查询词典 if and only if

Lastly , from a primitive rpp semigroup with zero , we built up a type A blocked Rees matrix semigroup and showed a semigroup S is a primitive rpp semigroup if and only if S is isomorphic toa type A blocked Rees matrix semigroup.

该结果的一个特例就是可消幺半群上的Rees矩阵半群。

A necessary and sufficient condition about the reducibility of central essential hyperplane arrangements is given:a central essential arrangement is irreducible if and only if the matroid is connected.

具体地，本文将对每一个超平面构形，构造一个拟阵，证明中心本质构形不可约的充分必要条件是对应的拟阵是连通的。

We can costruct an exterior n-form ξ for every hypersurface M in Euclidean space Rn+1. The submanifold M is minimal if and only if is closed (dξ= 0), then ξ is calibration and M is ξ-submanifold.

我们证明了对于欧氏空间R~(n+1)中每一超曲面M，可以构造η-微分式ζ，而超曲面极小的条件恰是ζ为闭形式，即dζ=0的条件。

In chapter 4, the factorization and cascade decomposition for first order singular systems have been discussed, the if and only if conditions have been obtained, the invariaty of minimality under factoiization and cascade decomposition has been proved.

第四章，讨论了一阶奇异系统的因子分解和级联分解，给出了其具有上述分解的充要条件，证明了极小性在分解下的不变性；对具有一阶奇异系统实现的有理函数矩阵，给出了判定其为正实函数的充要条件，推广了著名的正实引理。

We discuss the completely tr-rank nonincreasing linear maps on finite vN algebras and prove that a unital self-adjoint and surjective linear map on finite vN algebras is completely tr-rank preserving if and only if it is a spatial 〓-automorphism that leaves the central elements fixed.

我们刻画了有限vN代数上完全迹秩不增的线性映射；也证明了有限vN代数上保单位元的自伴线性满射完全保迹秩当且仅当它是空间〓-自同构且限制到中心上是恒等映射。

The nonstandard anslysis theory is used in the κ-saturated nonstandard model, the definition of the quasi-near-standard points in a metric space is given and it is proved that a point in nonstandard metric space is quasi-near-standard point if and only if its monad contained in every *-open ball of some standard point.

在κ-饱和的非标准模型下，采用非标准分析方法，提出了度量空间中的拟近标准点的定义，得到了非标准度量空间中的点是拟近标准点的充要条件是它属于某一个标准点的每一个*-开球，证明了度量空间的非标准完备化恰是该空间的非标准扩张中拟近标准点集的商空间。

Disjunction normal form theorem in the modal logic system S5 is inductively proved, which can be used for representing complex modal formulas by means of conjunction and disjunction of simplest modal formulas with depth at most 1 in the system S5. As application, it is proved that a knowledge base could answer KB-queries if and only if it could answer queries of non-modal propositions and their negations, which is a basic problem on knowledge base.

研究了模态逻辑系统S5中的析取范式定理的归纳证明，给出了在S5中用深度至多等于1的最简模态公式通过析取与合取运算表示含有多重模态词的公式的方法，作为范式定理的应用，讨论了知识库中的一个基本问题，证明了知识库能够回答KB命题式问题的充要条件是该知识库能够回答相关的非模态命题及其否定命题的问题。

Ureg such that =; E (the ideal extension of a ring R by its ideal I) is an exchange ring if and only if R and I are both exchange.

一个一般环I是exchange的当且仅当对它的任意理想L以及=2∈I/L，存在w∈r.ureg使得=；E(环R通过它的理想I生成的理想扩张)是一个exchange环当且仅当R和I都是exchange环。

Here, we characterize sequential separability and prove that l_p is a separable space if and only if E is a separable space and l_p is a GAK_space.

关于Banach序列空间lp，讨论的主要问题之一就是E的几何性质能否提升到lp中去，在文中，刻划了lp的序列可分性，证明了lp是可分的当且仅当E是可分的以及lp是GAK 空间

Two efficient portfolios p ≠mvp and zc in the efficient frontier satisfies Two Fund Separation Theorem if and only if 〓 where 〓.

有效边界线上的两个投资组合〓和〓满足两基金分离定理的充要条个是〓，其中〓。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。