非交换群

We describe the algebraic characteristic of the public-key cryptosystems based on algebraic structures such as elliptic curves,bilinear pairings,as well as braid group s,with the emphasis on the difficulties of constructing public-key cryptosystems based on non-commutative algebraic structures.

通过分析基于椭圆曲线、双线性对以及基于辫子群的公钥密码体制的代数学特征，着重讨论了构建基于非交换代数的公钥密码体制所面临的困难。

The technologies used to solve these problem is presented. The second part proposes a new access method of recycle links of internal speed-up space switching fabrics. It eliminate the main contrariety between network performance and complexity. Combined with dilated Banyan, two types of recycled Banyan network-expanded recycle dilated Banyan and recycle dilated Banyan network are developed.

第二部分提出一种循环线接入方式，使得反馈线数目不再成为交换网络的性能/复杂度的矛盾所在；并结合线群Banyan网形成RDBN交换结构，对RDBN在均匀和非均匀业务模型下的性能进行了理论分析和计算机仿真，得出参数的选择尺寸，并提出使用窗口重整算法以保证信元序列完整性。

The finite nonabelian simple group PSL(2,23) has the minimum degree 506 GR of connected cubic arc-transitive coset graphs.

有限非交换单群PSL(2，17)的最小级连通3度弧传递陪集图表示的级是102。

When G is not a commutative semitopological semigroup, Lau and Takahashi proved the ergodic theorem for right reversible semigroups of nonexpansive mappings by using the methods of invariant means.

而当G非交换时，Lau和Takahashi利用不变平均技巧，在假定G是右可逆，X具一致Frechet可微范数及RUC存在不变平均等条件下，给出了非扩张半群的遍历压缩定理。

Ruck, Hirano and Reich extended Baillon抯 theorem to a uniformly convex Banach space with a Frechet differentiable norm. Hirano-Kido-Takahashi, Oka, Park and Jenong proved the ergodic theorem for commutative semigroups of nonexpansive mappings and asymptotically nonexpansive mappings in the uniformly convex I3anach space with the Frechet differentiable nonn.

aillon的定理被Bruck，Hirano及Reich推广到具Frechet可微范数的一致凸Banach空间中，而当G是一般交换拓扑半群时，Hirano-Kido-Takahashi，Oka，Park及Jeong分别给出了具Frechet可微范数的一致凸Banach空间中非扩张半群及渐近非扩张半群的遍历压缩定理和遍历收敛定理。

In noncommutative scalar field theories, the appearing of nonplanar diagrams is related to permutation symmetry of field functions in the interaction Lagrangian, while in NCQED we can not arbitrarily change the positions of field functions in the interaction Lagrangian because different positions of the field functions correspond to different representations of the gauge group.

这里需要特别指出的是NCQED的非平面图产生的原因与非对易标量场根本不同，非对易标量场非平面图的产生是和相互作用拉氏量密度中场函数间位置的置换对称性有关，而在NCQED中我们不能随便交换相互作用拉氏量密度中场函数的位置，因为场函数的不同位置对应着规范群的不同表示。

We study noncommutitive harmonic analysis on semigroups in first part.

第一部分我们研究半群上的非交换调和分析。

The first part: Let μ be the ratio of the order of a non-abelian finite group G to the number of irreducible character of the group.

本文研究了非交换有限群G的不可约特征个数与群G结构之间的联系，由以下两个部分构成。

The second part: We study the connection between a non-abelian finite p-group G and the number of conjugacy class of it .

第二部分，我们建立了非交换有限p-群G与其共轭类个数之间的关系，并且得到了较小阶的p-群G与其共轭类个数之间一种更简洁的相互决定关系。

For a group G, and a subset S of G such that 5, the bi-Cayley graph BCay of G with respect to S is the bipartite graph with vertex set G {0,1} and edge set {{(g,0),(sg, 1)} In [1], the authors have discussed some semisymmetric cubic graphs.

对群G和G的子集S，关于S的双Cayley图Γ=BCay是一个二部图，满足：V=G×{0，1} E={{(g，0)，(sg，1)}|g∈G，s∈S}本文研究了有限非交换单群3度双Cayley图，在[1]中，已经讨论了关于A_n的3度半对称图的一些情况。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。