isomorphically

简明释义

英[ˌaɪsəʊˈmɔːfɪkli]美[ˌaɪsəˈmɔrfɪkli]

同态地

同形地

英英释义

单词用法

同义词

反义词

例句

1.In this paper, we discuss isomorphic factorization for tensor product of two divisible graphs and prove the conditions for the tensor product graphs to be factorized isomorphically.

本文讨论了两个可分图的张量乘积图的同构因子分解问题。

2.In this paper, we discuss isomorphic factorization for tensor product of two divisible graphs and prove the conditions for the tensor product graphs to be factorized isomorphically.

本文讨论了两个可分图的张量乘积图的同构因子分解问题。

3.In algebra, two structures are said to be related isomorphically when there exists a one-to-one correspondence between their elements.

在代数中，当两个结构之间存在一一对应关系时，它们被称为同构地相关。

4.The two groups can be represented isomorphically, showing that they have the same algebraic structure.

这两个群可以同构地表示，表明它们具有相同的代数结构。

5.In topology, spaces that are homeomorphic are often studied isomorphically due to their similar properties.

在拓扑学中，由于性质相似，通常以同构地方式研究同胚空间。

6.The programming languages can be transformed isomorphically, allowing for easier code translation.

这些编程语言可以同构地转换，从而使代码翻译更容易。

7.In graph theory, two graphs are isomorphic if they can be mapped isomorphically to each other.

在图论中，如果两个图可以同构地映射到彼此，则它们是同构的。

作文

In the realm of mathematics and computer science, the concept of isomorphism plays a crucial role in understanding the relationships between different structures. Two structures are said to be isomorphic if there exists a one-to-one correspondence between their elements that preserves the operations defined on them. This means that the two structures can be considered as essentially the same, even though they may appear different at first glance. The term isomorphically refers to this idea of structural similarity, where two entities can be transformed into one another without losing their inherent properties. For instance, consider the case of graphs in graph theory. If we have two graphs that can be mapped onto each other such that their connectivity remains unchanged, we say that these graphs are isomorphic. This relationship can be expressed isomorphically, highlighting how the fundamental nature of the graphs is preserved despite their different representations. Understanding this concept is vital for solving problems related to network design, optimization, and even social sciences, where relationships and structures can be modeled using graphs. Similarly, in algebra, we often deal with groups, rings, and fields. When we say that two algebraic structures are isomorphic, we mean that there is a bijective function between them that preserves the operations of addition and multiplication. This property allows mathematicians to transfer problems and solutions from one structure to another isomorphically, making it easier to analyze and understand complex systems. The application of the term isomorphically extends beyond pure mathematics into various fields such as biology, chemistry, and even philosophy. In biology, for example, the concept of isomorphism can be used to describe the similarities between different species or ecosystems that evolve under similar environmental pressures. By studying these relationships isomorphically, scientists can gain insights into evolutionary processes and ecological dynamics. In the field of chemistry, isomorphic compounds exhibit similar structures and properties, allowing chemists to predict the behavior of one compound based on the known characteristics of another. This isomorphically linked information is invaluable for drug development and materials science, where understanding molecular interactions can lead to significant breakthroughs. Moreover, in philosophy, the idea of isomorphism can be applied to theories and concepts that may seem disparate but share underlying principles. By analyzing these theories isomorphically, philosophers can draw connections between seemingly unrelated ideas, enriching our understanding of knowledge and existence. In conclusion, the term isomorphically encapsulates a profound idea of structural similarity and transformation across various disciplines. Whether in mathematics, biology, chemistry, or philosophy, recognizing and applying the concept of isomorphism allows us to uncover deeper connections and insights. As we continue to explore the complexities of our world, the ability to think isomorphically will undoubtedly enhance our understanding and foster innovation in diverse fields of study.

在数学和计算机科学的领域中，同构的概念在理解不同结构之间的关系时起着至关重要的作用。如果两个结构之间存在一一对应的关系，并且保留了定义在它们上的操作，那么我们就说这两个结构是同构的。这意味着这两个结构可以被视为本质上是相同的，即使它们乍一看可能显得不同。术语isomorphically指的是这种结构相似性的理念，其中两个实体可以相互转化而不失去其固有属性。 例如，考虑图论中的图的情况。如果我们有两个图，可以将其映射到彼此，使得它们的连通性保持不变，我们就说这些图是同构的。这种关系可以以isomorphically的方式表达，突显出尽管图的表示不同，但其基本性质得到了保留。理解这一概念对于解决与网络设计、优化乃至社会科学相关的问题至关重要，因为这些领域中的关系和结构可以通过图来建模。 同样，在代数中，我们经常处理群、环和域。当我们说两个代数结构是同构的时，我们的意思是存在一个双射函数在它们之间，保留了加法和乘法的运算。这一属性使得数学家能够以isomorphically的方式将问题和解决方案从一个结构转移到另一个结构，从而更容易分析和理解复杂系统。 术语isomorphically的应用超越了纯数学，延伸到生物学、化学甚至哲学等多个领域。例如，在生物学中，同构的概念可以用来描述在类似环境压力下进化的不同物种或生态系统之间的相似性。通过以isomorphically的方式研究这些关系，科学家可以深入了解进化过程和生态动态。 在化学领域，同构化合物表现出相似的结构和性质，使化学家能够根据已知特征预测一种化合物的行为。这种isomorphically关联的信息对于药物开发和材料科学至关重要，因为理解分子间的相互作用可以导致重大突破。 此外，在哲学中，同构的思想可以应用于那些看似不同但共享基础原则的理论和概念。通过以isomorphically的方式分析这些理论，哲学家可以在看似无关的思想之间建立联系，丰富我们对知识和存在的理解。 总之，术语isomorphically概括了一个深刻的结构相似性和跨学科转化的理念。无论是在数学、生物学、化学还是哲学中，认识并应用同构的概念使我们能够揭示更深层次的联系和见解。随着我们继续探索世界的复杂性，以isomorphically的方式思考无疑将增强我们的理解，并促进各个研究领域的创新。