向量

Definded a new combination rule for the vectors of a vector space, obtain a new special group, called Bai-Liang group,which is exchange group, i.e. Aber group.

定义了新的向量结合法的多维向量空间的所有向量，组成了一个特别的BAI-LIANG 群，是交换群，即阿贝尔群。

The optimal control law obtained consists of linear analytic functions and a compensation term which is a series sum of the adjoint vectors. The analytic functions can be found by solving a Riccati matrix difference equation and a matrix difference equation. The compensation term can be obtained by a recursion formula that solves adjoint vector equations.

得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成，其解析函数由一次性求解Riccati矩阵差分方程和矩阵差分方程得到，补偿项由求解伴随向量差分方程的递推公式得到。

We find serval conditions that are equivalent to 2-tournament matrices being singular,give the bound for the maximum algebraic multiplicity of 0 as an eigenvaulle of n order2-tournament,obtion the spectral radius of a singular 2-tournament matrix of order nis bounded above by n-2,and investigate 2-tournament matrix achieving this bound.

第五章讨论了2-竞赛矩阵的奇异性和特征值之间的关系，得到了2-竞赛矩阵奇异的充要条件，给出了2-竞赛矩阵的零化向量的刻划，得到了得分向量，3-圈数目与奇异性的关系；给出了2-竞赛矩阵的特征值0的代数重数的上下界，得到了奇异的2-竞赛矩阵谱根的最大值及谱根达到最大值的竞赛矩阵的得分向量的特征。

The nonlinear plant is first linearised, the fuzzy basis function vector is then introduced to adaptively learn the upper bound of the system uncertainty vector,and its output is used as the parameters of the compansator in the sense that both the robustness and the asymptotic error convergence can be obtained for the closed loop nonlinear control system.

在该方法中，首先将非线性系统线性化，然后利用模糊基函数向量自适应学习系统不确定向量的上界，模糊基函数向量可作为补偿控制器的一个参数。在控制系统的设计过程中可充分保证非线性控制系统的鲁棒性和跟踪误差的渐进收敛性。

The common method, that all strong-correlation terms of the model are eliminated, can bring the loss in the engineering application, so the new method is proposed that the identified model reserves some correlation. The augmented matrix A is constructed by the outputΔW and the matrix S. The"determinating order based on ratio of determinant"is brought out to screen the strong-correlation terms in the structure identification. The latent root estimation is improved in screening the eigenvalues and eigenvectors. Thus the estimation precision is improved greatly.The consistence check of guidance instrument error coefficients of flight test and ground test is the purpose of flight experiment. The causes of inconsistency of the two models are analyzed. The hypothesis test of linear regression model based on F statistics is proposed to check the consistence.Finally, the instability of error coefficients is probably caused by the change of the flight environments, therefore, the relation between the error coefficients and flight environment is analyzed. The approach is presented to identify SINS guidance instrument error models and compensate the error in the segmented sections corresponding to the change of vertical acceleration of aircraft.

在结构辨识中，常用的方法由于将模型中的强相关项全部剔除而给工程应用带来损失，因此，本文提出了新的有益思想，即在保留一定相关性的基础上进行辨识：将输出向量ΔW与环境函数矩阵S构成增广矩阵A，然后采用"比定阶行列式"来剔除相关向量的方法，这样既可以尽可能多地保留了对落点影响大的强相关参数，又可以对落点影响小的强相关参数给予剔除；在参数估计中，改进了特征根估计中特征根和特征向量的筛选方法，提出"近零"准则，从而大大提高了参数估计的精度；再者，鉴于天地模型"一致性"检验是飞行试验和SINS制导工具误差系数分离的主要目的，因此，本文又深入分析了造成天地模型不一致的原因，提出了采用基于F统计的线性回归模型假设检验方法来进行捷联制导工具误差模型的天地"一致性"检验；最后，鉴于飞行环境剧烈变化可能会对惯性仪表误差系数稳定性带来一定的影响，因此本文深入地分析了SINS制导工具误差系数与外界环境的关系，提出了基于过载变化大小的分段辨识和分段实时补偿的算法。

In order to improve the correct rate of enterprise's financial distress prediction and reduce the sample number and training time, renyi-entropy and least squares support vector machine is applied to the field of financial distress prediction on the basis of the traditional support vector machine prediction model and advances a kind of prediction model which is based on Renyi-entropy and LS-SVM.

为了提高企业财务困境预测的正确率，减少训练模型的样本数和训练时间，在传统支持向量机预测模型的基础上，将Renyi熵和最小二乘支持向量机算法应用于财务困境预测，提出了一种基于Renyi熵的最小二乘支持向量机预测模型。

The main research work in this paper is as follows:(1) A detailed analysis about the theory of the SVM is given in the paper. And one framework of the Network Fault Diagnosis System based on SVM in network Application Layer is proposed. The handle process and the function, mechanism of the components of this framework are discussed in the paper.(2) When the size of the training sets is uneven, the classification error rate of the results based on the traditional C-Support vector machine is undesirably biased with the less sample in the training sets.

由于故障诊断是有限样本学习问题在实际中的体现，因此可以将支持向量机方法引入到网络应用层的故障诊断中来，本文涉及的内容主要包括：(1)详细深入的分析了支持向量机的理论特点及其与网络应用层故障诊断的关联，并就构建的基于支持向量机的网络应用层故障诊断模型，阐述了该模型的处理流程以及其中各个模块的功能、机制。

This passage analyzes the advantage and disadvantage of the Boolean Model and the Vector Space Model in information retrieval model: the Boolean Model is simple to realize, but its classification ability is limited and the logic expression formula is strict.

本文分析了信息检索中传统文档特征表示的布尔逻辑模型和向量空间模型的优缺点：布尔逻辑模型虽机制简单、容易实现，但是它的分类能力有限且逻辑表达式过于严格；向量空间模型将文档映射到连续域向量空间，为进一步的权重计算等多元处理提供了基础，但容易忽略文档集合中各个文档的一些共有特征。

From Poisson matrix, we can observe volume-preserving vector fields. By using Geiges-Gonzalo's existence of contact circle Theorem [3] , we show the existence of volume-preserving circle on3-manifolds which says that every3-manifold admits two linear independent vector fields preserving a same volume form.

通过Poisson矩阵可以观察出保积向量场，再利用Geiges-Gonzalo的接触圆存在性定理[3]，我们证明了保积圆的存在性：每个闭的3-流形上都存在两个处处线性无关的保积向量场并且它们的常系数线性组合仍是保积向量场。

At polymorphic gene locus, the variance components of quantitative trait was described as follows:VA=2βp and VG=p′Xp-G2 in which p=column vector of polymorphic allele frequencies,β=row vector of2,X=［a2ij］i×i matrix,aij=genotype value,and G=population mean.

数量性状相对多态座位的加性方差和遗传方差分别为VA=2βp和VG=p′Xp-G2，其中p′和p分别表示多态等位基因频率的行向量和列向量，X表示以基因型值平方为元素的矩阵，β表示以基因均效平方为元素的行向量，G为群体均数。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。