必要条件

In the last chapter, by introducing the isochronous center of real systems into complex planar and defining complex center and complex isochronous center, a concise linear recursion formula for period constants is given, necessary and sufficient conditions of complex isochronous center (the Time-Angle Difference Theorem) proved, conditions of real systems with linearizable center and saddle treated unitedly and the isochronous center conditions discussed fully for a class of real planar cubic systems.

在第七章，通过把实系统等时中心引入复平面研究，定义了复中心和复等时中心，给出了等时中心周期常数计算的简明的线性递推公式，证明了等时中心判定的充分必要条件，统一地处理了实系统具有可线性化的中心和鞍点条件，并对一类实平面三次系统的等时中心条件进行了完整研究。

Taking the active network as a research task, the input accessibility, the Coates graph of matrix and graph transmission etc are used to analyze the relation between reducibility of the coefficient matrix of the state equation and the electric separability of the network or the electric accessibility of the network for the first time, acquiring sufficient and necessary conditions that coefficient matrix of the state equation is reducible. Network Graph Theory, Matrix Theory and System Theory over F etc are used to derive the structural controllability criterion of the passive network over F for the first time. Then according to these theoretic results, the structural controllability problems of the active network over F are studied, acquiring several structural controllability conclusions of the active network.

率先将状态方程的输入可达、矩阵的Coates图、流图传输系数等概念和方法引入到对F上有源电网络的研究，研究了网络状态方程的系数矩阵的可约性与网络电气可断性或电气可达之间的关系，研究了F上有源电网络的能控性问题，获得了状态方程的系数矩阵可约的充分必要条件、F上有源电网络系统的结构能控性判据等新的结论。

;Comparative;statics;is;that;mathematical;technique;by;which;an;economic;model;is;investigated;to;determine;if;refutable;hypotheses;are;forthcoming.;By;the;process;the;theories;in;economics;is;logically;simulated;for;the;testing;of;the;theories.;All;of;which;construct;the;paradigm;of;economics.;With;this;paradigm,;it;makes;out;by;the;comparative;statics;of;Shaanxi;province;developing;strategy—one;line,;two;zones—that;the;necessary;testing;condition;of;the;strategy's;theory;holding;is;that;the;government;investments;have;to;make;the;central;zones;increase;faster;than;the;other;areas;do.;Otherwise,;it;will;not;be;a;good;strategy.;Say,;if;the;north;of;Shaanxi;increase;faster;than;central;zones;do,;then;it;can;verify;the;strategy;is;not;a;good;one.

学研究的范式——比较静态分析，是一种技术，通过这一技术，理论可以被考察研究，以确定理论的可驳斥假说，它是对进行的一种符合的仿真。具体讲，比较静态分析是通过逻辑运算，模拟理论的可驳斥命题即检验条件是什么，从而为理论的验证提供方法。用经济学的研究范式对陕西省"一线两带"的比较静态分析显示，此战略成立的必要条件之一是：随着战略的实施即政府对极化地区的投入，其产出增加应该比其它地区产出增加大，否则这一战略就不成立。也就是说，如果陕北或陕南经济发展更快，集中投资于西安等中心城市，并不是更好的战略。

The existence of a regular Red Army of adequate strength is a necessary condition for the existence of Red political power.

相当力量的正式红军的存在，是红色政权存在的必要条件。

Some results on von Neummann regular ring are obtianed here,If R is von Neummann regular and X is a /?

随后我们又证明了P-内射模的商模是P-内射模的充分必要条件是R是一个PP-环。

The relative stability of ecosystem is indispensable to the existence and development of human being.

生态系统的相对稳定是人类赖以生存与发展的必要条件，维护与保持生态平衡，促进生态系统的良性循环和健康发展是关系到人类前途和命运。

Health and relative stability of ecosystem are necessary to human survival and development .

生态系统的健康和相对稳定是人类赖以生存和发展必要条件，维护与保持生态系统健康，促进生态系统的良性循环，是关系到人类前途和命运的重大课题。

It's a requirement to be an educated person.

这是受过教育的人的必要条件。

In this paper,in residue class ring Z_m,the concept of the strict avalanche criterion of order k of m-valued logical functions is presented.

给出了剩余类环Zm上逻辑函数的k阶严格雪崩准则的概念，用概率方法证明了m值逻辑函数满足高阶严格雪崩准则时一定满足低阶严格雪崩准则，并借助Chrestenson谱给出了m值逻辑函数满足k阶严格雪崩准则的一个充分必要条件。

In these cases increasing resiliency is a necessary precondition for finding narrower peaks.

在这样的情形里，渐增的弹力是发现窄峰的必要条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。