topologic

简明释义

英[ˌtɒpəˈlɒdʒɪk]美[ˌtɒpəˈlɒdʒɪk]

局部解剖学的

英英释义

单词用法

同义词

反义词

例句

1.The movability of the spatial four-bar linkages is analyzed by the principle of topologic transformation.

本文运用拓扑变换原理，对空间四杆机构的可动性进行了分析研究。

2.The system topologic structure, system reliability and functions of operating station, process station and modules are introduced.

介绍了系统的网络拓扑结构和可靠性及各个主要部件如操作站、过程站和模块的功能。

3.The example makes clear that this method is validity and feasibility, it can be effectively used to topologic analysis of complex electric networks.

算例表明方法的正确性和可行性，可有效地应用于复杂电网络的拓扑分析。

4.The description of the robot's work environment and the actualizing process was studied, and a new method of making topologic map of the environment was proposed.

针对机器人环境识别问题，研究其工作环境描述与实现过程，提出一种环境拓扑地图建立的新方法。

5.The generalized capability of feedforward nets is related to its topologic structure, a systematic review is made over those modified algorithms f...

网络的泛化能力依赖于网络的拓扑结构，对国际上为改进网络泛化能力而采用的几种修正学习算法的实际功能做了简要的评论。

6.A novel topologic structure of high frequency AC pulse density modulation converter is proposed, and its operation principle, control scheme and design are described in detail.

提出了一种新颖的高频交流脉冲密度调制变频器的拓扑结构，并详细阐述了工作原理、控制方案和设计方法。

7.Topologic bifurcation situation of maxima lines is also discussed. In the end, an estimation for multifractal spectrum is proposed in terms of wavelet module maxima lines.

探讨了分形测度小波变换极大值线的拓扑分岔情况，并提出了一种基于小波变换模极大值的多重分形谱估算方法。

8.Artists often explore topologic 拓扑的 concepts in their abstract works.

艺术家们常常在他们的抽象作品中探索拓扑的概念。

9.In computer science, understanding topologic 拓扑的 data structures can enhance algorithm efficiency.

在计算机科学中，理解拓扑的数据结构可以提高算法效率。

10.The topologic 拓扑的 properties of a network can affect its performance.

网络的拓扑的特性可以影响其性能。

11.The topologic 拓扑的 classification of surfaces is a key area in topology.

表面的拓扑的分类是拓扑学中的一个关键领域。

12.The study of topologic 拓扑的 spaces is fundamental in modern mathematics.

对拓扑的空间的研究是现代数学的基础。

作文

In the field of mathematics, particularly in topology, the term topologic refers to properties that are preserved under continuous deformations of objects. Topology is a branch of mathematics that studies the properties of space that are preserved under continuous transformations. It is fascinating how something as abstract as topologic concepts can have real-world applications. For instance, when we think about the shape of a coffee cup and a donut, from a topological perspective, they are considered equivalent because one can be transformed into the other without cutting or gluing. This equivalence is a fundamental idea in topology, illustrating how topologic properties focus on the nature of space rather than specific measurements or shapes.Topology has implications beyond pure mathematics; it also finds applications in various fields such as computer science, biology, and physics. For example, in computer graphics, topologic data structures help in modeling and rendering complex shapes. Algorithms that utilize topologic principles can efficiently manage and manipulate these shapes, ensuring that transformations maintain the integrity of the original object.Moreover, in the realm of data analysis, topologic methods are employed to study the shape of data. Techniques like persistent homology allow researchers to analyze the underlying structure of data sets, revealing insights that might not be immediately apparent through traditional statistical methods. This aspect of topologic analysis has become increasingly important in machine learning and artificial intelligence, where understanding the shape of data can lead to better models and predictions.The concept of topologic spaces also plays a crucial role in understanding continuity and convergence. In calculus, we often deal with limits and functions, but in topology, we extend these ideas to more abstract spaces. A topologic space is defined by a set of points along with a collection of open sets that satisfy certain axioms. This framework allows mathematicians to explore continuity in a broader context, providing tools to address problems in various domains.Furthermore, the study of topologic spaces leads to intriguing questions about the nature of infinity and dimensionality. For instance, mathematicians explore spaces that are not limited to three dimensions, such as four-dimensional spaces or even higher. These explorations challenge our intuitive understanding of geometry and force us to rethink what we consider 'space.' The implications of such studies can be profound, influencing theories in physics, particularly in the understanding of the universe's structure.In conclusion, the term topologic encompasses a vast array of concepts and applications that extend far beyond its mathematical origins. From shaping our understanding of continuity and space to influencing technological advancements in data analysis and computer science, topologic ideas are integral to both theoretical and practical pursuits. As we continue to explore the intricacies of topologic properties, we uncover deeper connections between mathematics and the world around us, reinforcing the importance of this fascinating field of study.

在数学领域，特别是在拓扑学中，术语topologic指的是在物体的连续变形下保持不变的属性。拓扑学是研究空间的性质的一个分支，这些性质在连续变换下得以保留。令人着迷的是，像topologic这样的抽象概念可以在现实世界中应用。例如，当我们思考咖啡杯和甜甜圈的形状时，从拓扑的角度来看，它们被认为是等价的，因为一个可以在不切割或粘合的情况下转变为另一个。这种等价性是拓扑学中的一个基本思想，说明了topologic属性关注的是空间的性质，而不是具体的测量或形状。拓扑学不仅在纯数学中有意义；它还在计算机科学、生物学和物理学等多个领域找到了应用。例如，在计算机图形学中，topologic数据结构有助于建模和渲染复杂的形状。利用topologic原理的算法可以有效地管理和处理这些形状，确保变换保持原始对象的完整性。此外，在数据分析领域，topologic方法被用来研究数据的形状。持久同调等技术使研究人员能够分析数据集的基础结构，揭示出通过传统统计方法可能无法立即显现的见解。这种topologic分析的特征在机器学习和人工智能中变得越来越重要，因为理解数据的形状可以导致更好的模型和预测。topologic空间的概念在理解连续性和收敛性方面也起着至关重要的作用。在微积分中，我们经常处理极限和函数，但在拓扑学中，我们将这些思想扩展到更抽象的空间。topologic空间是由一组点以及满足某些公理的开集合的集合定义的。这一框架使数学家能够在更广泛的背景下探索连续性，为解决各个领域的问题提供工具。此外，topologic空间的研究引发了关于无限性和维度本质的有趣问题。例如，数学家探索不限于三维的空间，如四维空间甚至更高的空间。这些探索挑战了我们对几何的直观理解，并迫使我们重新思考我们所认为的“空间”。这些研究的影响可能是深远的，影响物理学中的理论，特别是在理解宇宙结构方面。总之，术语topologic涵盖了广泛的概念和应用，超越了其数学起源。从塑造我们对连续性和空间的理解到影响数据分析和计算机科学中的技术进步，topologic思想在理论和实践追求中都是不可或缺的。随着我们继续探索topologic属性的复杂性，我们发现数学与周围世界之间更深的联系，强化了这一迷人研究领域的重要性。