一般方程

Exact linearization problems of general nonlinear control systems were discussed. At first, it defined an adjoint system by introducing an affine nonlinear system.

摘 要：讨论了一般非线性控制系统状态方程无反馈精确线性化及反馈精确线性化。

By analyzing the working characteristics of the laser crystal, the temperature field and thermal distortion field analytical expressions of Nd:GdVO4 crystals with super-beam end-pumped were obtained by the equation of aeolotropy heat conduction, which considered heat conduction aeolotropy characteristic of Nd:GdVO4 crystal.

通过激光晶体工作特点分析，考虑到Nd：GdVO4 晶体热传导各向异性的特点，采用各向异性传热的Poisson 方程，得出了超高斯光束端面泵浦Nd：GdVO4 晶体温度场以及热形变场的一般解析表达式。

Cardano's Ars Magna is a landmark in the history of mathematics. It started the theoretical research on algebraic equations, solved the polynomial equations of third-degree and forth-degree in a general and systematical way, and studied the imaginary number as well as its operations for the first time.

卡尔达诺的《大术》在数学史上具有重要的地位，它开创了代数方程的理论研究，首次系统地给出了三、四次多项式方程的一般解法，并且最早讨论了虚数及其运算。

In conclusion, all our results further enrich, develop and perfect the theoretical system of the algebraic multigrid method.

代数多重网格方法是根据一般多重网格方法的原理建立起来的一种自动求解线性代数方程组的快速算法，它采用分层思想通过一种纯代数的多水平方法处理矩阵方程，特别是二维或三维大规模无结构方程组。

The latter employs the suspected angular acceleration model, so that the uncertain vehicle dynamic model is avoided being utilized.

基于EKF的姿态求解算法，通过假定机体角加速度模型，避免了一般基于滤波方式的姿态算法中需要复杂刚体运动方程的缺点。

The generalized deformation equations and the distribution function of branch vector are derived, and the mathematical characteristics of fabric tensor N are also discussed.

在此基础上导出了形变方程的一般形式，对技向量的分布函数进行了理论上的推导，还对组构张量N的一般数学特征进行了讨论。

The first is that a symplectic structure or a Poisson structure exists on the even dimensional phase space or on the odd dimensional phase space of the corresponding equations. The second is that there is another symplectic structure or another Poisson structure on the generalized phase space which consists of original phase space and independent variable space.

第一、系统在相空间上存在一个一般辛结构或者Poisson结构；第二、系统整体在包括了自变量的增广空间上存在一个一般辛结构或者Poisson结构；第三、第一个结构若是依赖于自变量，那么系统必然受到外力作用（偏微分方程也有特殊的情形，我们在第五章会加以说明），而第二个结构的则给出了第一个结构和外力之间确切的对称关系。

First,making use of martingale method,pricing formula on European contingent claim,price of call and put option were obtained;Then the partial differential equation which price of European contingent claim satisfgied was deal with and hedging strategy for option was obtained.The sensitivity analysis was given.

首先利用鞅方法给出欧式未定权益一般定价公式，并得到欧式买权、卖权价格的解析表达式及平价关系，推广了一般Black-Scholes模型及Merton模型的结果；其次利用Ito公式给出欧式未定权益价格应满足的偏微分方程和套期保值策略；最后给出了欧式期权价格的灵敏度分析。

Firstly, using quadric surface to fit with given surface and calculate the error metric to identify free surface and general quadric surface.

首先用一般二次曲面方程拟合测量数据并计算曲面的拟合误差，比较拟合误差与阈值的大小来识别自由曲面和一般二次曲面。

In the low dimension of system ,the equations needed in present algorithm is less than those in normal methods such as QR, SVD etc.

该方法避免了一般算法的频繁的重正交过程；且在维数不高的情况下，所需求解的方程数也较一般方法更少。

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