查询词典 noncommutative

If we study further the characteristic of this algebraic structure under the action of permutation group elements, it would provide a new approach to solve the problem about the renormalization of noncommutative scalar fields.

如果进一步考察该代数形式在置换群作用下的置换性质，就为我们提供了一种完全解决非对易标量场重整化问题的一种可能途径。

The latter one is our effort in attacking the diagonalization of the Cauchy kernel on Schubert polynomials (the noncommutative version conjectured by Alain Lascoux is still open).

后者是我们在关于Schubert多项式的Cauchy核对角化方面所做的努力（Alain Lascoux猜想在非交换的情况下也成立，但目前为止还没有被证明）。

The idea that the space-time coordinates do not commutate is old. But noncommutative geometry cannot attract the physicists interest for a long time.

时空坐标非对易的思想已经有好久了，但是长期以来，非对易几何并未在物理上受到人们广泛关注。

Other semirings arise naturally in such diverse areas of mathematics as combinatorics, functional analysis, topology, graph theory, Euclidean geometry, probability theory, commutative and noncommutative ring theory, optimization theory, discrete event dynamical systems, automata theory, formal language theory and the mathematical modeling of quantum physics and parallel computation systems.

在许多不同的数学领域存在着其它形式的半环，比如组合学，泛函分析，拓扑学，图论，欧式几何，概率论，交换和非交换环，优化论，离散动力系统，自动化理论，形式语言理论，量子物理的数据模型和并行计算系统。

Nonlinear control system; transfer function; differential vector space; noncommutative ring

非线性控制系统；传递函数；微分向量空间；非交换环

Finally, in Chapter 4, we generalize the kq representation to 2N dimension. Based on Blocking theorem, the complete set of projectors on noncommutative Orbifold T〓/G are given.

第四章，我们建立了2N维空间的kq表象，证明了分块定理并由此构造出非对易可积Orbifold T〓/G上的投影算子完备集。

Finally, in Chapter 4, we generalize the kq representation to 2N dimension. Based on Blocking theorem, the complete set of projectors on noncommutative Orb-ifold T2N/G are given.

第四章，我们建立了2N维空间的kq表象，证明了分块定理并由此构造出非对易可积Orbifold T~(2N)／G上的投影算子完备集。

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。

Then we in-vest gate Seiberg-Witten map, which defines the equivalence relation of the gauge symmetries in different spaces. We also analyse the U gauge electromagnetic field in noncommutative space. Finally we discuss the ambiguities of Seiberg-Witten map, and find although that some part of the ambiguities can be absorbed by gauge transformation and hence negligible, the existence of the matter field makes some other parts difficult to be absorbed by gauge transformation or field redefinition.

然后利用Seiberg-Witten映射，我们研究了不同空间的规范对称性的等价问题，并对非对易空间的电磁场进行了微扰分析，最后我们对Seiberg-Witten映射的松动进行了讨论，研究发现这些松动中的一部分可以由规范变换吸收因而是可以忽略的，由于物质场的存在，另外一部分很难用规范变换和场的重定义吸收。

The progress make researchers pay more attention to noncommutative geometry and physics theories based on noncommutative space-time.

正是这一重大进展，促使人们投入大量精力重新开展对非对易几何及建立于非对易时空中的物理理论的研究。

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。