当且仅当

基本解释 (translations)

iff

词组短语

if and only if · when and only when

与当且仅当相关的网络例句 [注：此内容来源于网络，仅供参考]

A polynomial system PS over the rational number field is constructed from the formula...,in a given many-valued logic system such that follows from ...,iff the algebraic variety defined by PS is empty, iff the idealenerated by PS is trivial.

由给定的多值逻辑系统中的一组公式，。。。，，出发，构造出了一组有理数域上的多项式PS，使得是，。。。，的逻辑结论，当且仅当PS定义的代数簇为空集，当且仅当PS生成的理想是平凡理想。

Many scholars have studied these respects and given many important results, for example, the Hupperts famous theorem, namely, a finite group G is supersolvable if and only if every maximal subgroup of G has prime index; a finite group G is nilpotent if and only if every maximal subgroup of G is normal in G; a finite group G is solvable if and only if every maximal subgroup of G is c-normal in G (See it in [70]); etc.

很多学者都在这些方面进行了研究，得到了很多重要的结果，如：著名的Huppert定理，即有限群为超可解当且仅当它的所有极大子群的指数为素数；有限群为幂零当且仅当每个极大子群都正规；有限群为可解当且仅当它的极大子群均c-正规(见[70])；等等。

In this paper, the following statements were proved: is chaintransitive if and only if is chaintransitive; if a homeomorphism is a Lipschitz map, then has the average shadowing property if and only if has the average shadowing property.

设是紧致度量空间，：X→X是连续的，n为任一给定的正整数，证明了：是链可迁的当且仅当是链可迁的；若同胚是Lipschitz映射，则有平均跟踪性当且仅当有平均跟踪性。

In the last chapter, on the basis of theories in paper [4, 5], the notions of strong mixing, weak mixing, generator and expansion of the variable-parametric dynamical system are introduced, it turns out that in variable-parametric dynamical system strong mixing implies weak mixing and then implies transitivity; it is proved that if and both are variable-parametric dynamical system, F conjugates with G , the members of F are communicate with each other and the members of G are also communicate with each other, what's more, they are both homeomorphism, then F is strong mixing implies G has the same properties; futhermore, we prove that F is strong mixing implies F Devaney chaos in the sense of modification in variable-parametric dynamical system and that F Devaney chaos in the sense of modification if and only if G Devaney chaos in the sense of modification when semi-conjugate with and they both are communicate and homeomorphism; at last, we illustrate that F has generator if and only if it has weak generator, and we also prove that if F is expansion, then F has generator.

在第三章中，我们在文[4，5]的基础上，提出了变参数动力系统拓扑强混合、拓扑弱混合以及变参数动力系统的生成子、扩张的概念；证明了变参数动力系统拓扑强混合蕴含拓扑弱混合，进而蕴含拓扑传递；证明了：如果，为两个变参数动力系统，F与G拓扑半共轭，且F两两可交换，G两两可交换，它们均为同胚映射，那么F拓扑强混合，则G也有同样的性质；本章还证明了变参数动力系统拓扑强混合蕴含F在修改的意义下Devaney混沌；在此基础上得出了：如果变参数动力系统与变参数动力系统拓扑半共轭，它们都两两可交换，并且它们均为同胚映射，那么F在修改的意义下Devaney混沌当且仅当G在修改的意义下Devaney混沌；得出了F有生成子当且仅当F有弱生成子；如果F是扩张的，则F有生成子。

R is a regular ring if and only if every singular right R-module is P-flat if and only if every cyclic singular right R-module is P-flat if and only if the homomorphic image of every P-flat right R-module is P-flat.

得到了R为正则环当且仅当每一个奇异右R-模P-平坦当且仅当每一个循环奇异右R-模P-平坦当且仅当P-平坦右R-模的同态像P-平坦这一主要结果。

It is a natural generalization of the notion of implicative ideals in BCK algebras.

证明了BCI代数的一个非空子集是BCI关联理想当且仅当它既是BCI交换理想又是BCI正定关联理想，从而揭示了这三类理想之间的内在联系，并将BCK代数中知名论断：BCK代数的一个非空子集是关联理想当且仅当它既是交换理想又是正定关联理想，推广到BCI代数上去。

We have established some properties of languages of Lattice of Quantum Automata. For example, the definitions of Right-Linear Grammars of Lattice of Quantum, Regular Sets of Lattice of Quantum and Regular Expressions of Lattice of Quantum have been given.

我们证明了量子自动机格有一些重要的性质：它是分配格当且仅当自动机的基格是分配的；它是模格当且仅当自动机的基格是模格；它是完全格当且仅当自动机的基格是完全格。

The first chapter, main instead " duo-ring " condition of " every maximal left ideal is GW-ideal " condition,study strongly regularities of GP-V-ring on this condition.lt is shown that (1) R is strongly regular iff R is left GP-V-ring whose maximal left ideals are GW-ideal.(2)R is strongly regular iff R is left GP-V-ring whose maximal right ideals are GW-ideal. The second chapter, generalize some results of GP-V-ring to GP-V-ring, discuss regularity of GP-V-ring.It is shown that (1) R is left self-injective regular with non-zero socle iff R is left GP-V -ring with Soc = Soc and R contains an injective maximal left ideal.(2)R is regular ring and every maximal essential left ideal is ideal iff R is left GP-injective left GP-V -ring and every maximal essential left ideal is ideal.

第一章主要将"duo-环"条件替换成"每一极大左理想是GW-理想"条件，研究在此条件下，GP-V-环的强正则性，证明了：(1)R是强正则环当且仅当R是左GP-V-环且R的每一极大左理想是广义弱理想；(2)R是强正则环当且仅当R是左GP-V-环且R的每一极大右理想是广义弱理想，第二章，主要将GP-V-环上一些结果推广到GP-V′-环上，讨论GP-V′-环的正则性，证明了：(1)R是左自内射正则环且Soc≠0当且仅当R是包含内射极大左理想的GP-V′-环，且Soc=Soc；(2)R是正则环且每一极大本质左理想是理想当且仅当R是左GP-内射的左GP-V′-环且每一极大本质左理想是理想。

The following statements are proved:. A is equivalent to a diagonal matrix if and only if A is similar to a diagonal matrix.. If R is an APT ring, then A can be uniquely diagonalized as diag{e1,..., en} and ei divides ei+1.. R is an APT ring if and only if R/I is an APT ring, where I is a nilpotent ideal of R.

本文证明了以下结果：A相抵于一对角阵当且仅当A相似于一对角阵；若R是一APT环，则A在相似变换之下可唯一地化为对角形diag{e1，…，en｝，这里ei整除ei+1；R是APT环当且仅当R/I是APT环，这里I是环R的一幂零理想。

Finally, it shows that R is von Neumann regular ring if and only if every right .R-module is right pm-injective if and only if every right principal right ideal of R is right pm-injective if and only if every essential right ideal of R is right pm-injective. Furthermore, some good properties are obtained.

最后，得到R是von Neumann正则环当且仅当每个右R-模是右pm-内射当且仅当R的每个主右理想是右pm-内射当且仅当R的每个本质右理想是右pm-内射，以及其他诸多好的性质。

与当且仅当相关的网络解释 [注：此内容来源于网络，仅供参考]

if and only if：当且仅当

二个顶点有边联结,当且仅当(if and only if)这点代表的地区有桥联结起来. 这样欧拉就得到了一个图了. ...

if and only if：若且唯若 当且仅当

identifier 识别字、识别符号 标识符 | if and only if 若且唯若 当且仅当 | Illinois 伊利诺 伊利诺斯

if and only if：当且仅当 若且唯若

闲线路 idle channel | 当且仅当;若且唯若 if and only if | 条件子句;假设子句 if clause

if and only if/iff：当且仅当;若且仅若

identity relation 恒等关系式 | if and only if/iff 当且仅当;若且仅若 | if...., then 若....则;如果.....则

if and only if/iff：当且仅当

弹性壁|elastic barrier | 当且仅当|if and only if, iff | 当茹瓦积分|Denjoy integral

if and only if/iff：当且仅当;若且仅若Btu中国学习动力网

identity relation 恒等关系式Btu中国学习动力网 | if and only if/iff 当且仅当;若且仅若Btu中国学习动力网 | if..., then 若....则;如果.....则Btu中国学习动力网

iff = if and only if：当且仅当

牐燿iverge[数](级数等)无极限, 无限大 | 牐爄ff:if and only if 当且仅当 | 牐爏pectral 谱的

if and only ififf：当且仅当;若且仅若

identity relation 恒等关系式 | if and only ififf 当且仅当;若且仅若 | if..., then 若....则;如果.....则

Independent Set：独立集

当且仅当一个子集不被包含在一个更大的点集中时,该点集是图G的一个独立集(independent set),同时它也定义了图G的空子图. 最大独立集是具有最大尺寸的独立集. 对于任意图G,它的补图(c o m p l e m e n t) 是有同样点集的图,且当且仅当( u,

IFF：当且仅当

问题正在于此:诸如"已所不欲勿施于人"这样的人际共识是有效的,当且仅当(iff),一个社会具有共同价值观,也就是具有关于"想要的/不想要的"的价值共识. 这两个共识必须同时存在,否则传统金规则就不可能成立. 为什么古典的金规则在今天遇到困难了?