当且仅当

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

Zahavi (1975) suggested a mechanism for this, using the following recipe: signals are honest, if and only if they are costly to produce relative to the signaler's current condition and if the capacity to produce honest signals is heritable.

扎哈维为此提出了一个机制：运用下列理论：当且仅当杜撰信号发生装置相关的信息很麻烦，或产生诚实的信号是可遗传时，信号是真实的。

Coifman etc proved that the commutator T_f = f = T -bT is bounded on Lp if and only if b BMO, where T is a classical singular integral operator.

Coifman等人得到了交换子T_bf=f=T-bT在L~p(1＜p＜∞)上有界当且仅当b∈BMO，其中T是经典的奇异积分算子。C。

Coifman〓etc first proved that the comutator〓is bo-unded on〓if and only if b∈BMO,where T is a classical singular integr-al operator.

在〓上，Coifman等〓首先得到交换子〓上有界当且仅当〓，其中T是经典奇异积分算子。

The fact that a fuzzy ideal of a BCI algebra is closed if and only if it is a fuzzy subalgebra is proved.

证明了BCI代数的一个Fuzzy理想是闭的，当且仅当它是一个Fuzzy子代数。

It is shown that if L is a subalgebra of a Lie color algebra Q, then Q is an algebra of quotients of L if and only if Q is ideally absorbed into L.

利用没有非零零化子的理想对Lie color代数的商代数进行刻画，证明了：若L为Lie color代数Q的子代数，则Q为L的商代数当且仅当Q理想吸收于L。

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

In this paper, we replace the N normality with N subnormality in c-normal concept to get the weak c-concept.

推广了[1]中的定理3.5得到一个有限群G可解当且仅当每个在F~中的极大子群弱c-正规。

Some theories of morally correct action also introduce the category of the supererogatory: an action is supererogatory if and only if it is morally praiseworthy, but not obligatory.

有些道德正确的行为的理论还引入了多劳类别：一个行为当且仅当它在道德上值得表扬但不是义务时就属于多劳类别。

If we add a new independent variable to a regression equation, increases if and only if the t statistic on the new variable is greater than one in absolute value.

如果我们向回归模型加入一个新的解释变量，当且仅当新变量的t统计量的绝对值大于1时，调整过的R2增加。

Since historical times,England ,where the early inhabitants were Celts, has been conquered three times .

从有历史以来，英国，在此地早期居住的是凯尔特人，已经被征服了三次。

Bluetooth OBEX File Transfer Enables the sending and receiving of files on your phone via Bluetooth.

蓝牙OBEX文件移动允许经过蓝牙传送和接受文件。。。。