微分的

The surface representation in discrete form and its differential computation are important issues in computer graphics and geometric design.

0引言一般来说，曲面的一阶微分量是指曲面的切平面方向和法向量，二阶微分量是指曲面的曲率等有关量·它们作为重要的曲面信息度量指标，在计算机图形学，机器人视觉和计算机辅助设计等领域发挥了重要的作用·传统的曲面是连续形式的参数曲面和隐式曲面，其微分量的计算已经有了较完备的方法·随着激光测距扫描等三维数据采样技术和硬件设备的长足进步，以及图形工业对任意拓扑结构光滑曲面造型的需求日益迫切，离散形式的曲面———细分曲面、网格曲面和点云曲面正在逐渐成为计算机图形学和几何设计领域的新宠·于是，对这种离散形式的曲面如何估

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utilityfunction are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

Then the explicit expression of it under exponential claims and the differential equation are obtained.Thus we discuss the effects of credit and debit interests on it through data analysis. Through the research of the mean,the moment generating function and the higher moments of discounted aggregate dividend payments,we discuss the optimal dividend payments problems.

而对于Gerber-Shiu函数的研究，则是通过随机过程及随机微分方程的知识得到它满足的积分-微分方程及边值问题，然后得到了它在指数索赔下的明确表达式以及Erlang(2)索赔下满足的微分方程，并通过数值分析得到贷款利息及存款利息对它的影响。

Aim at the shortage of vertically additive method by which we can't discuss forced oscillations of systems of partial functional differential equations,we directly use the oscillatory definition,Green's formula and boundary condition of homogeneous Neumann to change the oscillatory problem of solutions to a class of systems of quasilinear parabolic equations of neutral type into the problem of which functional differential inequality haven't eventually positive solution.

针对垂直相加法无法讨论泛函偏微分方程组的强迫振动性的不足，直接利用振动的定义、Green公式以及齐次Neumann边界条件把中立型抛物微分方程组的振动问题转化为泛函微分不等式不存在最终正解的问题，然后利用最终正解的定义及上下极限得到了在齐次Neumann边界条件下判别其所有解振动或全振动的充分条件。

Around the finite solution problem of fuzzy differential equation, the fuzzy structure element method is put forward about the calculation of fuzzy analysis, and this method is applied to systematically study many problems such as formulation of fuzzy-valued function, difference of fuzzy-valued function, integration of fuzzy-valued function under the Riemann meaning, and the solution structure of fuzzy differential equation etc..

围绕模糊微分方程定解问题，提出了模糊分析计算的模糊结构元方法，并利用模糊结构元的方法对模糊值函数的表述问题、模糊值函数的微分、黎曼意义下的模糊值函数积分以及模糊微分方程的解的结构等问题，进行了深入系统的研究。

Avoiding the complex and precise discussion,this article,for a type of elemental heat equation,is going to give a convenient method of solving heat equation by separation of variables and to expand the range of solvable problems with the help of Fourier series.

本文避开微分方程定性理论的复杂、严谨讨论，想就一类最基本的热传导方程，通过分离变量的方法将偏微分方程的边值问题转化为常微分方程的边值问题，给出一种较简捷的定解模式，并利用Fourier级数，将解题范围加以推广。

Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.

本文结合微分几何学，基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上，得到了参数化曲面上的图像处理框架，并给出了边缘检测和形态学运算的算例；在已知给定曲面的隐式表达时，探讨了定义在任意曲面上的偏微分方程，解决了任意曲面上数据场的扩散问题。

Using the new comparative method, the variation of constants formula, M-matrix theory, integral differential inequality, new theoretical results on global exponential stability of neural networks with bounded time-varying delays and Lipschitz continuous activation functions have been obtained.

利用新的比较方法的思想，改进了一维线性和非线性纯时滞微分系统的3/2稳定性定理，推广了Yorke条件到具两个时滞项的情形，将Yorke等人的3/2稳定性定理推广到具两个时滞项的线性和非线性纯时滞微分系统，进一步还推广到N维纯时滞微分系统，为纯时滞神经网络的研究打下理论基础。

To investigate the dynamic stability of a two-degree-of-freedom manipulator as a system,differential equations of motion for this system were established on the basis of the Lagrange equation,and perturbed differential equations with period coefficients were derived for the period motion of this system by applying the perturbance theory.

为了研究两自由度机械手系统的动力学稳定性，基于拉格朗日方程给出了它的运动微分方程，并用扰动理论确定系统周期运动具有周期系数的扰动微分方程；根据F loquet理论对该系统扰动微分方程的平衡点的稳定性进行了分析，并用数值方法研究了平衡点失稳后的倍周期分岔过程。

An algorithm called initial function method for the solution of differential equation with tension is also given.

推导出了不考虑拉伸和考虑拉伸情况的弹性环形变微分方程，导出了求解不考虑拉伸情况的弹性环形变微分方程的差分方程和算法，还给出了可谓之初参数法的求解考虑拉伸情况的弹性环形变微分方程的算法。

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％。