二次导数

This text studies the obstacle problems associated with nonhomogeneous elliptic equation, gives the definition of solutions of second order degenerate nonhomogeneous obstacle problems, and making use of the Poincaré inequality and others,acquire some properties of these solutions and their lead number,filling up the blank of an nonhomogeneous obstacle problem research.

本文研究了非齐次椭圆方程的障碍问题，给出了二阶非齐次障碍问题解的定义，利用Poincar啨不等式，获得非齐次障碍问题的解及其导数的一些性质，填补了对非齐次障碍问题研究的空白。

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。

Firstly, we prove that if we select nodes properly, and let the distance between these nodes sufficiently small, cubic polynomial spline can approximate a continuously differentiable function, which with continuous derivatives of second order and discontinuity of the first kind in the derivatives of fourth order, to any desirable accuracy. This result lays a theoretical foundation for representing trajectories by splines and double orthogonal basis.

一是证明了适当选取节点并使节点距充分小时，三次多项式样条可以逼近具有二次连续导数的分段四次连续可微函数到足够的精度，这一结论为用样条和双正交基表示弹道打下了理论基础。

To recover the time function of source, the deconvolution procedures based on least square method were developed, and to obtain the Frechet derivative of this function, we assumed it as a polynomial of tenth order, then the time function can be treated as a parameter to be identified.

至於波源时间之反求，则以最小二乘法为之，并假设其为十次多项式，而由此求出Frechet导数，并将其视为欲辨识之参数之一，由所得之结果得知，辨识出来之参数和事先假设者颇为相符。

Finally, in the third section, by constructing some functional which similar to the conservation law of evolution equation and the technical estimates, we prove that in the inviscid limit the solution of generalized derivative Ginzburg—Landau equation converges to the solution of derivative nonlinear Schrodinger equation correspondently in one-dimension; The existence of global smooth solution for a class of generalized derivative Ginzburg—Landau equation are proved in two-dimension, in some special case, we prove that the solution of GGL equation converges to the weak solution of derivative nonlinear Schr〓dinger equation; In general case, by using some integral identities of solution for generalized Ginzburg—Landau equations with inhomogeneous boundary condition and the estimates for the L〓 norm on boundary of normal derivative and H〓 norm of solution, we prove the existence of global weak solution of the inhomogeneous boundary value problem for generalized Ginzburg—Landau equations.

第三部分：在一维情形，我们考虑了一类带导数项的Ginzburg—Landau方程，通过构造一些类似于发展方程守恒律的泛函及巧妙的积分估计，证明了当粘性系数趋于零时，Ginzburg—Landau方程的解逼近相应的带导数项的Schr〓dinger方程的解，并给出了最优收敛速度估计；在二维情形，我们证明了一类带导数项的广义Ginzburg—Landau方程整体光滑解的存在性，以及在某种特殊情形下，GL方程的解趋近于相应的带导数项的Schr〓dinger方程的弱解；在一般情形下，我们讨论了一类Ginzburg—Landau方程的非齐次边值问题，通过几个积分恒等式，同时估计解的H〓模及法向导数在边界上的模，证明了整体弱解的存在性。

In Part 5, the stability of linear large-scale singular dynamic system is investigated by using the method of vector generalized Lyapunov function and the sum type of scalar generalized Lyapunov function, respectively.

首先研究线性广义系统二次型李雅普诺夫函数的存在性；然后建立按线性近似系统决定非线性广义系统稳定性的准则；进而改进广义李雅普诺夫函数法以研究广义系统的稳定性；最后提出利用非线性函数的偏导数矩阵判别非线性微分-代数系统稳定性的若干简便判据。

In this paper,based on an improved orthogonal expansion in an clement , using the new idea of Ref.[3] ,a new error expression of n-degree Hermite finite element approximation to one-dimensional 4-degrec 2-point bounded problem and 2-degree ordinary differential problem, and then optimal order superconvergence for their first derivatives is obtained.

本文针对在改进的单元正交性估计的基础上，利用文[3]提出的新想法，得到一维四阶两点边值问题和二阶常微初值问题的n次赫米特有限元u_h∈C~1的新误差估计式，以及导数误差的最佳阶超收敛，并且两者有相同的超收敛结果。

The model of programmed crystallization of SPM was proposed based on the moment transformation of the population considering the agglomeration. The optimal temperature-time curves in a batch crystallizer which maximized the terminal mean size and mean weight size can be determined from the application of the Pontryagin Maximum Principle. The calculated crystallization results heating under optimal temperature were compared with ones under linear or natural heating temperature.

根据第四章所得到的螺旋霉素晶体二次成核和晶体生长和布朗扩散引起的聚集动力学，利用第六章所描述的晶体尺寸分布的各阶矩对时间的一阶导数所构成的自封闭的一阶常微分方程组，采用庞得里亚金极大值原理，以温度为控制变量，在满足某些约束条件下，以最大平均尺寸和最大晶体重量平均尺寸为性能指标，计算出了螺旋霉素间歇结晶的最优温度—时间曲线，并同线性加热和自然方式进行了比较。

Firstly, the existence of Lyapunov function with the quadratic form for linear singular systems is discussed.

然后指出对X的任何正定二次型V，它沿线性广义系统的导数V都不会是X的负定函数。

Every function whose derivative is linear is a quadratic function.

任意一个导数为线性函数的函数都是二次函数。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。