查询词典 if and only if

The definition of the absolute value for a fuzzy number is obtained.Furthermore,a lot ofproblems,such as absolute integrability,bounded variation and absolute continuity,arepresented and discussed.The representation theorem of the absolute values of fuzzy num-bers is established.It plays an important role in discussing the problems conceming theabsolute value.The relation between the absolute integrability and integrabili-ty is discussed,and the following result is obtained:aintegrable fuzzy-number-valued function is absolutely integrable iff it is integrable.The relation between theabsolute integrability and the absolute continuity of the primitive for fuzzy-number-valuedfunctions is dealt with.It is also pointed out that a fuzzy number valued function is ab-solutelyintegrable if and only if its integral primitive is fuzzy absolutely continuous.

提出了模糊数绝对值的概念并讨论了与绝对值相关的一系列问题，如绝对可积性、有界变差性、绝对连续性等，给出了模糊数绝对值的定义以及表示定理，该表示定理在涉及绝对值问题的讨论中起非常重要的作用；讨论了绝对可积与可积之间的关系，得到了结论：可积的模糊数值函数绝对可积的充要条件是该模糊数值函数可积；给出了模糊数值函数绝对可积与其积分原函数绝对连续性之间的关系，指出模糊数值函数绝对可积的充要条件是其原函数模糊绝对连续。

In particular, we compute Hochschild homology and cohomology groups of infinitedimensional path algebras and some of their quotient algebras, and we prove that for a general monomial algebra (not necessary finite-dimensional), all Hochschild cohomology groups of positive degrees vanish if and only if its Gabriel quiver is a finite tree.

特别地，我们计算了无限维路代数以及某些商代数的Hochschild同调群和上同调群，而且给出了一般单项代数的各正次Hochschild上同调群为零的充分必要条件，即它的Gabriel箭图是有限树。

Firstly, it's proved that the base of free monoid is unique, and that the equation of a base, a generating set and a irreducible generating set in the semigroup with length; Secondly, it's given the relation of a primitive word and a word of indecomposable--Let and is indecomposable, then is primitive ;And by using the length's method and chart,some properties of primitive word have been proved and the solutions of the equation , are discussed; Lastly, on the base of some proposition in Free monoids and Languages ,the proofs of some properties are improved by instruction. For example: Let be a primitive word over X, where .Then is a code. And let then if and only if {} is a code.

首先，讨论了含幺半群中基的基本性质及基与最小生成元集的联系，并给出了含幺半群中基、生成元集、不可约生成元集三者之间的关系；证明了在有唯一长度的半群S中，不可约生成元集、基、最小生成元集三者之间的等价关系；其次，讨论了字的组合与分解性，得出了字的本原性与不可分解性之间的关系---若为不可分解的，则一定是本原的，反之，不一定真；并运用图示法证明了字的可补性理论，讨论了方程，的可解性；在此基础上，用归纳法进一步证明了本原字与码的有关命题--若是X上的一个本原字，其中，则是一个码；若则当且仅当{}是一个码。

In the chapter two, we will recall some basic concepts and propertiesin commutative algebra and homological algebra. In the chapter three,wewill defineⅠ-flat modules and give equivalent conditions: one module M isanⅠ-flat R-module if and only if for all prime ideals p,SuppTor_1~R

本文首先介绍了关于平坦模的一些基本概念和性质，而后将平坦模的概念在一定意义上进行推广，定义了I-平坦模，并得到了模M是I-平坦R-模的等价条件：对R中所有素理想p，有suppTor_1~R

"Logicians distinguish two main types of implication, material and strict. Proposition p materially implies proposition q if and only if the material conditional p q (read "if p then q") is true"

逻辑学家将蕴涵分成实质的和严格的两种主要类型。p命题实质蕴涵q命题，若且唯若实质条件pq为真

A topological spaces X is minimal CH if and only if for each x∈X and each open CH-filterbase μ,if {x}=∩U∈μU=∩U∈μclU, then μ is a neighborhood base of x.

4拓扑空间 X是极小 CH空间，当且仅当对任意的 x∈X和任意开 CH滤基μ，若{ x}=∩U∈μU=∩U∈μcl U，则μ是 x的一个邻域基。

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。

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。

In this note the author showed that if s is nonnegative integer and A∈B n,n+s, then |R|=2 n if and only if A contains a submatrix which is permutation equivalent to the unit matrix of order n.

作者证明：如果s是一个非负整数且A ∈Bn ，n+s，那么｜R ｜=2 n 当且仅当A含有置换等价于n阶单位矩阵的一个子阵

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。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。