上微分

Through careful analysis of the mathematics model of daily dispatching optimization of the cascade hydropower station, a new method based on the combination of two dimensional dynamic programming and discrete differential dynamic programming is proposed.

通过仔细分析梯级水库日优化调度的数学模型，提出了一种基于二维动态规划和离散微分动态规划相结合的混合求解策略，该策略理论上严谨，计算时间比较短，能满足日常调度的需要。

It mainly carries on the continuous process stochastic differential equation discretization of the research.

技术上的思想主要是将连续过程的随机微分方程离散化来进行研究。

Therefore, an immediate experimental measurement of p-13N elastic scattering at the energy of 1 GeV is urgently demanded.

因此，实验上测量p-13N弹性散射的微分截面就是当前需要马上进行的一个实验研究工作。

Many high-rise buildings can be simplied into variable cross-section cantilever beam, which equation of free vibration is variable coefficient differential equation of higher order and there is no general solving process for which in mathematics.

对这类方程，数学上没有提供一般的解法。本文采用的级数解法可求出任何变系数的四阶微分方程，在给定边界条件下的解。

The differential equations of equilibrium and natural boundary conditions are given.

在曲梁精确的翘曲位移基础上，根据变分原理，提出了对任意开口薄壁截面圆弧曲梁通用的线性理论，给出平衡微分方程和相应的边界条件。

Half penalty method and optimism design of ten connecting bar mechanism of plunger slide in double action drawing press;2. The essential boundary condition is imposed by employing a penalty method .

将选择施加在"虚结构"控制点上的虚载荷作为形状优化的设计变量，并将它与无网格Galerkin法相结合来开展结构形状优化研究，采用罚函数法来施加边界条件，通过直接微分法建立了结构形状优化的离散型灵敏度分析算法，利用无网格法研究了节点坐标关于设计变量导数的计算。

Thirdly, on the base of the existent error estimate of elliptical Galerkin projection operator, obtain semi-discrete and complete-discrete error estimates betwent EFG solution and exact solution of parabolic partial differential equation. Semi-discrete error estimate show that the rank of r is accordance with the approximation rank of subspace S_h. Complete-discrete error estimates show that it not only have relation with radius r of domain of influence, but also have relation with the step length of time variable and the way of discrete.Lastly, give typical examples and draw up procedures of MATLAB.

再次，在"椭圆Galerkin投影"算子的误差估计的基础上，对用EFG法解抛物型偏微分方程的EFG解与精确解之间作了半离散和全离散的误差估计，半离散的误差估计表明所给出的误差界限关于r的阶是与子空间S_h的逼近阶相一致的，全离散的误差估计表明所产生的误差不但与影响域半径r有关，而且与离散时间变量的步长τ及其离散方式有关。

In chapter 3,we prove that a complete noncompact n-dimensional Riemannian manifold M whose Ricci curvature Ric_M ≥(n- 1) has finite topological type or diffeomorphic to R~n if its Excess function has some upper bound at a point.

第三章，我们证明了对于Ricci曲率Ric_M≥-(n-1)的完备非紧n维Riemann流形M，若它的共轭半径有正的下界且共轭半径的某个函数为M在某一点的Excess的上界时，它就有有限拓扑型或者微分同胚于n维欧几里德空间。

Aiming at the physical model inapplicability of flash method to measure thermal diffusivity of semi-transparentmaterials, a new physical model was proposed. In the model, according to the permeance of materials, the pulse laserabsorption of materials is of exponential type, and the authors establish a relevant differential equation and get a analyticalform.

针对传统的闪光法在物理模型上不适于用来测试半透光物质热扩散率的问题，提出了一个新的物理模型，该模型根据物质的透光性，确定样品对脉冲激光的吸收为指数型，建立了相应的微分方程并求得其解析解。

To our knowledge, this is the first work for the existence of periodic solutions for neutral systems by generalized Schaefer fixed point theorem of seperate contraction mapping.

第四章，讨论了两类依赖于参数的泛函微分系统，用锥上的Deimling不动点定理，证明了系统的正周期解的个数与参数的取值以及非线性项的渐近行为有关。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。