isomorphism

简明释义

英[ˌaɪsəʊˈmɔːfɪzəm]美[ˌaɪsəˈmɔrfɪzm]

n. 类质同像，[物化] 类质同晶；同形

英英释义

单词用法

同义词

反义词

例句

1.The Process Isomorphism pattern, defined by Jason, is an important instrument for formalizing alignment between services and processes which could improve both.

由Jason Bloomberg提出的流程同构模式是形式化服务和流程之间对齐的重要工具，同时也是改善两者的重要工具。

2.There are a number of classes of mathematical objects for which the problem of isomorphism is a GI-complete problem.

有一些类型的数学对象的问题，这是一个同构起完整的问题。

3.This paper prove that there are only eleven four—rings up to isomorphism.

本文证明了在同构意义下四元环仅有十一个。

4.The Process Isomorphism pattern, defined by Jason, is an important instrument for formalizing alignment between services and processes which could improve both.

由Jason Bloomberg提出的流程同构模式是形式化服务和流程之间对齐的重要工具，同时也是改善两者的重要工具。

5.Only by taking an iterative approach where each iteration combines top-down and bottom-up design is an organization likely to achieve Process Isomorphism.

只有采用迭代的方式，在每个迭代中结合自顶向下和自底向上的设计，组织才有可能获得流程同构。

6.The path layer matrix is closely related to graph isomorphism.

图的路径层矩阵与图的同构问题密切相关。

7.However, paraffin wax molecules could keep shortrange regular arrangement and possess the properties of so-called isomorphism in crystallography.

但石蜡分子能在较小的范围内保持着短程有序排列，并且具有晶体学中所谓的类质同晶的特性。

8.The manifest correlation of General fluid intelligence and Working memory should be the covariant relations, and they are analogy isomorphism.

一般流体智力和工作记忆所体现出来的相关应该是共变关系，两者是同功同构的。

9.In category theory, an isomorphism 同构 between two objects indicates that they are structurally the same.

在范畴论中，两个对象之间的isomorphism 同构表明它们在结构上是相同的。

10.The isomorphism 同构 between the two algebraic structures allows us to transfer properties from one to the other.

这两个代数结构之间的isomorphism 同构使我们能够将属性从一个转移到另一个。

11.In computer science, a data structure can have an isomorphism 同构 with another data structure if they can be transformed into each other.

在计算机科学中，如果一种数据结构可以转换为另一种数据结构，则它们之间可以存在isomorphism 同构。

12.The concept of isomorphism 同构 is crucial in understanding symmetries in mathematical objects.

理解数学对象中的对称性时，isomorphism 同构的概念至关重要。

13.Two graphs are said to be isomorphic 同构的 if there exists a bijection between their vertex sets that preserves adjacency.

如果两个图之间存在一个保持邻接关系的顶点集合的双射，则称它们是isomorphic 同构的。

作文

The concept of isomorphism has profound implications in various fields, including mathematics, computer science, and even biology. At its core, isomorphism refers to a structural similarity between two entities, allowing for a one-to-one correspondence between their elements. This idea can be illustrated through numerous examples, helping us understand its significance more clearly. In mathematics, particularly in abstract algebra, isomorphism plays a crucial role in understanding the relationship between different algebraic structures, such as groups, rings, and fields. For instance, if we have two groups that are isomorphic, it means there exists a bijective function between them that preserves the group operation. This notion allows mathematicians to classify and compare different algebraic systems effectively, revealing deeper insights into their properties and behaviors. Similarly, in the realm of computer science, isomorphism is often encountered in graph theory. Two graphs are said to be isomorphic if there is a mapping of their vertices that preserves the edges. This concept is essential for solving problems related to network design, optimization, and data structure analysis. By identifying isomorphic graphs, computer scientists can simplify complex problems, making them more manageable and easier to solve. Moreover, the idea of isomorphism extends beyond abstract concepts; it can also be applied to real-world scenarios. For example, in biology, the genetic makeup of different species can exhibit isomorphic traits, indicating common evolutionary paths. Understanding these similarities helps biologists trace lineage and comprehend the intricate web of life on Earth. The study of isomorphism in biology underscores the interconnectedness of all living organisms, revealing how evolution shapes diversity while maintaining fundamental similarities. In philosophy, isomorphism can also represent the relationship between mental states and physical states. The idea that our thoughts and perceptions can be mapped onto physical processes suggests a form of isomorphism between the mind and body. This perspective invites discussions about consciousness, identity, and the nature of reality itself, challenging us to consider how we understand existence. In conclusion, the concept of isomorphism serves as a bridge connecting various disciplines, highlighting the underlying similarities that exist across different domains. Whether in mathematics, computer science, biology, or philosophy, isomorphism provides a framework for understanding complex relationships and structures. By studying isomorphism, we gain valuable insights that not only enhance our knowledge but also encourage interdisciplinary collaboration, fostering innovation and discovery in an increasingly interconnected world.

“同构”这一概念在多个领域中具有深远的意义，包括数学、计算机科学，甚至生物学。在其核心上，“同构”指的是两个实体之间的结构相似性，允许它们的元素之间存在一一对应的关系。这个思想可以通过众多示例来说明，有助于我们更清楚地理解其重要性。 在数学中，特别是在抽象代数中，“同构”在理解不同代数结构（如群、环和域）之间的关系中发挥着至关重要的作用。例如，如果我们有两个群是“同构”的，这意味着它们之间存在一个保持群运算的双射函数。这个概念使数学家能够有效地对不同的代数系统进行分类和比较，从而揭示出它们的性质和行为的更深层次的见解。 同样，在计算机科学领域，“同构”经常出现在图论中。当两个图之间存在一个保留边的顶点映射时，我们称这两个图是“同构”的。这个概念对于解决与网络设计、优化和数据结构分析相关的问题至关重要。通过识别“同构”的图，计算机科学家可以简化复杂问题，使其更易于处理和解决。 此外，“同构”的思想超越了抽象概念；它也可以应用于现实世界的场景。例如，在生物学中，不同物种的基因组成可能表现出“同构”的特征，表明共同的进化路径。理解这些相似性有助于生物学家追踪谱系，理解地球上生命的复杂网络。“同构”在生物学中的研究强调了所有生物体之间的相互联系，揭示了进化如何塑造多样性，同时保持基本的相似性。 在哲学中，“同构”也可以代表心理状态与物理状态之间的关系。我们的思想和感知可以映射到物理过程的观点表明心灵与身体之间存在一种形式的“同构”。这种观点引发了关于意识、身份和现实本质的讨论，挑战我们思考如何理解存在。 总之，“同构”这一概念作为连接各个学科的桥梁，突显了不同领域之间存在的潜在相似性。无论是在数学、计算机科学、生物学还是哲学中，“同构”为理解复杂关系和结构提供了框架。通过研究“同构”，我们获得了宝贵的见解，不仅增强了我们的知识，还促进了跨学科的合作，推动了在日益互联的世界中创新和发现。