isomorphic

简明释义

英[ˌaɪsəʊˈmɔːfɪk]美[ˌaɪsəˈmɔrfɪk]

adj. [物] 同构的；同形的

英英释义

单词用法

同义词

反义词

例句

1.Some techniques might be used to overcome these limitations, but they would not exhibit the same strengths as an isomorphic notation such as JSONx.

可以通过一些技术来克服这些限制，但它们的效果不如同构表示法，比如 JSONx。

2.We also point out that the integral sum labelling of the double star is unique in the isomorphic sense.

我们还指出在同构的意义下双星的整和标号是唯一的。

3.This article makes attempts to study the law in the establishment of school children's isomorphic concept.

本文试图探索小学儿童形成量度同构概念的规律。在研究中我们调查并测试了一至六年级的儿童。

4.If a matrix game is isomorphic to a matrix game with zero game value, then the latter is called annihilation of the former.

如果矩阵对策同构于一个对策值为零的矩阵对策，那么后者称为前者的零化。

5.Mimetite group minerals are a group of isomorphic series minerals with hexagonal system, which include mimetite, vanadinite and pyromorphite.

砷铅矿族矿物是一族六方晶系的类质同象系列矿物，包括砷铅矿、钒铅矿和磷氯铅矿。

6.If a loop is isotopic to a group, then it is isomorphic to that group and thus is itself a group.

如果一个圈与某个群同痕，那么它与此群同构，因此也为一个群。

7.Because it can cause isomorphic reaction and spot expanding.

因为它能引起同构反应和现场扩大。

8.What you describe is so called 'Isomorphic' approach.

你所描述的是所谓的“同构”的方法。

9.In mathematics, two structures are said to be isomorphic 同构的 if there exists a bijective mapping between them that preserves their properties.

在数学中，如果两个结构之间存在一个保留其性质的双射映射，则称这两个结构是isomorphic 同构的。

10.The concept of isomorphic 同构的 graphs is crucial in graph theory for determining when two graphs can be considered the same.

在图论中，isomorphic 同构的 图的概念对于确定两个图何时可以被视为相同至关重要。

11.In computer science, we often deal with isomorphic 同构的 data structures to optimize algorithms.

在计算机科学中，我们经常处理isomorphic 同构的 数据结构以优化算法。

12.The study of isomorphic 同构的 algebraic structures helps mathematicians understand their underlying principles.

对isomorphic 同构的 代数结构的研究帮助数学家理解其基本原理。

13.In topology, two spaces are isomorphic 同构的 if they can be transformed into each other without tearing or gluing.

在拓扑学中，如果两个空间可以在不撕裂或粘合的情况下相互转化，则它们是isomorphic 同构的。

作文

In mathematics and computer science, the term isomorphic refers to a fundamental concept that describes a relationship between two structures. When two mathematical objects are said to be isomorphic, it means that there exists a one-to-one correspondence between their elements that preserves the operations defined on those structures. This concept is not only crucial in theory but also has practical implications in various fields, including algebra, topology, and even in data structures in computer science. To illustrate this concept, consider two groups in abstract algebra. If we have two groups, G and H, they can be considered isomorphic if there is a function f: G → H such that f is a bijection (one-to-one and onto) and respects the group operation. This means that for any elements a and b in G, the equation f(a * b) = f(a) * f(b) holds true. This property indicates that G and H are structurally the same, even if they may appear different at first glance. The idea of isomorphic structures extends beyond mathematics into computer science as well. In programming, when we talk about data structures being isomorphic, we refer to the ability to transform one data structure into another while preserving its properties and relationships. For example, two binary trees can be considered isomorphic if one can be transformed into the other by swapping left and right child nodes. This type of relationship is essential for optimizing algorithms and understanding the efficiency of different data representations. Moreover, the concept of isomorphic can also be applied in other areas such as biology and linguistics. In biology, two species might be isomorphic in terms of their genetic structures, meaning they share a similar genetic makeup despite being different species. In linguistics, two languages can be described as isomorphic if they share similar grammatical structures, which can facilitate language learning and translation processes. Understanding isomorphic relationships allows us to recognize patterns and similarities across various disciplines. It encourages a deeper comprehension of how different systems can exhibit similar behaviors or structures, leading to insights that can be applied across diverse fields. The study of isomorphic connections fosters creativity and innovation, as it encourages individuals to think outside the box and draw parallels between seemingly unrelated subjects. In conclusion, the concept of isomorphic serves as a bridge connecting various domains of knowledge. Whether in mathematics, computer science, biology, or linguistics, recognizing isomorphic relationships enhances our understanding of complex systems. As we continue to explore these connections, we can unlock new ways of thinking and problem-solving that transcend traditional boundaries, ultimately enriching our intellectual landscape. Therefore, grasping the essence of isomorphic structures is not merely an academic exercise; it is a key to unlocking the interconnectedness of knowledge in our world.

在数学和计算机科学中，术语同构指的是描述两个结构之间关系的基本概念。当两个数学对象被称为同构时，这意味着它们的元素之间存在一种一一对应的关系，并且保持在这些结构上定义的运算。这一概念不仅在理论上至关重要，而且在包括代数、拓扑以及计算机科学中的数据结构等多个领域都有实际应用。 为了说明这一概念，考虑抽象代数中的两个群。如果我们有两个群G和H，如果存在一个函数f: G → H，使得f是一个双射（单一且满射）并且尊重群运算，那么这两个群可以被视为同构。这意味着对于G中的任意元素a和b，等式f(a * b) = f(a) * f(b)成立。这一性质表明，G和H在结构上是相同的，即使它们在表面上可能看起来不同。 同构结构的概念不仅限于数学，还扩展到了计算机科学。在编程中，当我们谈论数据结构是同构时，我们指的是将一种数据结构转化为另一种数据结构，同时保持其属性和关系的能力。例如，如果一棵二叉树可以通过交换左右子节点转换为另一棵二叉树，则这两棵二叉树可以被认为是同构的。这种关系对于优化算法和理解不同数据表示的效率至关重要。 此外，同构的概念还可以应用于生物学和语言学等其他领域。在生物学中，两种物种在其遗传结构上可能是同构的，意味着它们尽管是不同的物种，但却共享相似的遗传构成。在语言学中，如果两种语言共享相似的语法结构，那么它们可以被描述为同构，这可以促进语言学习和翻译过程。 理解同构关系使我们能够识别各个学科之间的模式和相似性。它鼓励我们更深入地理解不同系统如何表现出相似的行为或结构，从而产生可以应用于不同领域的见解。对同构连接的研究促进了创造力和创新，因为它鼓励个人跳出框架思考，并在看似不相关的主题之间建立联系。 总之，同构的概念作为连接各种知识领域的桥梁。无论是在数学、计算机科学、生物学还是语言学，识别同构关系增强了我们对复杂系统的理解。随着我们继续探索这些联系，我们可以解锁新的思维和解决问题的方法，这些方法超越了传统界限，最终丰富了我们的智力领域。因此，掌握同构结构的本质不仅仅是一个学术练习；它是解锁我们世界知识互联性的钥匙。