三线性形式

It separated 3-D space, 2-D space, temporal space and abstract space (focused on the first 3). 3-D space/2-D space belong to the same category in syntactic model; but 2-D space/ temporal space /abstract space share the same category when we talked about how to confirm the spatial direction. 2. It investigated a spatial system proposed by Mr. Qi Huyang, and argued that there is necessity to modify this system. 3. It enumerated a series of grammatical forms which are involved in the "Spatial System", and pointed out that there exits a relation among these forms: words representing "Spatial and Locative"→ phrases representing "Spatial and Locative"→ sentences representing "Spatial and Locative".

第三章研究"空间系统"的子系统。1、分出立体空间、线性空间、时间和抽象空间几大领域，在句法上，立体空间/线性空间是一类；但在如何确定方向场的问题上，线性空间/时间/抽象空间是一类。2、省视了齐沪扬先生已提出的一个空间系统体系，指出很有改进的必要。3、归纳了"空间系统"所涉及的各种语法形式，并指出它们构成"表示空间方位意义的词→表示空间方位意义的短语→表示空间方位意义的句子"的层次关系。4、辨析各种语法形式的语义域及其语义结构，并考察语法意义与语法形式的对应情况。

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。

This thesis mainly studies the problem of the boundary value of second-order and third-order nonlinear and linear difference equation.

本篇硕士论文主要研究了一般形式的二阶和三阶非线性和线性差分方程的边值问题。

In Chapter Three, we use the method of interpolation spline of differential operater to come up with the reproducing kernel in H01 with respect to bounded linear operator in H10. Then we use the reproducing kernel to develop the expression of the best approximating of bounded linear operator in H10 and prove its convergence.

第三章中，对于H_0~1中的有界线性算子，用微分算子插值样条函数的方法给出了H_0~1空间中的再生核，利用此再生核给出了H_0~1上的有界线性算子的最佳逼近的表达形式，并证明了其收敛性。

The effect of the form(including individual,complex and complex proportion),the dose of graphite,carbon black,carborundum and the alkalinity of base slag on the melting speed were studied.

以石墨、炭黑、碳化硅等三种含碳材料和碱度分别为0.8、1.0和1.2的基渣为原料，研究了炭黑、石墨和SiC加入形式(单独或复合，包括复合时的比例)和加入量以及基渣的碱度等因素对保护渣熔化速度的影响，并对试验数据进行了多元线性回归分析。

Using a perturbation method, these linearized equations are solved for a composite sphere with the charge densities of the rigid core surface and of the surface layer as the small perturbation parameters. Analytical expressions for the settling velocity and electrophoretic mobility of the composite sphere in closed form have been obtained from a balance among its hydrodynamic, electrostatic, and/or gravitational forces.

以复合粒子之固体核心表面的电荷密度和多孔性表面层内的固定电荷密度为二个微小扰动参数，应用正规微扰法来求解这些已线性化之主导方程式，再藉平衡作用於复合粒子的重力、静电力和流体阻力等三种力后，可得到带电球形复合粒子的沉降速度及电泳可动度的解析形式表示式。

The topics covered in these sections are the geometric interpretation of systems of linear equations, the classification of finite symmetry groups in two and three dimensions, the exponential of a matrix and its application to solving systems of first order linear differential equations with constant coefficients, and Hurwitz's theorem on the composition of quadratic forms.

这些条文所涉及的主题是线性方程组的几何解释，在两个和三个有限对称群的分类方面，一个矩阵及其应用，以解决一阶常系数线性差分方程，系统指数赫尔维茨定理在二次形式组成。

Two basic theorems are given by researching Hamilton's two steps linear differential equations of bender equations which provide widespread application methods of normal differential operator correspond to ladder operators,then the solutions of general equations are obtained by taking advantage of the two above theorems: The energy eigenvalue equation of one-dimensional oscillator; the common state of ; the radial equation of a bondage state of hydrogen atom; the radial equation isotropic three-dimensional harmonic oscillator; the infinity deep potential well of ball

本文通过研究束缚态本征方程里的哈密顿算符的二阶线性常微分形式，给出两个基本定理并证明，提供构造二阶线性常微分算符相应的阶梯算符的普遍实用的方法，然后利用这两个定理构造量子力学中常见力学量的阶梯算符，并用以计算其能量本征值和对应本征函数：一维谐振子的能量本征方程；共同本征态；氢原子束缚态径向方程；三维各向同性谐振子的径向方程；无限深球势阱。

This approach first aligned 3D faces based on non-uniform mesh re-sampling which result the uniform number of vertex and topology structure and kept in a vector. Second, we changed the vector to the matrix by division and overlap, and then 2DLDA suggests a feature selection strategy to select the most discriminative features from the corner.

该算法首先使用基于非均匀网格重采样的方法对所有三维人脸做规格化处理，使三维人脸具有统一的点数和拓扑结构；其次，以先分段、再重叠的形式将原本一维向量表示组织为二维矩阵表示，然后使用二维线性判别分析方法(2DLDA)对获得的数据进行特征抽取。

Especially, it is found that there exists three types of relative permeability of water such as concave, convex to the water saturation ax and the reversed "S" pattern. The super-low permeability reservoir is sensitive to pressure, apparent with millipore undersaturation and water blocks. In this study, a new concept of irriducible undersaturation is brought up. And a new mode to describle the process of imbibition dynamics is used to reveal and confirm the mechanism of pinhole enveloping macropore as following: pendular ring of wetting phase gathers→it fills throat→it truncates nonwejting phase . The expression of pressure distribution and the equation of oil production are deduced under conditions of non-darcy linear seepage and non-linear seepage.

尤其发现水相相对渗透率曲线存在凹向、凸向含水饱和度轴及反S形三种形式；特低渗透储层的压力敏感性强，微孔隙的欠饱和及水锁效应显著，本文研究中提出欠束缚水饱和度的概念，引用一种描述渗吸动态即湿相液环聚集→充填喉道→截断非湿相的演化过程的新方法，更深刻地揭示和证明了&小孔包围大孔&机理；推导出了非达西线性渗流和非线性渗流条件下的压力分布表达式和油井产量方程。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。