当且仅当

（1-）环的直接和。于是，R是交换的，当且仅当N是交换的。

Thus , R is : commutative if and only if N is commutative .

主要结果有：T3~s空间X是仿紧的当且仅当X是仿近似紧的；

T_3 ~ s space X is paracompact if and only if X is para-nearly-compact space ;

当且仅当这两个条件元素都等于true时，才执行规则的结果元素。

Only when both conditional elements evaluate to true are the rule 's consequence elements executed .

证明了偏序集P是连续偏序集当且仅当S-极限是σ（P）拓扑决定的；

It is proved that a poset is continuous iff the S-limits for P are σ( P ) topological determined .

当且仅当（有限生成）拟投射左R－模的直极限为直投射模。

If and only if a direct limit of ( finitely generated ) quasi-projective R-modules is direct-projective .

将伪轨跟踪性的一些性质推广到弱跟踪性上，证明了：（i）f有弱跟踪性当且仅当逆极限空间上的转移同胚σf有弱跟踪性；

Some properties of the pseudo-orbit tracing property is generalized to the weak shadowing property .

R为左IF环当且仅当任一有限生成左R&模均可嵌入平坦模；

R is left IF ring iff every finitely generated left R-module is embeddable in a flat module .

（iv）R是半本原环当且仅当A是半本原环。

( iv ) R is a semiprimitive ring if and only if so is A.

相反地，当且仅当角色在此资源上的所有权限都被允许时，返回TRUE。

In other words , this method returns true if and only if the Role is allowed all privileges on the Resource .

局部有限散度半序集P的区间拓扑是连通的，当且仅当P是稠的且条件备；

In a partially ordered set P of locally finite width , the interval topology is connected if and only if P is dense and conditionally complete ;

证明了一个p－半单BCI－代数是单的当且仅当它的阶是素数；

We show that a p-semisimple BCI-algebra is simple if and only if its order is prime .

证明了有界齐性算子空间H（X，Y）为Banach空间当且仅当空间Y是完备的。

H ( X , Y ) is complete if and only if the space Y is Banach space .

R是GPP-环当且仅当R是拟π-正则的GPF-环。

R is a GPP - ring if and only if it is a quasi π - regular ring and GPF - ring .

P.环（Baer环）当且仅当R是分次P。

Ring ( Baer ring ) if and only if Ris a graded P.P.

给出了R的紧致子集的一个新刻画，证明了R的子集E是紧致子集当且仅当E是星紧致子集。

The author prove that a subset E of R is a compact subset if and only if E is a star-compact subset .

证明了相对映射芽的强有限决定性与相对映射芽的通用开折存在性之间的等价关系，即相对映射芽f是强有限决定的当且仅当f具有通用开折。

We prove the strong relative AS , T finite determinacy of map germs and the relative versal unfolding are equivalent .

完全函数f是无穷保上下文无关函数当且仅当函数f是保上下文无关函数。

A total function fis a Context free Infinite Preserving Function if and only iff is a Context free Preserving function .

本文证明T是分次右遗传环当且仅当（i）A和B都是分次右遗传环；

In this paper , we show that T is graded right hereditary ring if and only if ( I ) A and B are both graded right hereditary ;

若MR在σ[M]中投射且MR半单，则M是非M-奇异模.并且还得出，若R是左对偶环或左拟对偶环，则R是半单环当且仅当R非奇异。

It deduced that if R is a left dual ring or a left quasi - dual ring , then R is a semisimple if R is nonsingular .

若I是X的一个真理想，则I是固执的当且仅当商代数

I is a maximal and positive implicative ideal . If I is a proper ideal of X , then I is obstinate if the quotient algebra

其中，第h段的指针可以跨越2h个节点，条件是当且仅当每一段中不是所有的节点都离开网络。

Each segement-h pointer traverses nearly 2h nodes if and only if not all nodes in a segment leave the network .

M是Ecs模当且仅当Mi均是Ecs模（（？）

M is Ecs module if and only if M_i is Ecs module ((?)

这样推断，端点当且仅当资源更新时才会收到RSS条目片断。

Presumably the endpoint would then receive RSS item fragments when and only when that resource updated .

本文给出了模的矩阵表示，进而研究了环的Morita结构，主要结果：R为投射自由环当且仅当R上非零幂等矩阵具有特征根为1的特征向量。

In this thesis , the matrix expression of module is given , and the morita structure of ring is stadies .

引入了fuzzy有理语言的概念，得到了∑~+的子集可识别当且仅当有理的。

In this paper the notion of rational fuzzy language is introduced , and a important theorem is obtained : a fuzzy subset of Σ is recognizable if and only if it 's rational .

考虑服务台由N个不同部件串联而成的M/G/1可修排队系统，其中服务台正常当且仅当N个部件都正常。

We consider the M / G / 1 repairable queueing system with N units series structure , in which it operates if and only if all of the N units operate .

子环eΩe为质核环（本原核环），当且仅当eΩeK。

The subring e Ω e is a prime kernel ring ( or primitive kernel ring ) if and only if e Ω eK .

当且仅当每个线程希望访问运行时的时候，按需创建VM对象。

A VM object is created at demand and only once for every thread that wants to access the runtime .

空间X是几乎亚紧的当且仅当X的每一单调开覆盖U有一个开加细，且在X的某一稠密子集上是点有限的；

A space X is nearly metacompact if and only if every monotone open cover U has an open refinement that is point-finite on some dense subset of X ;

弱基B对X的任意一个子空间遗传当且仅当对于任意x∈X，对于任意P∈Bx，x∈P°；

The weak base B is " hereditary " to any subspace of X if and only if for any x ∈ X , for any P ∈ B_x , x ∈ P °;