边值

Based on Pontryagin maximum principle, the lunar soft landing problem is transformed into a two-point boundary value problem in mathematics. In consideration of the bound condition and transversality condition, the resulted two-point boundary value problem is converted into a parameter optimization problem aiming at the initial values of conjugate variables and the terminal time, then it is solved by the nonlinear programming.

首先，从庞德里亚金极大值原理出发，将有限推力作用下月球软着陆问题转化为数学上的两点边值问题；在考虑边界条件及横截条件的前提下，将该两点边值问题转化为针对共轭变量初值和末时刻的优化问题；然后应用非线性规划方法求解所形成的参数优化问题。

This OCVC problem was converted to a typical two-point boundary-value problem according to Pontryagin maximum value principle, and this TPBVP was a first order optimality condition which could be solved by Radau collocation method.

根据Pontryagin极大值原理建立该协调电压控制问题的1阶最优性条件，该条件是一个典型的两点边值问题。在此基础上采用拉道排列法求解这个两点边值问题。

In recent years, Feng Kang has advanced a more natural and direct redu-ction, i. e. the reduction via Green's formula and Green's function.

近年来冯康又提出一种更自然而直接的归化，即从Green公式及Green函数出发将微分方程边值问题化为边界上的含有广义函数意义下发散积分有限部分的奇异积分方程，这种归化在各种边界归化中占有特殊地位，被称为正则边界归化，本文将这一理论应用于重调和椭圆边值问题，研究了其正则归化的性质，并通过利用Green函数、Fourier分析及复变函数论方法等不同途径求出了在上半平面、单位圆内部、单位圆外部三种区域的Poisson积分公式及正则积分方程，其离散化可用于实际计算。

Then, in second part, we consider the existence and uniqueness of global regular solution for one-dimensional and 2-D radial symmetric Landau-Lifshitz equation.

第二部分我们研究一维Landau-Lifshitz方程齐次Neumann边值问题和二维柱对称Landau-Lifshitz方程Neumann边值问题解的正则性。

The existence of triple positive solutions for second order multi-point boundary value problem is investigated by using Avery-Peterson fixed point theorem. Gives the sufficient conditions for the existence of three positive solutions of the problems.

研究一类二阶非线性微分方程的n点边值问题正解的存在性，应用Avery-Peterson不动点定理，给出这类边值问题至少存在3个正解的充分条件。

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。

On the basis of Nagumo′s existence theorem for the singular case, we obtain the existence of solutions of singular equations satisfying nonlinear boundary value conditions and periodic boundary value conditions by means of approximations.

在Nagumo型存在定理的基础上，我们应用逼近的方法给出了奇性方程满足非线性边值条件和周期边值条件的解的存在性。

In thesequel,the definition of singular point is given,and then the Laurent's expansionof a LR regular function with isolated singular points is obtained in the corre-sponding Laurent domain,after that,we introduce the definition of residue,andthe residue theorems are obtained.

虽然这仅仅讨论的是在Clifford分析中的较为特殊的Riemann边值问题与奇异积分方程，但它仍然改进了以前文献的结果，从而也为更进一步地解决Clifford分析中一般的Riemann边值问题与奇异积分方程提供了基本的解决思想。

For the third boundary value problem under ellipsoidal boundary, firstly we simplify the form of the third boundary value problem. Then, the solution of the the third boundary value problem under ellipsoidal boundary is discussed in detail, along with its series solution, the integral expression is mainly studied.

对于椭球界面下的第三类边值问题，先简化其形式，然后详细讨论了椭球界面下简化形式的第三类边值问题的求解方法，在给出级数解的同时，主要研究了它的积分解的表达式。

By the proposed method, the exact calculation of the 3-D complexly structured waveguide EM fields is realized.

该方法克服了目前的有关数值分析方法在处理三维复杂结构波导边值问题所遇到的主要困难，实现了三维复杂结构波导边值问题的精确而有效的数值计算。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。