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The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

Since it is usually necessary to de-energize the winding before measuring R H, and the resistance of the coil may change rapidly as the temperature decreases, it may be necessary to determine the value of R H at the end of the test by taking several resistance measurements at short intervals, beginning as quickly as possible after the instant of shutdown.

人们一般在测R H时，通常要断掉线圈绕组的电，温度下降了线圈的电阻变化很快，所以有必要在断电的一瞬间尽快地测取电阻，而且还要以较小的时间间隔多测几次，从而得到R H 值。

A necessary and sufficient condition for a fx + t(y + g to be a bent function is disscussed,on which basis a necessary and sufficient condition for a function F = fix + tq + g to be a bent function is given when q is not a balanced-function by use of cyclic walsh spectrum and decomposition formula of walsh spectrum.

讨论了形如fx+τ(y+g的布尔函数是Bent函数的充分必要条件，在此基础上利用Bent函数的循环Walsh谱及谱分解式，进一步给出了当q不是平衡函数时，形如F=fx+τ(yq+g布尔函数是Bent函数的充分必要条件。

Sound card driver is installed, it is necessary to choose "the driver provided by manufacturers" and do not choose "Windows default driver," If the "Add New Hardware" installed, it is necessary to choose "Have Disk" instead of from the list box choose.

在安装声卡驱动程序时，要选择"厂家提供的驱动程序"而不要选"Windows默认的驱动程序"如果用"添加新硬件"的方式安装，要选择"从磁盘安装"而不要从列表框中选择。

In chapter 5, we study necessary conditions for difference sets and we obtain the following: we proved that there are no nontrivial difference sets in dihedral group of order 4p〓, where p is a prime, d is a positive integer; we give a necessary condition for Hadamard difference sets in some group of order 4p〓, and completely solve a general case left in Dr.

在第五章中，我们研究了差集存在的必要条件。

In this paper,a necessary condition that a cut vertex belongs to every γ s set of G is discussed,and a necessary and sufficient condition of existing indepedent set dominating set in G is given.

本文讨论了割点属于G的任一最小集控制集的必要条件，并且给出了G有独立集控制集的充要条件。

Next it is necessary to actively push forward the socialist political and legal reforms, establish a complete socialist legal system, improve the effectuation effectiveness of laws in actual life, providing necessary legal system conditions for the formation and development of citizens'modern legal consciousness.

基于以上分析，本文认为，要实现"依法治国、建设社会主义法治国家"的目标，推动中国法制现代化的全面实现，必须大力培养公民现代法律意识，实现社会主体法律意识现代化。

The hypothetical proposition under necessary conditions ; the Chinese expression and its classification ; the basis of the true or false judgment ; the equivalent expression of the true proposition ; the and - syllogism under necessary conditions

徐州师范大学文学院； 221116；徐州师范大学学报，，编辑部邮箱 2003年 03期必要条件假言命题；汉语表达形式及其分类；判定真假的依据；真命题的等值式；必要条件反三段论

Flue gas and thus the realization of such acquisition is necessary is necessary.

因而实现这样的烟气采集是必要的也是必须的。

Specifically, a preliminary design of the content of the programme should include : plans, the necessary elevation, some hand-painted the galley proof, and a description of some of the necessary construction design estimates.

具体地说，一份初步设计方案应该包括的内容有：平面图、必要的立面图、一些手绘的小样、一些必要的施工说明以及一份设计概算。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。