必要条件

This paper introduce Lagrange multiplier method and its expandings first, and show the necessary condition of Multivariate function's extreme value, and use it to solve the Multivariate function's extreme value problem.

本文首先介绍了拉格朗日乘数法及其拓展，给出了多元函数条件极值的必要条件，并利用它求解了多元函数的条件极值问题。

On the basis of analyzing detailedly the correlative conclusions of the extreme value problem of two variable Function , this paper extends the essential condition and sufficient condition to multi-variable function by using the Taylor Formula 、Quadratic Form 、Hesse Matrix and so on,and gives a method to judge the extreme value of point whose vice-derivative doesn't exist by utilizing Lagranges theorem ,so that compensates for the blank above ,which turns idea that solve the extreme value of multi-variable function problem one by one into realities.

摘要本文在对二元函数极值问题的相关结论进行分析的基础上，用泰勒公式、二次型、海赛矩阵作为工具，将二元函数极值的必要条件和充分条件推广到多元函数的情形，而且还利用拉格朗日中值定理找到了一个判别不可导点处极值的方法，从而弥补了多元函数不可导点处极值无法判断的空缺。因而，使得用穷举判断的方法来解决多元函数的极值问题这一思路成为现实。

Only with trade and investment liberalization and facilitation, can we achieve world economic recovery and growth.

贸易和投资自由化便利化是恢复和保持世界经济增长的必要条件。

Finally, we get a necessary condition under which the distance between a feasible sequence and the KT point set converges to zero.

最后，还给出了可行解点列至KT点集的距离趋于零的必要条件。

Logistics, as a modern concept, is defined as the process of planning, implementing and storage of raw material, in-process inventory, finished goods and related information from point of origin to point of consumption for the purpose of conforming to customer requirement.

物 流作为一个富有现代内涵的概念，被定义为"为了符合顾客所需要的必要条件，所发生的从生产地到销售地的物质、服务以及信息的流动过程，以及为使保管能有效、低成本的进行而从事的计划、实施和控制行为"。

In chapter one, by using Krasnoselskii s fixed point theorem, necessary and sufficient c...

第一章讨论了一类带阻尼项的高阶非线性中立型差分方程正解的存在性，利用Krasnoselskii不动点定理，得到了非振动解存在的若干充分必要条件，这些结果改进和推广了一些已知的结果。

And folk wisdom of ? Beating means love, scolding means affection.? And so on.

认为痛苦和磨难是获得成功的必要条件。

In theory and practice.there are shott of some essential factors for folkways and conventions being used into judicature.

在理论和实践中，民俗习惯的司法运用还欠缺一些必要条件，只有清除这些障碍，民俗习惯的作用才能得以有效发挥。

For a class of generalized fractional programming whose objective function is composed of infinite fractions,the saddle-point type optimality criteria are proven by using the existing necessary conditions,under the assumption of the class of B--invexity.

对于一类目标函数中有无限个分式的广义分式规划，给出一个不完全Lagrange函数，并利用已有的最优性必要条件，在B--不变凸性的条件下，证明了鞍点最优性准则。

In addition, for a class of first-order predicate expression namely first-order predicate expression without free variable and with one quantifier, a necessary and sufficient condition for such first-order predicate expressions to be equivalent and a corresponding judging algorithm are come up with.

另外，对于一阶谓词公式的一个常见子类——无自由变元单量词的一阶谓词公式，提出了一个判定这种一阶谓词公式等价性的充分必要条件和判定算法。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。