查询词典 if and only if

Furthermore,it shows that if E is a barrelled space with continuousdual 〓,then 〓 contains no copy of 〓 if and only if each〓 is compact operator.

据此证明了若E是桶型空间，那么〓〓不拓扑同胚地包含〓的充要条件是每个〓都是紧算子。

Next,it shows that if vectorvalued normed sequence space Ehas the bounded uniformly convergence property or0-GHP,then Eis a barrelled space if and only if 〓.

其次证明了，若矢值赋范序列空间E有界一致收敛或者E具有0-GHP，那么E是桶型空间的充要条件为〓〓。

We prove that if the subgroup G of I somis dis-crete,then G is Martin nonelementary if and only if G is Bowditch nonelementarygroup.

在第三章中，我们研究了Pinched Hadamard流形上等距群Isom各种非初等群之间的关系及其应用。

In order to study the popular curve shortening flow in the plane, Gage[3] has shown in 1983 the following inequality, if k is the signed curvature of a closed convex plane curve γ with length L and enclosing area A, then one gets Gage calls it an isoperimetric inequality in [3], but he does not show that the equality holds if and only if the curve γ is a circle, while as an isoperimetric-type inequality, one should prove this kind of result.

Gage称之为等周不等式，但他没有证明其中等号成立当且仅当，γ为圆周，而作为等周型的不等式是应该证明这种结果的，本文我们利用单位速率外法向量流，通过努力证明了这种结果，从而把Gage不等式加强成更加等周的形式。

This thesis has mainly contributed two results in theory: one is that the covariance matrix is not positive definitive if the number of sampling is least than the number of variables, the other is that the covariance matrix of discrete sample is positive definitive if and only if the sum of every random column vector of data matrix is non I-linear combination.

本论文在理论上，主要得出两个新的结果：ⅰ抽样调查中，若样本的个数少于变量的个数则样本协方差矩阵恒为非正定；ⅱ离散型样本协方差矩阵正定的充要条件是样本资料阵的各随机列向量是非I-线性组合。

Results Two new characterizations of regular rings are given.(1) If R is a left SF'-ring and R/Z is reduced, then R is strongly regular;(2) R is strongly regular if and only if R is a left SF'-ring whose every idempotent element of R is left semi-center and is LANE-ring.

结果 得到了SF'-环是强正则环的两个充要条件：(1)R是左SF'-环，如果R/Z是约化的，则R是强正则环；(2)R是强正则环当且仅当R是满足幂等元左半中心的左SF'-环，且R是LANE-环。

More precisely,we shall say that two graphs are isomorphic if there is a one-one correspondence between their vertices which has the property that two vertices are joined by an edge in one graph if and only if the corresponding vertices are joined by an edge in the other [3],Another graph isomorphic to the graphs in Figs.

更准确地说，如果两个图的顶点间存在一一对应，使得在一个图中有一条边连接两个顶点在另一个图中相应也有且仅有两个对应顶点由一条边相连，则说这两个图是同构的。

If N is a nonempty subset of a left R module M, then N is a submodule of M if and only if the following conditions hold:(1) x+y is in N for any element x,y in N;(2) rx is in N for any r in the ring R, and any x in N.

假设 N 是左模的非空子集合，那么N 是子模的充分必要条件是，对N 中的任何两个元素x，y有

If deg f = n, then Rfc is an empty set. For all the functions of degree 2, Rf have at least 2n-1 vectors, when Rf is a linear subspace, the relationships between Rf and Lf are discussed . Boolean functions have no nonezero linear structure if and only if there are n linear independence vectors in f, the correlation of the vectors in ?

证明了，若degf=n，则R_f~c为空集，对于所有的二次布尔函数而言，均有R_f~c中的元素个数大于等于2~(n-1)，给出了R_f构成线性子空间时，R_f和L_f之间的关系，还给出布尔函数不含有非零线性结构的充分必要条件是ζ_f中含有n个线性无关的元素。

Moreover, it is obtained that, if X is a core compact and locally connected space, then the Isbell and Scott topologies agree on functions space for all continuous L-Domain L with a least element if and only if X is an RW-space.

而且还证明了，若X是核紧的局部连通空间，则对所有有最小元的连续L-DomainL，上的Isbell拓扑和Scott拓扑相同当且仅当X是RW-空间。

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％。