译码算法。

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。