系数矩阵

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

Generalized ridge estimation ; kantorovich inequality ; eigenvalue ; trace of matrix ; canonical correlation coefficient ; generalized correlation coefficient

广义岭估计； Kantorovich不等式；特征值；矩阵的迹；典型相关系数；广义相关系数

Using the properties of reciprocal judgment matrix. A Theil coefficient method for priority of reciprocal judgment matrices which is based on the point of correlation is proposed, and some important properties are studied.

利用互反判断矩阵的性质，从相关性的角度提出了互反判断矩阵排序的Theil不等系数新方法，研究了该方法下一些重要性质。

This software uses Visual Basic programming language which establishes procedures, it made the computer can self-action recognize the network's spanning tree, associated matrix, loop matrix, drag coefficient vector ,and flowrate vector and so on, then solute the problem according to flow calculation simulation model that has been established.

该软件利用可视化的Basic软件编制程序使计算机能够自动识别出用户所输入管网的生成树、关联矩阵、回路矩阵、阻力系数向量、流量向量等，然后根据己建立的数学模型进行求解。

There is a very simple computing formula for coefficient,moreover,thecoefficient matrix is skew symmetric,and its element have some cycle property.

本文得到了十分简单的刚度矩阵系数的计算公式，而且刚度矩阵是斜对称的，还具有某种循环性。

The fractal theory is discussed used in urban spatial morphology. From the psychologic cognition mechanism aspect, according to cognitive superincumbent process, the indexes system and research frame for quantitatively descriptive urban spatial morphology are constructed.

基于以上研究，笔者探讨了网络分析和特征值分析中的主要指标，即对线状要素描述的主要指标有：方向均值、关联矩阵、邻接矩阵、回路数H、β指数、α指数、γ指数等，对面状要素描述的指标有：圆形率、紧凑度、形状系数、标准面积指数、放射状指数等；并探讨了分形理论在城市空间形态研究中的应用，在此基础上，从心理学的认知机理出发，按照自上而下的认知过程构建了定量描述城市空间形态的指标体系和研究框架。

The results show the superior performance and reliability of the kernelized Xie-Beni index in comparison to other indices, and it can take priority of being employed as the validity criterion for the kernel fuzzy clustering algorithm.

划分系数VPC，划分熵VPE等指标由于仅使用隶属度矩阵，可直接用于KFCM；而Xie-Beni的VXB等为数众多的指标不仅使用了隶属度矩阵，还使用了数据集的

Stability analysis of nonlinear magnetic suspension, the magnetic suspension system model was found based on electromagnet dynamics and voltage balance of the electromagnet coil; The feedback of position and velocity and current are used as the control variable; After the control rule was applied to the electromagnetic system, the louts criterion was used to get the range of the control parameter in which the system was steady-going.

非线性磁悬浮系统的稳定性分析，通过电磁铁动力学和电磁线圈的电压平衡方程，建立磁悬浮系统基本模型。求出系统奇点后，通过系统线性展开求出系统矩阵。用PD控制外加电流反馈量，将控制规律带入系统模型方程组求出矩阵的特征方程，由劳斯判据得知非线性系统稳定的位置反馈系数及取值范围。

Using the judgment matrix of detectable and locatable of gross errors in surveying error and reliability theory, it is proved firstly that the number of zero column vectors in LZD\'s judgment matrix equals to the rank defects of LZD\'s coefficient matrix. And then, LZD\'s matching equation having the detectability and locatability of gross errors is verified by a series of tests. These conclusions powerfully support the following researches on algorithms of detecting DEM deformations in theory.

运用误差与可靠性理论中的粗差可发现和可定位判断矩阵，证明了LZD算法判断矩阵中零列向量的个数等于LZD算法系数阵列秩亏数，试验验证了LZD算法匹配方程具备粗差发现和定位能力，为DEM差异探测算法提供了理论支持。

First, based on the relations of stress and strain between the whole medium and its macroscopically isotropic constituents, an explicit relation between elastic matrices of the whole medium and its constituents was derived. Combining the explicit relation of elastic matrices with the strain's relation, two coefficient tensors were defined and analyzed to get a general relation between the hulk and shear modulus of the whole medium under the assumption that all the field variables are in a unified coordinate system. Secondly, combining these relations with the classical Hashin-Shtrikman elastic modulus bounds, four new expressions of elastic medium of the whole medium were obtained and compared with the original hounds. Last, these formulae were applied in the computation of effective elastic moduli of clean sandstone saturated with pore water.

首先基于整体介质与宏观各向同性组分满足的应力和应变组分关系，推导出整体介质弹性矩阵与组分弹性矩阵之间的显式关系，联合其应变关系，定义和分析了对应的两个系数张童，并据此导出了相关场变量位于统一坐标系时整体介质体积模量与剪切模量的关系；然后将经典的Hashin-Shtrikman弹性模量边界模型与上述关系式结合，得到4个新的整体介质弹性模量的估算公式，再与原始的Hashin-Shtrikman弹性模量边界进行了比较，最后针对饱和水纯净砂岩介质进行了试算。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新