topological

简明释义

英[,tɒpə'lɒdʒɪkl]美[tɑːpəˈlɑːdʒɪkl]

adj. 拓扑的；[解剖] 局部解剖学的；[地理] 地志学的

英英释义

单词用法

同义词

反义词

例句

1.This is done by using a topological sort algorithm on the graph.

这通过图表中的拓扑排序算法实现。

2.An initial topological mesh object, connecting on six distributed anchor points within the space, is submitted to an iterative surface tension process.

初始拓扑网格物体连接到空间内六个分布式锚点，形成了一个重复的表面张力。

3.But the creation of topological forms capable of reconfiguration, like those produced by nature, has proven more challenging.

但是，能够重新配置拓扑形式像自然生产的，已经证明了创造更具挑战性。

4.Studies have shown that the Hilbert curve preserves very well the topological information, even better than the Z-ordering.

研究表明，Hilbert曲线可以很好地保存拓扑信息，甚至优于Z顺序曲线。

5.An initial topological mesh object, connecting on six distributed anchor points within the space, is submitted to an iterative surface tension process.

初始拓扑网格物体连接到空间内六个分布式锚点，形成了一个重复的表面张力。

6.The topological sorting algorithm works on unconnected graphs as well as connected graphs.

拓扑排序算法既可以用于连通图，也可以用于非连通图。

7.The method exploits regularities both in the communication phases and in the topological communication structure of a binomial tree.

这一方法不仅利用二项树通信步中的规则性，而且利用了二项树拓扑结构的规则性。

8.The generation employs space filling curves to preserve the spatial and topological properties (see the Resources section for the H. Sagan book).

这里使用空间填充曲线来保存空间和拓扑属性（请参阅参考资料一节，找到 H.Sagan 撰写的书籍）。

9.The study of topological 拓扑的 spaces is essential in modern physics, particularly in quantum field theory.

对 topological 拓扑的 空间的研究在现代物理学中至关重要，特别是在量子场论中。

10.We can use topological 拓扑的 methods to analyze the connectivity of networks.

我们可以使用 topological 拓扑的 方法来分析网络的连通性。

11.In computer science, topological 拓扑的 sorting is used to order tasks based on their dependencies.

在计算机科学中，topological 拓扑的 排序用于根据任务之间的依赖关系来排序任务。

12.In mathematics, a topological 拓扑的 space is defined by its properties that are preserved under continuous deformations.

在数学中，topological 拓扑的 空间是通过其在连续变形下保持的性质来定义的。

13.A topological 拓扑的 graph can reveal important information about the relationships between different data points.

一个 topological 拓扑的 图可以揭示不同数据点之间关系的重要信息。

作文

In the realm of mathematics, the term topological refers to a branch that studies properties of space that are preserved under continuous transformations. This field, known as topology, is concerned with the qualitative aspects of geometric objects rather than their precise measurements. To illustrate the significance of topological concepts, consider the classic example of a coffee cup and a donut. In topological terms, these two objects are equivalent because one can be transformed into the other without cutting or gluing. This idea challenges our conventional understanding of shapes and dimensions, emphasizing the importance of connectivity and continuity over rigid forms.Topology has numerous applications across various scientific disciplines. For instance, in computer science, topological data analysis is employed to extract meaningful patterns from complex datasets. This approach allows researchers to understand the shape of data, revealing insights that traditional statistical methods might overlook. By analyzing the topological features of data, scientists can identify clusters, holes, and voids, leading to more informed decisions in fields such as machine learning and artificial intelligence.Moreover, in physics, topological concepts play a crucial role in understanding the behavior of materials. Topological insulators, for example, are materials that behave as insulators in their bulk form but conduct electricity on their surface. The topological properties of these materials arise from their electronic structure, which is protected from perturbations, making them robust against defects and impurities. This discovery has opened up new avenues for research in quantum computing and advanced materials, highlighting the profound implications of topological phenomena.The study of topological spaces also extends to biology. Researchers have begun to explore how topological principles can explain the intricate structures of biological systems. For instance, the arrangement of neurons in the brain can be analyzed using topological methods to understand how information is processed and transmitted. Similarly, the topological organization of proteins can shed light on their functions and interactions within cellular environments.In conclusion, the term topological encompasses a vast and fascinating area of study that transcends traditional boundaries of mathematics, science, and engineering. By focusing on the properties that remain invariant under continuous transformations, we gain valuable insights into the nature of space and its applications across various fields. As we continue to explore the topological aspects of our world, we uncover new dimensions of understanding that challenge our perceptions and inspire further inquiry. The versatility of topological concepts serves as a reminder of the interconnectedness of all things, urging us to appreciate the underlying structures that shape our universe and our lives.

在数学领域，术语topological指的是一个研究空间在连续变换下保持的性质的分支。这个领域被称为拓扑学，关注几何对象的定性方面，而不是它们的精确测量。为了说明topological概念的重要性，可以考虑经典的咖啡杯和甜甜圈的例子。在topological术语中，这两个物体是等价的，因为可以在不切割或粘合的情况下将一个变换为另一个。这个想法挑战了我们对形状和维度的传统理解，强调了连通性和连续性的重要性，而不是刚性的形式。拓扑学在各个科学学科中有着众多应用。例如，在计算机科学中，topological数据分析用于从复杂数据集中提取有意义的模式。这种方法使研究人员能够理解数据的形状，揭示出传统统计方法可能忽视的见解。通过分析数据的topological特征，科学家可以识别集群、孔洞和空隙，从而在机器学习和人工智能等领域做出更明智的决策。此外，在物理学中，topological概念在理解材料行为方面发挥着至关重要的作用。拓扑绝缘体就是一个例子，它们在其整体形式中表现为绝缘体，但在表面上导电。这些材料的topological性质源于它们的电子结构，这种结构对扰动具有保护作用，使其对缺陷和杂质具有稳健性。这一发现为量子计算和先进材料的研究开辟了新的途径，突显了topological现象的深远影响。对于生物学的研究也开始探讨topological原理如何解释生物系统的复杂结构。例如，研究人员开始使用topological方法分析大脑中神经元的排列，以理解信息是如何处理和传递的。同样，蛋白质的topological组织可以揭示其在细胞环境中的功能和相互作用。总之，术语topological涵盖了一个广泛而迷人的研究领域，超越了数学、科学和工程的传统界限。通过关注在连续变换下保持不变的性质，我们获得了对空间本质及其在各个领域应用的宝贵见解。随着我们继续探索世界的topological方面，我们揭示了新的理解维度，这挑战了我们的认知并激励了进一步的探究。topological概念的多样性提醒我们所有事物的相互联系，促使我们欣赏塑造我们宇宙和生活的基本结构。