近似微分

The finite difference is used to approximate differential operation; the reflectance map equation described by the first order nonlinear differential equation is transformed into an algebraic equation about the unknown surface heights, and then the objective equation is constructed by the reflectance map equation and gradient information of image. Moreover, the Newton iterative algorithm is utilized to obtain the numerical solution and 3D shape of the surface.

采用有限差分近似微分运算，将一阶非线性微分方程所描述的反射图方程转化为关于未知表面高度的代数方程，再由反射图方程和图像梯度信息构造目标方程，进而用Newton迭代算法求出该方程的数值解，得到表面三维形状。

The main idea of the finite difference method is as follows: We consider the discrete difference equation with the finite alphas as approximate substitution for the differential equation with the continuous variant and boundary conditions.

有限差分方法的基本思想是用离散的，只含有有限个未知数的差分方程去近似代替连续变量的微分方程及边界条件，并把相应的差分方程解作为微分方程的近似解。

Firstly, the isotropic difference templates were introduced to approximate the differential in the ADI-FDTD method, and the weighting coefficients of difference terms were determined for implementing isotropic numerical dispersion; Then the permittivity and permeability were adjusted manually to reduce the numerical dispersion error in any directions. Therefore the simulation accuracy and efficiency can be improved effectively for time domain problems with some finite bandwidths.

该方法在ADI-FDTD方法的差分近似微分中引入各向同性差分模板，并通过确定各向同性差分的加权系数来近似实现各向同性，然后人为修正空间的介质参数来减少各个方向上的数值色散误差，因此在模拟一定带宽的时域问题时可有效提高计算精度和计算效率。

The basic idea is to set a continuous solution of the region with a finite number of discrete points instead of a grid consisting of, these discrete points called grid nodes the solution of a continuous area on a given function of continuous variables used in the definition of discrete grid variable function approximation the original equation and boundary conditions in the micro-business operators to approximate differential, integral with the points and to approximate, so the original differential equations and boundary conditions are replaced by algebraic equations near Side, that is, finite difference equations , solve this equation group can get the original problem in discrete points on the approximate solution.

基本思想是把连续的定解区域用有限个离散点构成的网格来代替，这些离散点称作网格的节点；把连续定解区域上的连续变量的函数用在网格上定义的离散变量函数来近似；把原方程和定解条件中的微商用差商来近似，积分用积分和来近似，于是原微分方程和定解条件就近似地代之以代数方程组，即有限差分方程组，解此方程组就可以得到原问题在离散点上的近似解。

Because any reports on the active control of rotating disk haven't be seen in China up to now, and this experiment research is important, so the complete set of active control system of rotating disk are built independently. The push-pull type electromagnet is applied to control the vibration of the circular disk. The power amplifier circuit that can respond to wide scope in frequency from DC to AC is designed by improving the existing circuit. The sensor signal is first low-pass filtered, then the proportional control plus the differential control circuit easy used in practice are applied to finish the more effective control. The electromagnetism shield is used as possible to decrease the signal disturbance from the electromagnet to eddy sensor.

考虑到目前国内尚未见到有关旋转圆盘振动主动控制的相关报导以及实验的重要性，自行设计制作了一整套旋转圆盘振动主动控制系统：提出并采用推拉型电磁作动器来控制圆盘的振动；在改进现有电路的基础上，自行设计了具有较理想特性的驱动电磁作动器的功率放大器；根据实际控制环境的特点，设计了先进行低通滤波，再采用比例和实用的近似微分电路构成的控制器，并采用了电磁屏蔽来减小电磁铁对传感器的干扰，以实现更有效的控制。

Classical Statistical Mechanics; Hamiltonian and Ideal Gases; Factoring the Partition Function with the Semi-classical Approximation; PVTN Properties via Configuration Integral from Intermolecular Effects; Grand Canonical Ensemble I

经典统计力学；Hamilton函数与理想气体；半经典近似微分函数因数；对分子间作用，作定积分而得的PVTN性质；巨正则效果I。

When discrete characteristic of digital images is considered, finite difference approximates differential operator.

考虑数字图像离散化特征，用有限差分近似微分运算，将由PDE描述的反射图方程转化为关于未知高度的代数方程，然后使用迭代算法求解，得到新的SFS算法。

Numerical differentiation is that derivative value of a function at a certain point is approximately solved in discrete method.

中文摘要：数值微分就是用离散方法近似地求出函数在某点的导数值，关于数值微分已有许多求解方法，但这些方法都有各自的局限性，并且关于高阶导数近似逼近的方法研究相对较少。

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。