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- noncommutative semilocalring 非交换半局部环
- Then we study several quantum mechanics systems on the noncommutative space. 接着用前面得到的表示方法，来研究了几个量子力学系统。
- The algebra of quaternions, the first noncommutative algebra was thus suddenly born. 四元数的代数，第一非交换的代数，就这样在一夜之间诞生了。
- The space between the two sides of the paper is an extra discrete (noncontinuous), noncommutative space. 介于这张纸两面之间的空间是一个额外的、离散的（不连续的）非可换空间。
- Connected graded algebra is the main object studied in noncommutative projective geometry. 连通分次代数是非交换射影几何主要研究的具体对象之一。
- The proposed research direction of black holes and cosmology on noncommutative spacetime has also led to unexpected productions. 关于非对易时空中的黑洞和宇宙学的研究方向也取得了意料之外的成果。
- Based upon this geometric construction, scalar field, fermionic field, and gauge field are generalized onto such types of noncommutative spaces. 半直积有限群上的质量矩阵理论；点阵上非么正的规范场论，循环点阵规范理论的经典解。
- In this paper,we study the relationship between convergence in probability and noncommutative independence (monotonic independence and Boolean independence. 研究了依概率收敛和非交换独立性(单调独立性和布尔独立性)之间的关系.
- In this paper, we study the relationship between convergence in probability and noncommutative independence (monotonic independence and Boolean independence. 研究了依概率收敛和非交换独立性(单调独立性和布尔独立性)之间的关系。
- Abstract : In this paper, we discuss the connection between the rigid graded selfduality over some noncommutative graded ring and the selfduality over its initial subring. 摘要 ： 本文讨论非交换分次环上的纲性分次自对偶与其初始子环上的自对偶之间的关系.
- The relation between renormalization and noncommutative geometry serves as a starting point to unite relativity and quantum mechanics and thereby fully describe gravity. 重整化理论和非可换几何之间的关系，可以做为统一相对论与量子力学的起点，因此也能完整地描述重力。
- The Berry phase, AB effect and AC effect on the noncommutative phase space, which means the coordinate and momentum both are noncommutative, is studied. 接着研究了非对易空间中的量子力学相，给出了非对易效应对相位的修正。
- Furthermore, in the noncommutative Chern-Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is also identified with the moment map eqaution of the noncommutative sun(T) cotangent bundle with marked points. 而且，在量子Hall效应的非对易陈-Simons理论里，具有准粒子源的约束方程也与具有marked点的非对易su_n(T)余切丛的momentmap方程相同。
- Furthermore, the double complex symmetric gravitational action in the double noncommutative spacetime can be constructed by extending the double complex coordinates to the double noncommutative relation satisfied and by doubling the Moyal star product. 同时，通过将二重复坐标推广到满足二重非对易关系以及Moyal星积的二重化，构造出二重非交换复对称引力场作用量。
- All that is needed is a tool to peer into the complexity, the way the electron microscope reveals molecular structure, remarks Connes, whose “electron microscope” is noncommutative geometry. 他说，我们所需要的就是能够看穿复杂计算的工具，就像电子显微镜能揭露分子结构那样；
- Connes's idea was to extend the relation between geometric space and its commutative algebra of Cartesian coordinates, such as latitude and longitude, to a geometry based on noncommutative algebras. 巩讷的想法是将几何空间与其卡式座标（即一般常用的直角座标）的可换代数，推广到一种奠基于非可换代数的几何。
- The statistic characteristic and energy distribution of coefficients are analyzed.Theory of noncommutative wavelet is applied to digital image hiding to accomplish the information blindly extracting. 文中分析了变换系数的统计特性和能量分布，并将非交换小波理论用于图像隐藏中，实现了信息的盲提取。
- In the recent year, more and more physical problems on the noncommutative background are regarded as important for people with the study of the quantum Hull Effect and the string theory. 近几年,随着对量子霍尔效应和弦理论的研究,越来越多的非对易背景上的物理学问题引起人们的重视。
- A straightforward way to study noncommutativity of space is to study the quantum mechanics on the noncommutative space. 而对非对易理论的研究，最直接的想法就是研究非对易量子力学系统。
- A First Course in Noncommutative Ring 非交换环入门
