noncommutative

简明释义

英[nɒnkəˈmjuːtətɪv]美[ˈnɑːnkəˈmjuːtətɪv]

非可换的

非交换的

英英释义

单词用法

同义词

反义词

例句

1.In Chapter 1, briefly introduce the concept of noncommutative space and nori-commutative field theory, review the history and important results of studying the noncommutative soliton solution.

第一章，简要介绍非对易的概念及非对易场论，回顾前人在非对易孤子解方面的研究。

2.The invariant space has to be as well a deformation of a classical space, a deformation that makes it noncommutative.

这些不变的空间同样也是经典空间的变形，它们通过这种变形成为非对易空间。

3.Indeed, noncommutative geometry has arisen in at least three distinct but closely related contexts in string theory.

实际上在弦理论中，非对易几何自然地出现在至少三种不同而又密切相关的背景里。

4.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。

5.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。

6.In the first paper of the second part , it studies two dimensional noncommutative Lie algebra and its solvability, completeness and nonsemisimplicity and so on .

在第二部分第一篇论文中，我们系统研究了二维非交换李代数及其全形的可解性、完备性与非半单性等性质。

7.Encyclopedia of Mathematical Physics, Complex Geometry; Differential Geometry; Low Dimensional Geometry; Noncommutative Geometry.

复几何；微分几何；低维几何；非交换几何（英文影印版）

8.Rules can also be used for commutative and noncommutative algebra.

规则可以用于交换和非交换代数。

9.In quantum mechanics, the position and momentum operators are noncommutative 不交换的, which leads to the Heisenberg uncertainty principle.

在量子力学中，位置和动量算符是不交换的，这导致了海森堡不确定性原理。

10.The noncommutative 不交换的 nature of certain mathematical functions can complicate integration and differentiation.

某些数学函数的不交换的特性可能会使积分和微分变得复杂。

11.In programming, some operations on data types may be noncommutative 不交换的, leading to different results depending on the order of execution.

在编程中，对数据类型的一些操作可能是不交换的，根据执行顺序会导致不同的结果。

12.In certain algebraic structures, such as groups, operations can be noncommutative 不交换的, affecting the properties of the group.

在某些代数结构中，如群，运算可以是不交换的，这会影响群的性质。

13.The multiplication of matrices is noncommutative 不交换的, meaning that the order in which you multiply them matters.

矩阵的乘法是不交换的，这意味着你乘法的顺序是重要的。

作文

In mathematics, the concept of noncommutative operations plays a vital role in various fields, particularly in algebra and quantum mechanics. To understand this term, it is essential to first grasp the meaning of commutative operations. In simple terms, an operation is said to be commutative if changing the order of the operands does not change the result. For instance, in basic arithmetic, addition is commutative because a + b equals b + a. However, when we delve into the realm of noncommutative operations, we encounter scenarios where the order of the operands significantly affects the outcome.One of the most straightforward examples of noncommutative operations can be found in matrix multiplication. If we take two matrices A and B, the product AB is generally not equal to the product BA. This characteristic is what makes matrix multiplication noncommutative. Understanding this property is crucial for anyone studying linear algebra, as it influences how we manipulate and interpret matrices in various applications, such as computer graphics, engineering, and data science.Moreover, the implications of noncommutative operations extend beyond mathematics into the physical sciences. In quantum mechanics, the observables that describe physical properties are represented by operators, which are often noncommutative. For example, the position and momentum operators do not commute, meaning that the measurement of one affects the uncertainty of the other. This principle is encapsulated in Heisenberg's uncertainty principle, which is fundamental to our understanding of quantum systems.The significance of noncommutative structures is also evident in the field of functional analysis, where the study of noncommutative algebras has led to the development of various theories and applications. These include noncommutative geometry, which provides a framework for understanding spaces that cannot be described using traditional geometric concepts. This area of study has implications for theoretical physics, particularly in attempts to unify general relativity and quantum mechanics.Furthermore, noncommutative concepts have been applied in areas such as cryptography and information theory. The security of certain cryptographic systems relies on noncommutative properties, making it difficult for potential attackers to decipher encrypted messages without the proper keys. As technology continues to evolve, the importance of understanding noncommutative structures will only grow, especially in the context of quantum computing, which leverages the principles of noncommutative mathematics to perform computations at unprecedented speeds.In conclusion, the term noncommutative refers to operations where the order of the operands matters, leading to different results depending on their arrangement. This concept is foundational in various mathematical disciplines and has far-reaching implications in science and technology. As we continue to explore the complexities of the universe, the understanding of noncommutative structures will remain a critical component of both theoretical and applied research, shaping the future of mathematics and its applications in the real world.

在数学中，noncommutative（非交换）运算的概念在各个领域中发挥着至关重要的作用，特别是在代数和量子力学中。要理解这个术语，首先必须掌握交换运算的含义。简单来说，如果改变操作数的顺序不会改变结果，则该操作被称为交换的。例如，在基本算术中，加法是交换的，因为 a + b 等于 b + a。然而，当我们深入研究 noncommutative 运算的领域时，我们会遇到操作数的顺序显著影响结果的情况。非交换运算的一个最简单的例子可以在矩阵乘法中找到。如果我们取两个矩阵 A 和 B，乘积 AB 通常不等于乘积 BA。这一特性使得矩阵乘法成为 noncommutative 的。理解这一属性对任何学习线性代数的人来说都是至关重要的，因为它影响我们在各种应用中如何操作和解释矩阵，例如计算机图形学、工程和数据科学。此外，noncommutative 运算的影响超越了数学，延伸到物理科学。在量子力学中，描述物理属性的可观察量由算符表示，这些算符通常是 noncommutative 的。例如，位置和动量算符不交换，这意味着对一个的测量会影响另一个的不确定性。这个原则被包涵在海森堡的不确定性原理中，这是我们理解量子系统的基础。noncommutative 结构的重要性在泛函分析领域也很明显，noncommutative 代数的研究导致了各种理论和应用的发展。这些包括非交换几何，为理解无法用传统几何概念描述的空间提供了框架。这一研究领域对理论物理有着深远的影响，特别是在试图统一广义相对论和量子力学方面。此外，noncommutative 概念还应用于密码学和信息理论等领域。某些密码系统的安全性依赖于 noncommutative 属性，使潜在攻击者在没有适当密钥的情况下难以解密信息。随着技术的不断发展，理解 noncommutative 结构的重要性只会增加，尤其是在量子计算的背景下，量子计算利用 noncommutative 数学的原理以空前的速度进行计算。总之，术语 noncommutative 指的是操作数的顺序很重要，导致根据其排列不同而产生不同的结果。这个概念是各种数学学科的基础，并在科学和技术中具有深远的影响。随着我们继续探索宇宙的复杂性，理解 noncommutative 结构将仍然是理论和应用研究的关键组成部分，塑造数学及其在现实世界中应用的未来。