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1·All these results are the non-commutative generalizations of the corresponding ones of the filter theory of NM algebra.

它们是NM代数滤子理论相应结果的非交换推广。

2·Recently physicists working on superstring theory paid much attention to the quantum mechanics on non-commutative Spaces (NCQM).

非对易空间中的量子力学(NCQM)最近引起了超弦理论领域物理学家们的兴趣。

3·The contents of this thesis are the following: 1 the spectra and the wave functions of 2d harmonic oscillator in non-commutative space.

主要内容如下：1、非对易空间(？)中二维谐振子的能谱及波函数的研究。

4·The braid group is infinite non-commutative group, and it has many hard problems that can be utilized to design cryptographic primitives, such as the word problem, conjugacy problem and root problem.

辫群是一种非交换的无限群，该群中有许多困难问题是不可解的，如字问题、共轭问题和根问题等，利用这些困难问题可以去设计一些密码协议。