线性

Ects, the covariance matrix of observation vector has special structure,and using the linear transformation for original model by idempotent matricesin the spectral decomposition of the covariance matrix, the problem of estima-tion of the covariance matrix becomes simultaneous estimation of all the distincteigenvalues of it.

在带有随机回归系数的一般线性模型中，首次提出了随机回归系数和参数的Minimax估计问题，分别在齐次线性估计类和一切估计类中研究了一个线性估计的Minimax性。

The research of this paper includes: 1. We corrected an incomplete expression of a known theorem on singular eigenvalues of matrix.

由这两种方法得到两种线性系统，一种是稳定化的线性系统，另一种是稳定的线性系统。

Firstly, we give out a reduction way for quasilinear generalized system A〓=G , and the concept of the index κ geometrically nonsingularity, where A is singular and of smooth kernal space. By using the canonical projection mappings onto the space of ker A , a class singular pointimpasse point only owned by nonlinear generalized system is also studied and we also prove that the regular index κ quasilinear generaized system A〓=G defined on the region W is equivalent with an ODEs 〓 defined on a submanifold W〓 of the W, so we reduce the problem of quasilinear generalized system to the problem of an ODEs.

首先利用投影函数，给出了拟线性广义系统A〓=G的一种归约方法，提出了指数κ几何非奇异的概念，同时对广义系统特有的一类奇点-寂点进行了研究，证明了正则指数κ的拟线性问题A〓=G等价于在其定义域W中某一个子流形W〓上的正常微分方程〓，从而将拟线性广义系统的问题归结为常微分方程问题。

By synthetically analysizing the physical and chemical properties of all components and particle size, the content of F2641 in the JOB-iC is determined by gravimetric analysis after F2641 is seperated from HMX,TATB and PNP through ? alkali reflux. Determination conditions is set as follows the sample is boilingly refluxed for six hour in a constant temperature bath after adding lOOm! 8.0 ?? 0.1% NaOH. The solvent DMF saturated by TATB is used for extracting HMX,F21 and PNP from the sample and TATB is seperated by crucible filter G4. The mass precent of TATB is determined by extraction fractionation. The mass percent of PNP is measured by multiwavlength linear regression ultraviolet spectrophotometry. The testing conditions are set as follows:multiwavlength constitution: X=267nxn, 275nm, 283nm, 29mm, 299nm,the application scope of the Lambert-Beer law: the concentration of PNP is O.005?0.O25mgIml, the concentration of HMX is 0.060.3Omg/ml,absorption coefficents of PNP and HMX are solved by the slope of linear regression curve of absorbency- concentration of standard solution of PNP and HMIX for measuring wavelengthes,on the basis of the Lanibert-Beer law and absorbancy additivity principle, the slope of linear regression curve of A/E(1) and E1 of PNP and HMX solution is regarded as the concentration of PNP in the solution.

根据传爆药中各组分的物理、化学性质及主体炸药的粒度大小，进行综合分析，确定了采用碱回流重量法测定JOB-1C 中F_(2641)的含量，测定条件：加入100ml浓度为8.0±0.1％的氢氧化钠，在恒温水浴中煮沸回流6h；采用溶剂萃取法测定JOB-1C中TATB的含量，选择TATB饱和的二甲基甲酰胺为萃取溶剂，用G4坩埚式过虑器进行萃取分离；采用多波长线性回归紫外分光光度法测定JOB-1C中PNP的含量，通过实验确定了多波长组合：λ=267nm，275nm，283nm，291nm，299nm；朗波—比耳定律的适用范围为PNP浓度：0.005～0.025mg/ml，HMX浓度：0.06～0.30mg/ml；在测定波长下，对PNP、HMX标准溶液的吸光度—浓度进行线性回归，由回归曲线的斜率得出PNP、HMX的吸收系数；根据朗波—比耳定律和吸光度加和性原理，在测定波长下，对PNP、HMX 两组分混合溶液A_i/E_HMX(i与E_PNP(i/E_HMX(i进行线性回归，回归曲线的斜率即为混合溶液中PNP的浓度。

In addition, the nonlinear processes such as cross-phase modulation, non-degenerate two-photon absorption, and stimulated Raman scattering must also be considered for double wavelengths propagating in waveguide.

在归纳分析了SOI对光信号处理的研究进展的基础上，进一步完善了超快脉冲在脊形硅波导中演变时所满足的线性和非线性传输方程，在此非线性方程中包括波导线性损耗、群速度色散和三阶色散等线性效应；同时也包含了自相位调制、简并双光子吸收、自由载流子吸收和自由载流子色散等非线性过程；当双光场在波导中传输时，脉冲之间的交叉相位调制、非简并双光子吸收和受激拉曼散射效应等非线性效应也被考虑。

Firstly, we collected and sorted out the GPS data, established the uniform velocity field for the Chinese mainland and the surrounding regions, and the horizontal deformation field relative to the Eurasia plate; Secondly, we established a motion model for the entire rotation and homogeneous strain of the first and second level blocks in Chinese mainland, analyzed the motion pattern and strain behavior of active blocks in Chinese mainland, as well as the motion pattern of principal fault zones in Chinese mainland; Thirdly, considering the heterogeneity of strain distribution inside a block and supposing that the strain tensor inside the block is the linear function of location, we derived and established an equation for the entire rotation and linear strain of block and a motion model for the entire rotation and linear strain of principal blocks in Chinese mainland; We also calculated the principal strain field and the maximum shear strain field in Chinese mainland and the surrounding regions, analyzed the basic characteristics of strain field in Chinese mainland, as well as the relationship between the spatial distribution of strain field and large tectonic zones; Finally, we established the 2-D geotectonic model and digital model for Chinese mainland and the surrounding regions, calculated the stress field in Chinese mainland and the surrounding regions, and analyzed the basic features of stress field in Chinese mainland and the principal driving force for the motion and deformation in Chinese mainland.

收集整理了已有GPS资料，建立了中国大陆及周边地区统一的速度场以及相对欧亚板块的水平形变场；建立了中国大陆一、二级地块整体旋转与均匀应变的运动模型；分析了中国大陆活动地块的运动状态，应变状态，以及中国大陆主要断裂带的运动状态；考虑到一个块体内部应变张量空间分布的非均匀性，假设块体内部的应变张量是位置的线性函数，推导建立了块体整体旋转与线性应变方程，建立了中国大陆主要地块整体旋转与线性应变的运动模型；计算了中国大陆及周边地区的主应变场与最大剪应变场，分析了中国大陆应变场的基本特征，以及应变场的空间分布与大型构造带的关系；建立了中国大陆及周边地区二维的地质构造模型和数值模型，计算了中国大陆及周边地区的应力场，分析了中国大陆应力场的基本特征以及中国大陆运动、形变的主要驱动力。

As an application of continuous wavelet transform,we discuss the relationsbetween some differemtial equaltions and the integral equations by using thecontinuous wavelet transform in 〓,vector function space andabstract function space respectively;prove that they are equivalent not only in theweak topology but also in the strong topology.

作为连续小波变换的应用，分别利用〓上的，多元函数空间上的，向量函数空间上的和抽象函数空间上的连续小波变换分别得到了某些线性微分方程，某些线性偏微分方程，某些向量线性微分方程和某些抽象函数的微分方程分别等价于其相应的积分方程，证明了它们不仅在弱收敛意义下而且在范数收敛意义下是等价的。

The local superlinear convergence of line search type algorithm are proved under some condition.

本文在理论分析了相关算法的对称正定性及线性不变性，并证明了满足一定假设条件下线性搜索型算法具有局部超线性收敛性。

This paper studies the invariant, which is the linear preserving problem based on generalized inverse of matrices. The generalized inverse of matrices and the research status of preserving problems of generalized inverse are outlined. In the basis of deeply understanding the basic knowledge of linear maps, the definition, characteristics of generalized inverse and decomposition of matrix, the author analyzes the decomposition form of preserving idempotence and preserving tripotence in the PID, then studies on the linear maps form of preserving group inverses of symmetric matrices.

本文研究的不变量是矩阵广义逆线性算子的保持问题，概述了广义逆矩阵，广义逆保持问题的研究现状，在对线性映射的基础知识，广义逆矩阵的定义、性质和矩阵的分解深入理解的基础上，深入分析了保幂等、保立方幂等矩阵在主理想整环上的分解形式，继而研究了保对称矩阵群逆的线性算子形式。

In section 2,we characterize the minimal ideals of finite dimensional symmetricself-dual Lie algebras over the complex field and gives an optimistic lower bound for thedimension of the space of invariant symmetric bilinear forms on a symmetric self-dualLie algebra by means of the number of linearly independent minimal ideals.

在第二节中，我们完全刻划了有限维对称自对偶李代数的极小理想；用线性无关极小理想的个数给出了一个对称自对偶李代数上由不变对称双线性型构成的线性空间维数的最好下界

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。