homological

简明释义

英[hɒməˈlɒdʒɪk(ə)l]美[ˌhoʊmoʊˈlɑːdʒɪkəl]

adj. 相应的；一致的；同源的（等于 homologic 或者 homologous）

英英释义

单词用法

同义词

反义词

例句

1.Hyperspectral remote sensing is an art, which integrates the spectrum representing to the radiant attributes of ground object with the homological images standing for spatial and geometric relations.

高光谱遥感是一门将反映地物辐射属性的光谱与反映地物空间和几何关系的图像结合在一起的技术。

2.Hyperspectral remote sensing is an art, which integrates the spectrum representing to the radiant attributes of ground object with the homological images standing for spatial and geometric relations.

高光谱遥感是一门将反映地物辐射属性的光谱与反映地物空间和几何关系的图像结合在一起的技术。

3.Abstract In this paper, we investigate the difference between PS-ring and nonsingular ring, and obtain a formula of the homological dimensions.

本文刻划了PS-环与非奇异环的差距，给出了一个计算同调维数的公式。

4.REP-PCR is a valid and rapid genotyping method for homological analysis and tracking the source of infection during epidemic outbreak.

REP-PCR是一种有效快捷的基因分型法，可为细菌同源性分析以及爆发流行时追根溯源建立简便可行的方法。

5.Conclusions There exists a close relationship between No. 3 vertebral transverse process syndrome and homological nerves refl...

结论第三腰椎横突综合征的发病过程与其同根神经反射现象存在着密切关系。

6.Prediction of lowly homological protein secondary structure is still a difficult problem up to now.

低同源蛋白质的二级结构预测至今仍然是一个困难的问题。

7.Conclusions OMP28 is highly homological and characterized by stable antigen.

结论布鲁杆菌omp28基因高度保守，具稳定的抗原特征。

8.The structure of R with small homological dimension is discussed.

讨论论了R在小同调维数时的结构。

9.The concept of homological 同调的 algebra is fundamental in modern mathematics.

同调代数的概念在现代数学中是基础性的。

10.In topology, homological 同调的 methods are used to study the properties of spaces.

在拓扑学中，使用同调方法来研究空间的性质。

11.The homological 同调的 dimension of a module can provide insights into its structure.

一个模的同调维数可以提供对其结构的洞察。

12.Researchers often utilize homological 同调的 techniques to solve complex problems in algebraic geometry.

研究人员常常利用同调技术来解决代数几何中的复杂问题。

13.The homological 同调的 approach allows mathematicians to classify different types of objects.

同调的方法使数学家能够对不同类型的对象进行分类。

作文

In the realm of mathematics, particularly in algebraic topology and category theory, the term homological is frequently encountered. It pertains to the study of homology, which is a fundamental concept used to understand the structure of topological spaces. Homology provides a way to associate a sequence of algebraic objects, such as groups or modules, with a topological space, thereby enabling mathematicians to extract significant information about the space's shape and features. The study of homological algebra, for instance, focuses on the relationships between these algebraic structures and their applications in various fields, including geometry and physics. One of the primary motivations behind the development of homological methods is the desire to classify and analyze different types of mathematical objects. For example, through the use of homological techniques, mathematicians can discern whether two topological spaces are equivalent by examining their respective homology groups. These groups capture essential characteristics, such as the number of holes of different dimensions within a space. By comparing these groups, one can conclude whether the spaces share similar properties, even if they appear different at first glance. Moreover, homological algebra has profound implications in other areas of mathematics and science. In representation theory, for instance, homological methods are employed to study the representations of groups and algebras. This intersection of algebra and geometry allows researchers to gain insights into the symmetries and invariants of mathematical structures. Furthermore, homological techniques are also utilized in theoretical physics, particularly in string theory and quantum field theory, where the underlying mathematical frameworks often rely on complex topological concepts. Another significant aspect of homological theory is its application in data analysis and machine learning. Researchers have started to employ homological methods to analyze high-dimensional data sets, leveraging the principles of topology to uncover patterns and relationships that may not be immediately apparent through traditional statistical techniques. For example, persistent homology, a method derived from homological algebra, allows analysts to study the changing topology of data as parameters vary, providing a robust framework for understanding the intrinsic geometric structure of the data. In conclusion, the term homological encapsulates a rich and intricate field of study within mathematics and its applications. From its roots in algebraic topology to its diverse applications in various scientific domains, homological concepts offer powerful tools for understanding and analyzing complex structures. As research continues to evolve, the significance of homological methods will undoubtedly expand, revealing new connections and insights across disciplines. Therefore, grasping the essence of homological theory is not only crucial for mathematicians but also for anyone interested in the underlying patterns that govern our understanding of the world around us.

在数学领域，特别是在代数拓扑和范畴理论中，术语homological经常被提及。它涉及到同调的研究，这是一个用于理解拓扑空间结构的基本概念。同调提供了一种将一系列代数对象（如群或模）与拓扑空间关联起来的方法，从而使数学家能够提取有关空间形状和特征的重要信息。例如，同调代数的研究集中于这些代数结构之间的关系及其在几何和物理等各个领域的应用。 发展homological方法的主要动机之一是希望对不同类型的数学对象进行分类和分析。例如，通过使用homological技术，数学家可以通过检查各自的同调群来判断两个拓扑空间是否相等。这些群捕捉了空间中不同维度孔的数量等基本特征。通过比较这些群，可以得出空间是否具有相似属性的结论，即使它们在第一眼看起来不同。 此外，homological代数在其他数学和科学领域也有深远的影响。例如，在表示理论中，研究人员利用homological方法来研究群和代数的表示。这种代数与几何的交叉使研究人员能够深入了解数学结构的对称性和不变量。此外，homological技术还被应用于理论物理学，特别是在弦理论和量子场论中，这些基础数学框架通常依赖于复杂的拓扑概念。 homological理论的另一个重要方面是它在数据分析和机器学习中的应用。研究人员开始采用homological方法来分析高维数据集，利用拓扑原理揭示传统统计技术可能无法立即显现的模式和关系。例如，持久同调，一种源自homological代数的方法，允许分析师研究数据随参数变化而变化的拓扑，为理解数据的内在几何结构提供了一个强大的框架。 总之，术语homological概括了数学及其应用中的一个丰富而复杂的研究领域。从其在代数拓扑中的根源到其在各个科学领域的多样化应用，homological概念为理解和分析复杂结构提供了强有力的工具。随着研究的不断发展，homological方法的重要性无疑会扩大，揭示跨学科的新联系和见解。因此，掌握homological理论的本质对于数学家以及任何对支配我们对周围世界理解的基本模式感兴趣的人来说都是至关重要的。