导数

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对"中间点"的渐近性进行了研究，得出了一系列"中间点"的渐近性的结果，概括了有关文献对微分中值公式的"中间点"的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

Firstly, The sufficient con-ditions of the existence and uniquity of the positive equlibria by applying functional derivative isobtained; Secondly, the global attractability of the positive equlibria is investigated by charateristicroots theory and oscillation theory; Thirdly, regarding the delay as a parameter, conditions of theexistence of Hopf bifurcation and the peridic solution, furthermore, the form of the approximateperidic solution are obtained; Finally, Some specific examples are given and the solution diagrameappears by Matlab.

首先利用导数性质，得到了该模型正平衡态存在惟一性的充分条件；其次，利用特征值和振动性理论得到了该模型正平衡态全局渐近稳定性充分条件；然后，应用Hopf分支理论证明了该模型Hopf分支及近似分支周期解的存在性，并给出了周期解的近似表达式；最后，借助于MATLAB数学软件，举例并绘出了模型数值解的拟合图象，验证了文中定理条件的可行性。

Via these formulas, the numerical solutions are incorporated with the analytical solution on the auxiliary circle.

在此基础上进一步建立了杂交元算式，它能保证在圆形人工边界上数值解和解析解两种场函数及其导数的相容性。

Local discontinuous Galerkin method for convection-dominated diffusion problems with periodic boundary conditions is constructed. To deal with the derivative of second order, an auxiliary variable is introduced. The stability and error estimations are presented simultaneously.

针对具有周期性边界条件对流占优的扩散问题中的二阶导数，引入辅助变量，构造了局部间断Galerkin方法，并给出了方法的稳定性结果和误差估计式。

Douglas and Russell first presented the idea of characteristics in[13],in whichthe diffusion term is included in the derivative of characteristic direction of the solu-tion and the backward difference quotient along the time axis was replaced by it alongcharacteristic direction.

Douglas，Russell[13]最先提出了特征法的思想，其主要特点是将模型方程的对流项隐含在解沿特征方向的导数之中，以沿特征方向的向后差商逼近取代通常方法中沿时间方向的向后差商逼近。

And that method is different from the adding base point method and impact method from importing derivatives of higher order.

他与增加基点数目的方法和引入高阶导数的紧致方法不同，是微分方程差分近似高精度化的一种新方法。

By making use of the property that the zero-order Bessel function's derivative J′0(0)=0, the DQDHT can calculate the values on the symmetry axis directly.

通过利用零阶贝塞尔函数导数在零点处为零的特性，所提出的准离散汉克尔变换算法可以直接计算光束传输时对称轴上的值。

Because the derivation of the extended system has a block lower triangular form, the method of splitting iteration is applied to compute simple bifurcation point, not only computational work is reduced, but also local quadratic convergence is achieved.

由于所构造的扩充系统的导数具有分块下三角形式，采用分块迭代的方法进行数值求解，不仅减少了计算量，而且是二次收敛的，从而为Navier-Stokes方程非退化简单分歧点的数值逼近提供了有效的算法。

In Part I, the biharmonic equation are chosen, and the boundary peanlty finite method using piecewise cubic Hermite elements is used to seek their approximate solutions, in particular satisfying the derivative and periodical boundary conditions.

在第一部份里，选择使用片断三次 Hermite元素的边界惩型有限元素法来求解满足边界导数条件和边界周期条件的重调和方程式的近似解。

We apply not only the Bouguer gravity anomaly data but also the first derivative of the Bouguer gravity anomaly.

在应用布格重力异常数据的同时，还应用了布格重力异常一阶导数。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。