双射

We show that Jordan multiplicative bijective maps on prime operator algebrasmust be additive. As its application, we show that every Jordan * multiplicative bijec-tive map on every factor C~* algebra is a C~* isomorphism or a conjugate C~* isomorphism,in the special case of B, it must be a *-isomorphism or a conjugate *-isomorphism.We also prove the additivity of Jordan multiplicative bijective maps on nest algebras.

证明了素算子代数上Jordan可乘双射的可加性，利用这一结论刻画了因子C~*代数上的Jordan*可乘双射，我们的结果表明这样的映射一定是C~*同构或共轭C~*同构；证明了套代数上的Jordan可乘双射的可加性。

Let F be a bijection from set A to set B. Denote M={a Aa F}. If in a theory that ME B is legitimate, then the question m E M?

令F是从集合A到集合B的双射，记M＝aAaF，如果在某个理论中M B是合法的则问题m M？

By the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proof is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity.

恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

Moreover, by the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proofs is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity. Because of the 1-1 property of bijection, the identity is proved.

此外，恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

Head to tail type: front is a dense source of the corresponding optical galaxy, and then there are several pairs of gradually increasing bijection of electronic sources and dragged gradually widened the scope of the spectrum index steepens, the intensity gradually weakened radio tail.

头尾型：前面是一个有光学星系对应的致密源，随后有几对逐渐增大的双射电子源并拖着范围逐渐增宽、频谱指数逐渐变陡、强度逐渐减弱的射电尾巴。

Firstly, the performance indices of S-box were summarized. Five properties such as nonlinearity, SAC, BIC, differential uniformity and bijection, were employed as the main indices to evaluate S-boxes.

首先对评价S盒性能的指标进行了分析，以非线性度、完全雪崩准则、输出比特间独立性、差分均匀性和双射作为主要的评价指标。

In this paper, each of single data stream that is included in data streams has same attributes set as other,the unit of single data stream is tuple,and same attributes set is included in each of these tuples.Reservoir algorithm is used to sample from these single data stream respectively,then some multiple snapshot windows are constructed,the relationship between these single data stream and multiple snapshot windows is bijective mapping,the relationship between attributes that are included in tuple and snapshot windows that are included in relative multiple snapshot windows is bijective mapping,and the relationship between basic windows that belong to same snapshot window and the attribute values that come from different single data stream is bijective mapping as well,that is,these attribute values come from same attribute that is comprised by different single data stream.

针对以元组为单位流入的具有相同属性集的多支单数据流组成的多数据流，提出了分别对每支单数据流进行蓄水池抽样，构造一一对应于各单数据流的若干个多快照窗口，即两者之间是双射关系，可以将多快照窗口串行置于主存中，将元组包含的属性与多快照窗口中的各个快照窗口一一对应，且使得同一快照窗口中的各基本窗口与取自其对应的单数据流的属性值样本一一对应，然后对这些相互独立的样本进行方差分析。

Through the analysis of the second power Cartesian product of natural number set N——N×N and the thirdpower Cartesian product of natural number set N——N×N×N,obtains the conclusion that they all have the bijective relation to natural number set N,it means that the set N×N and the set N×N×N are all countably infinite.

通过对自然数集合N的二次笛卡尔积运算———N×N和三次笛卡尔积运算———N×N×N的详细分析，得出了它们与自然数集合N之间都存在双射关系结论，即集合N×N和集合N×N×N都是可数无穷的。

We alsostudy the Lie skew multiplicative bijective maps on B that is, the maps satisfyingΦ(AB- BA~*=ΦΦ-ΦΦ~*, and show that these maps must be of theformΦ=UAU~*, where U is a unitary or a conjugate unitary operator.

刻画了B(H是复Hilbert空间)上的Lie-skew可乘双射即满足Φ(AB-BA~*=ΦΦ-ΦΦ~*的双射，结果表明这样的映射一定是UAU~*的形式，其中U是酉算子或共轭酉算子。

A loop has the inverse property if it has both the left and right inverse properties.

一个合伦是使得中所有的三个映射都是双射的拟群同伦。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。