必要条件

In the second chapter, the problem of the optimal inputting rate control for a class of competitive population dynamics system with age-structure is discussed. By means of characteristic line, Gronwall Lemma, Bellman Lemma, adjoint system and so on, the Lipschitz continuity properties of the system in terms of the control variable is certificated, and the necessary condition of the optimal control is obtained.

第二章讨论了一类具有年龄结构的竞争种群系统最优输入率控制问题，综合应用特征线法，Gronwall引理，Bellman引理，共轭系统等知识，证明了系统解关于控制变量的Lipschitz连续性，给出了控制为最优的必要条件。

In Brunn-Minkowski-Firey theory, we establish two extremum properties of the new ellipsoid; Then we generalize Petty\'s affine projection inequality and monotonicity results related to affine surface area to L_p—affine surface area; We establish the Brunn-Minkowski type inequalities for the volume of the L_p centroid body and its polar body with respect to the normalized L_p radial addition. At last, we introduce the minimal L_p—mean width of a convex body and generalize the minimal mean width to the Brunn-Minkowski-Firey theory.

在L_p-Brunn-Minkowski理论中，我们首先给出了两个关于新椭球的极值性质；然后研究了L_p仿射表面积，将Petty仿射投影不等式和Winterniz单调性问题推广到L_p仿射表面积；建立了L_p质心体和其极体的Brunn-Minkowski型不等式；研究了凸体的最小L_p平均宽度，给(来源：3bABbeC论文网www.abclunwen.com)出凸体K具有最小L_p平均宽度的充分必要条件，最后给出了凸体L_p平均宽度位置的稳定性。

In our pioneering days this aggressiveness was essential to survival.

在开拓时期，这种进攻性是生存的必要条件。

Study on the stability,the key condition of the VAV operation,the paper divides the VAV system into AHU part and terminal part.

针对变风量空调系统正常运行的必要条件——稳定性问题进行研究，把变风量空调系统基于分解协调的策略合理地分解为机组部分和末端部分。

For most people, trying to get a good rate on airfare is a necessity.

对大多数人来说，要获得一个好的税率机票是一个必要条件。

With the Ben Tal generalized algebraic operation of 2 , we obtained some necessary and sufficient conditions for the class of generalized convex programming, and the results generalize the corresponding ones for the convex Programming.

利用文〔2〕中定义的Ben－Tal广义代数运算，本文得到了这类广义凸规划的Kuhn－Tucker充分条件和必要条件，所得结果推广了通常凸规划相应的结

An action for alienation of affection does not require proof of extramarital sex .

第三者插足构成侵权行为并不以婚外性行为为必要条件。

The necessary conditions of the formation of halo are: weekly bound, low orbit angular momentum and short distance interaction.

形成晕结构的必要条件是：弱束缚、低轨道角动量和短程相互作用。

In the last section, we obtain a sufficient and necessary condition for an antichain to be the set of all circuits of a combinatorial scheme.

在最后一节，我们得到了组合概型的一个反链是其所有圈集的充分必要条件。

This paper,by means of a new method,the graph theory,reanalyses the stability of antisymmetric discrete Hopfield networks,avoiding the construction of energy function.The nessesary and sufficient conditions for a network to converge to a cycle of length 4 are presented,and the number of cycles of length 4 associated with a p-order antisymmetric discrete Hopfield network is discussed,with some suspicions presented.

本文应用一种新的方法——图论方法重新系统地研究了反对称离散Hopfield网络的稳定性理论，这种方法回避了构造能量函数的麻烦，本文给出了网络收敛于长度为4的环吸引子的充分及必要条件，讨论了p阶反对称离散Hopfield网络含有长度为4的环吸引子的数目，并提出了几个尚待解决的猜想。

Recall that, in the Kolmogorov axiomatization, measurable sets are the sets which have a probability or, in other words, the sets corresponding to yes/no questions that have a probabilistic answer.

延期开工的Kolmogorov宣布要衡量所有套职能有限许多坐标限制在于衡量子寅。换句话说，如果是/否的问题回答f可看的价值观念在许多最有限坐标，然后它有一个概率的答案。

The experimental results showed that the algorithm can filter singular points and remain fixity of the target edge.

实验表明：基于模糊理论的图像智能滤波方法比常规图像滤波方法运算量小，它既能去除奇异点，又能保持图像中目标的边缘不变性，具有很好的滤波效果。