微分的

Two types of new Abel differential equation are structured by method of variation replacement, variation position transformation and compound function derivation law.

借助变量替换法、交换变量位置法及复合函数求导法则，构造出两类新的 Abel型微分方程，论证它们的可积性，提供可积的判据，从而推广有关文献的结论，扩大微分方程的可积范围。

In this dissertation, the following critical theoretical problems on local La-grangian numerical differentiation are studied: explicit formulas, local estimate for the remainder, and the highest order of approximation in the case that the values of the function at these interpolation nodes have perturbationsLagrangian numerical differentiation is a method that the Lagrange interpolation polynomialis differentiated to approximate the derivative, where Tn ={t_0,t_1,......

本文主要研究有关局部Lagrange数值微分法的一些关键性的理论问题：公式的显式表示，余项的渐近估计，以及在插值数据有扰动的情况下，局部Lagrange数值微分法的最大逼近阶。

Curvature is the result of geometric structure in image; a new third order partial differential equation is proposed which transports curvature information along isophotes. The third order POE is morphologically invariant. Helmholtz vorticity equation which annihilates vorticity and third order POE which forward transports curvature information are coupled to be a new model.

曲率是图像几何特征作用的结果，本文提出沿等照度线方向传输曲率信息的三阶形态学不变偏微分方程，并将抑制涡量的无粘亥姆霍兹方程和正向传输曲率信息的三阶偏微分方程耦合。

It also derives calculation formulas of various dispersed coefficient to set up three-dimensional turbulence model of draft tube and confirm the solving method.

对流场控制方程及三维湍流模型进行了深入的分析与研究，导出了通用微分方程，用有限体积法推导了通用微分方程的离散形式，并导出了各种离散系数的计算公式，建立了尾水管的三维湍流模型，并确定了求解方法。

The finite difference time-domain method is stable and easy to be used, but due to the fact that it approximates the space derivatives in Maxwells curlequations by central difference, FDTD usually requires more than 20 grids perwavelength to achieve acceptable accuracy. As a contrast, pseudospectraltime-domain method approximates the space derivatives by pseudospectralmethod, which guarantees the accuracy, theoretically requiting only 2 grids perwavelength.

传统的电磁场数值算法——时域有限差分法稳定而易于实现，但由于FDTD采用中心差分近似Maxwell旋度方程的微分，每个波长上需要取的网格数通常较多，而时域伪谱法采用伪谱法求微分，理论上每个波长只需要取两个网格便可以达到较高的精度。

Qualitative theory, which directly judges the qualitative properties of solutions by ordinary differential equations themselves, is very important in the study of ODEs.

定性理论在常微分方程的研究中是十分重要的，它是由常微分方程来直接研究和判断解的性质的理论。

In chapter 3,we discuss the existence of solutions for impulsive differential equations with two-point boundary condition.

通过使用脉冲不等式和分析方法，得到了一阶脉冲微分方程周期边值问题新的比较结果，借助所给的新的上下解，结合单调迭代技巧，建立了一阶脉冲微分方程周期边值问题极值解的存在结果。

We discuss a class of second order self-adjoint matrix differential systems with damping term and self-adjoint Hamiltonian matrix differential systems, etc.

在第五、六章中，考虑一类线性泛函g和一类对s偏导数不一定非正的Hk型函数，分别研究了自伴的带有阻尼项的二阶矩阵微分系统和自共轭的Hamilton矩阵微分系统。

Then by using the generalized Gronwall inequalities, the oscillation for second-order self-adjoint differential equations is discussed and new oscillation criteria are obtained.

第一章为综述，简要回顾常微分方程、泛函微分方程及时标上的动态方程等的振动理论的发展与现状，同时介绍了本文的主要工作。

Adopting Lorentz-invariant coupling model of neutron-antineutron and neutral meson strong interaction, we have physical analysis and accurate calculation on the neutron and antineutron to two neutral meson renormalization chain diagram propagator, and acquire the theoretical result; furthermore, after application of it to the physical process analysis and cross-section evaluation in this reaction , the differential cross-section of which is given. Moreover, through the comparison among this calculation and those scenarios: neutron-antineutron tree diagram and renormalization chain diagram propagator contribution, some important information about radiative correction was obtained.

采用中子-反中子与中性介子强相互作用的Lorentz不变耦合模型，对中子反中子重整化链图传播子作了有关物理分析及其严格解析计算，获得精确理论计算结果；进而将此结果用于中子反中子反应生成两个中性介子反应的物理过程分析及其截面的计算研究中，并精确计算出中子反中子重整化链图传播下中子反中子反应反应微分截面；最后还将此计算结果与中子反中子树图和重整化单圈链图传播下该反应微分截面作了对比分析，获得了有相关辐射修正的重要信息。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷