centralizers

简明释义

英[ˈsɛntrəlaɪzəz]美[ˈsɛntrəˌlaɪzərz]

[数] 中心化子

英英释义

单词用法

同义词

反义词

例句

1.The multifinger caliper tool string to be used for casing inspection was centralized using the combination of a strong, optimally placed, spring loaded roller and stiff arm centralizers.

用于检查套管尺寸的多触点井径测量工具管串，采用结实的、安放位置经过优化的、弹簧加载的滚子及刚性臂扶正器进行居中。

2.The multifinger caliper tool string to be used for casing inspection was centralized using the combination of a strong, optimally placed, spring loaded roller and stiff arm centralizers.

用于检查套管尺寸的多触点井径测量工具管串，采用结实的、安放位置经过优化的、弹簧加载的滚子及刚性臂扶正器进行居中。

3.In the first section, namely 3.1, we obtained some description of the structure of some finite groups whose centralizers or normalizers of Abelian subgroups satisfy some conditions.

在第一部分3.1中，给出了若干由交换子群的中心化子或正规化子满足的条件所确定的有限群的结构描述。

4.For deviated wellbores, where gravitational force pulls casing to the low side of the hole, more robust solid-bladed centralizers are better if hole conditions allow their use.

对于斜井，由于重力迫使套管平躺于井壁的下侧，如果井眼条件允许，更为结实的固体刀翼式扶正器更为合适。

5.Hold centralizers cement baskets on any position of casing, which ensures the positions of centralizers cement basket to meet the design.

可将弹性套管扶正器或水泥伞置于套管本体上的任意部位，确保扶正器的安放位置满足设计要求。

6.There are two distinct classes of centralizers. The older and more common is a simple, low-cost bow-spring design.

有两大类扶正器：有一种使用时间长，且比较普遍、简单、成本低的弓型弹簧设计的扶正器。

7.For straight holes, bow spring centralizers are sufficient and commonly used.

对于直井，弓型弹簧扶正器足以满足上述功能，并被通常使用。

8.The engineers decided to use centralizers for the new drilling project to ensure proper casing alignment.

工程师们决定在新的钻探项目中使用centralizers（中心器）以确保套管对齐。

9.In pipeline construction, centralizers are crucial for maintaining the correct position of the pipes.

在管道施工中，centralizers（中心器）对于保持管道的正确位置至关重要。

10.The use of centralizers can significantly reduce the risk of casing deformation during installation.

使用centralizers（中心器）可以显著降低安装过程中套管变形的风险。

11.During the well completion phase, operators often rely on centralizers to enhance the cementing process.

在井完成阶段，操作员通常依赖centralizers（中心器）来增强水泥灌注过程。

12.The team evaluated different types of centralizers to determine which would best suit their needs.

团队评估了不同类型的centralizers（中心器），以确定哪种最能满足他们的需求。

作文

In the realm of mathematics and abstract algebra, the concept of centralizers plays a vital role in understanding the structure of groups. A centralizer is defined as the set of all elements in a group that commute with a particular element. More formally, if G is a group and g is an element of G, the centralizer of g in G, denoted as C_G(g), is given by C_G(g) = {x in G | xg = gx}. This definition highlights the importance of the relationship between elements in a group and how they interact with each other through the operation defined on the group. Understanding centralizers is crucial for several reasons. Firstly, they help in classifying groups based on their structures. By analyzing the centralizers of various elements, mathematicians can determine whether a group is abelian, meaning that all elements commute with each other, or non-abelian, where some elements do not commute. For instance, in the symmetric group S_n, which consists of all permutations of n elements, the centralizers of certain permutations can reveal a lot about the group's overall structure and properties. Secondly, centralizers are instrumental in the study of group actions. When a group acts on a set, the centralizers can be used to identify stabilizers, which are subsets of the group that leave certain elements of the set unchanged. This connection between centralizers and stabilizers is particularly useful in representation theory, where we explore how groups can be represented through linear transformations. By examining the centralizers, one can gain insights into the irreducible representations of the group, which are fundamental to understanding its representation as matrices. Moreover, centralizers find applications beyond pure mathematics. In physics, for example, the concept of symmetry is often analyzed using group theory. The centralizers of symmetries can help physicists understand conservation laws and the invariance of physical systems under certain transformations. This interplay between group theory and physics illustrates the profound impact of centralizers in various scientific fields. In addition to their theoretical significance, centralizers also possess computational aspects. Algorithms that compute centralizers can be implemented in software to assist mathematicians in exploring complex group structures. These algorithms can provide valuable information about the size and nature of centralizers, aiding researchers in their investigations. In conclusion, the concept of centralizers is essential in the study of group theory and its applications. By understanding the centralizers of elements within a group, mathematicians can classify groups, analyze their structures, and apply these concepts to various fields, including physics and computer science. The exploration of centralizers not only enriches our knowledge of abstract algebra but also bridges connections with other disciplines, showcasing the unity of mathematical concepts across different areas of study.

在数学和抽象代数的领域中，centralizers 的概念在理解群体结构方面发挥着至关重要的作用。centralizers 被定义为群中与特定元素交换的所有元素的集合。更正式地说，如果 G 是一个群，g 是 G 的一个元素，那么 g 在 G 中的 centralizer，记作 C_G(g)，由下式给出：C_G(g) = {x 属于 G | xg = gx}。这个定义强调了群中元素之间的关系及其通过群上定义的运算相互作用的重要性。 理解 centralizers 对几个原因至关重要。首先，它们有助于根据结构对群进行分类。通过分析各种元素的 centralizers，数学家可以确定一个群是否是阿贝尔群，即所有元素彼此交换，或者是非阿贝尔群，其中某些元素不交换。例如，在对称群 S_n 中，S_n 包含 n 个元素的所有排列，某些排列的 centralizers 可以揭示该群的整体结构和性质。 其次，centralizers 在研究群作用中也很重要。当一个群作用于一个集合时，centralizers 可用于识别稳定子，即群的子集，使得集合中的某些元素保持不变。centralizers 与稳定子之间的这种联系在表示理论中尤其有用，我们探讨群如何通过线性变换进行表示。通过检查 centralizers，人们可以深入了解该群的不可约表示，这对于理解其作为矩阵的表示至关重要。 此外，centralizers 的应用超越了纯数学。在物理学中，例如，对称性的概念通常通过群论进行分析。对称性的 centralizers 可以帮助物理学家理解守恒定律以及物理系统在某些变换下的不变性。这种群论与物理学之间的相互作用展示了 centralizers 在各个科学领域的深远影响。 除了它们的理论意义外，centralizers 还具有计算方面。可以在软件中实现计算 centralizers 的算法，以帮助数学家探索复杂的群结构。这些算法可以提供有关 centralizers 的大小和性质的宝贵信息，帮助研究人员进行调查。 总之，centralizers 的概念在群论及其应用的研究中至关重要。通过理解群中元素的 centralizers，数学家可以对群进行分类，分析其结构，并将这些概念应用于包括物理学和计算机科学在内的各个领域。对 centralizers 的探索不仅丰富了我们对抽象代数的知识，而且还与其他学科建立了联系，展示了不同研究领域之间数学概念的统一性。