线性的

We first state general linear model, ridge-type estimator and general ridge-type estimator, and the constraint biased estimator. And then, we introduce some basic theory about matrix and some conclusion about the admissibility of estimator in Gauss-Markov model. In the third chapter, we discussion several equivalent characterization of the best linear unbiased estimation, we proved that admissible characterization of admissible of linear estimation is as conditional general ridge-type estimation in general linear model. A necessary and sufficient condition that homogeneous linear estimator is admissible estimator is obtained.

本文首先概述了一般线性模型，岭估计及约束岭估计的发展历史和研究现状，在第二章介绍了矩阵的一些基本知识和可容许性的一些基本结论，第三章讨论了一般线性模型最佳线性无偏估计的几个等价条件，以及线性估计的可容许性特征，得到了一般线性模型的可容许线性估计均具有条件广义岭估计的形式，给出了一个齐次线性估计为可容许估计的充分必要条件。

In the fourth chapter, we discussion the characterization of admissible in the general linear model under equality constraint and inequality constraint, we give the necessary and sufficient condition that homogeneous linear estimator is admissible estimator, and by using the relationship between homogeneous and inhomogeneous linear estimator, we obtain the characterization of admissible inhomogeneous linear estimator.

第四章分别在带等式约束条件以及不等式约束条件下，讨论了一般线性模型线性估计的可容许性特征，给出了在约束条件下齐次线性估计为可容许估计的充分必要条件，同时利用齐次线性估计与非齐次线性估计之间的关系，把齐次线性估计的可容许性特征推广到了非齐次线性估计的可容许性特征。

Content of the course consists of:(1)Basic Theories of Polynomials ;(2)Linear Algebra: topics on basic matrix theory, determinant, system of linear equations, vector space, linear transformation, eigenvalue problems, inner product and Euclidean space , and quadratic form etc.;(3) Analytic Geometry: topics on algebraic operations of vectors, coordinates, lines and planes, curves and curved surfaces, etc.

学习本课程后，学生应学会用线性空间与线性变换的观点处理包括线性代数方程组在内的有关理论与实际问题；学会熟练地运用矩阵工具；本课程还学习基本的多项式知识和空间解析几何的基本知识。课程内容包括几个主要部分：（1）多项式代数；（2）线性代数：矩阵，行列式，线性代数方程组，向量空间与线性变换理论，特征值问题，欧氏空间理论，二次型等；（3）解析几何：几何空间向量代数，通过建立坐标系以及借助向量方法研究空间平面与直线及点﹑线﹑面的相互关系，借助曲面方程研究空间曲面，尤其是柱面，锥面，旋转面和二次曲面以及曲面的交线等。

Using this method, the controller design for performance and robustness can be designed separately, which has the potential to overcome the conflict between performance and robustness in the traditional feedback framework. Third, to make the vehicle meet the performance index in full flight envelop, a H∞ gain-scheduled controller based on Linear Varying Parameter system are designed. A LPV plant with a linear fractional dependent variable can be represented by upper LFT (Linear Fractional Transformation) interconnection.

通过把非线性系统简化为了线性变参数系统，再有通过线性分式变换将LPV系统转化为一个线性定常系统和不确定性组成的LFT互联形式，使之转换成为一个经典鲁棒控制问题，然后通过求解一组线性矩阵不等式得到变增益H_∞控制器。

A decoupling control approach based on inverse system method had been applied for the permanent magnet synchronous motor, which was multi-variable, nonlinear and coupled system. PMSM was decoupled into second-order linear speed subsystem and first-order linear flux subsystem. The servo robust controller was used to design linear closed-loop controller for the pseudo-linear subsystems.

针对永磁同步电机这种多变量、非线性、强耦合的控制对象，应用逆系统方法，将永磁同步电机解耦成二阶线性转速子系统和一阶线性磁链子系统；在此基础上，采用鲁棒伺服控制器对伪线性子系统进行线性闭环控制设计。

Since convergencehas a close relationship with normed space itself, the definition which is normedspace (Y_1) stronger than normed space (Y_2), and normed space is presented innormed space for further research.

由于收敛性与赋范线性空间Y本身关系密切，文中引入了赋范线性空间Y_1强于赋范线性空间Y_2的定义，并将赋范线性空间Y具体到赋范线性空间l_p中进行研究。

The result shows that the relationship of conopy density with living cover plant space expresses a negative correlation, age class expresses a positive correlation, age class expresses a positive correlation; the relationship of conopy density with the dead covering plant and general covering plant expresses a positive linear covrelation, age class expreses an indicial ...

研究结果表明，郁闭度与活地被物负荷量呈负线性相关关系，龄级与其呈正线性相关关系；故郁闭度与死地被物和总地被物负荷量呈正线性相关关系，龄级与其呈正线性相关关系；蓄积量与地被物的负荷量呈线性正相关关系，但相关性较小。

Unitary linear regression is done between w~e、 w~ρ、 e~ρ、w_L~w_P. For α_v 、 C_ c between w、ρ、 e、 w_P in eastern China, unitary linear regression is done to silty clay as well as multivariant regression with coefficient iteration method and least-squares procedure are done to all kinds of soil, and the two results are compared. Unitary linear regression and multivariant regression are done to c_q、φ、 c_d、φ_d between e and I_P. Unitary linear regression and multivariant linear regression are done to napierian logarithm of q_u between e 、 I_L、 w_P and w_L, then the equations of regression are checked with other parameters.

对物理指标含水量～孔隙比、含水量～湿密度、孔隙比～湿密度、液限～塑限作了一元线性回归；对华东地区粉质粘土的压缩系数、压缩指数和含水量、湿密度、孔隙比及塑性指数作了一元线性回归；对华东地区所有土类的压缩系数、压缩指数和物理性质参数用系数迭代法和最小二乘法作了多元线性和非线性回归，并对两种方法得到的回归结果作了比较；作了快剪强度指标和固结快剪强度指标关于孔隙比和塑性指数的一元线性回归和多元线性及非线性回归；对无侧限抗压强度的自然对数值和孔隙比、液性指数、液限及塑限作了一元和多元线性回归，并用其它工程的参数对回归方程进行了检验。

Modeling and stability analysis problem of linear switched system are emphasized in this part and main results include:(1) Through investigation in the projection of 〓 on x, where x denotes continuous state vector, a series of sufficient conditions for stability, asymptotic stability and unstability of linear switched system's equilibrium in the sense of Lyapunov are achieved. And also, a sufficient and necessary condition for state bounded stability of linear switched system is received.(2) For a class of periodical linear switched system whose switching sets are a group of ordinal lines starting from the original point, it's proved that state bounded stability can be defined by the running characteristic in a single period (3) Based on linear switched system, the concept of linear switched system network is put forward. Linear switched system network is a complex network interconnected by many linear switched systems.

这部分着重研究线性切换系统的建模与稳定性分析问题，主要成果包括：（1）通过考察〓在x上的投影，得到线性切换系统的平衡点在Lyapunov意义下稳定、渐近稳定及不稳定的一系列充分条件，并得到了线性切换系统状态有界稳定的一个充要条件；（2）证明了对于一类切换集为从原点出发的一组射线的周期线性切换系统，其状态有界稳定可根据一个周期内的系统运行特性来判定；（3）在线性切换系统的基础上提出了线性切换系统网络的概念，线性切换系统网络是由多个线性切换系统交互作用而形成的复杂网络。

Then gives judging the vector linear relevance by the value of determinant, the order of matrix, the solution to uneven sublinear system of equations, Cramer principle, linear substitution, the theory of matrix and so on in the linear space and Ou Shi space, produces 13 equivalences of the vector linearity relevant under the dissimilar condition, and elaborates the widespread application of the vector linearity relevant through concrete examples.

在线性空间、欧氏空间中给出了运用行列式的值、矩阵的秩、齐次线性方程组的解、Cramer法则、线性变换、矩阵理论等知识来判定向量的线性关系，及不同条件下向量线性相关性的十三个等价命题，并通过具体例题阐述向量线性相关性的广泛应用。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。