一般方程

The general form of solution for the non symmetric matrix A is given, the expression of optimal approximation solution is presented, and an algorithm for solving the problem is described. The total least squares problem with symmetric and bisymmetry constraints is discussed respectively. A sufficient condition for existence of solution is derived by use of the theory of matrix Ricaati equation. The general form of solution is given if the problem has a solution, and the expression of optimal approximation solution is presented. Some numerical examples are given.

对矩阵A是非对称情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，并给出了其解的表达式，描述了求解问题的算法；讨论了带对称和双对称约束的总体最小二乘问题，利用Ricaati矩阵方程的理论得到了解存在的一个充分条件，分别对对称矩阵和双对称矩阵两种情形，给出了解的一般表达式，证明了最佳逼近问题解的存在唯一性，给出了其解的表达式，提出了求解这些问题的算法，并给出了数值例子。

Based on the discussion,a simple and clearly defined vector equation of kinematic error for robots,has been derived for practical use by means of space vector,characteristicsof space vecto...

据此，利用D-H 坐标变换与空间矢量的关系，以及空间矢量导数性质，推导了简洁实用、意义明确的机器人运动误差矢量方程，并就该方程在一般空间机构运动精度研究时的应用实例作了说明。

In order to understand the weak solutions like piece-wise smooth solution, we must investigate the structures and properties of global smooth solution.

一般情况下，要研究清楚分块光滑解等常见的弱解，我们必须研究光滑解尤其是全局光滑解的结构和性质，这是研究高维守恒律方程方程全局解的基础。但用以往的处理方法一般来说是很困难的。

Adsorption isotherm of nitrogen in MCM-41 at temperature 7=77 K was measured, by using the ASAP2010 volumetric adsorption analyzer produced by Micromeritics Instrument Corp.

虽然微扰方程一般较优，但是在近似胶体的情况下，本文提出的方程却更好。

Base on the work above,a more general model for calculating gas solubility is proposed,which can by applied to both pure water system and brines with any concentration.

在此基础上推导出与亨利定律和气体在纯水中溶解度方程具有良好相溶性的，更具一般意义的关于气体溶解度的基本方程。

Base on the work above,a more general model for calculating,.solubility is proposed,which can be applied to both pure water system and brines with any concentration.

在此基础上推导出与亨利定律和气休在纯水中溶解度方程具有良好相溶性的，更具一般意义的关于气体溶解度的基本方程。

The dynamics equation is established using Lagrange method, and the formula of free frequency is deduced according to modality analysis of general viscous damp. Instantaneous wallops are applied to X, Z dimension respectively, observing the movement of the moving platform, and use ADAMS software to validate the free frequency of the system.

采用Lagrange方程建立了系统动力学方程，根据一般粘性阻尼系统的模态分析法，推导了求解固有振型的公式；分别在X、Z方向上施加一定的瞬时冲击力，观察动平台的运动情况，并采用ADAMS软件验证系统的固有频率。

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r&‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

To any positive integer n, we apply the general term formular for the equation of devision that can produce a general equation or nth degree in one unknown, i.

对任意正整数n，运用等分方程定理的通项公式，就可产生一个一元n次方程的一般式。

Multiple linear regression were used for analyzing factors that influence occupational safety behavior. the first equation contained wages and personal character,the second equation included safety behavior of the enterprise,individual safety psychology and safety knowledge.

采用多元线性回归分析，一般相关因素中进入方程的显著性变量是月收入和性格，职业相关因素中进入回归方程的显著性变量是企业安全行为、职工的安全心理和安全知识。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷