manifolds

简明释义

英[ˈmænɪfəʊldz]美[ˈmænəˌfoʊldz]

n. 集合管；阀组（manifold 的复数形式）

v. 复写；繁殖（manifold 的单三形式）

英英释义

单词用法

同义词

反义词

例句

1.The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented.

在黎曼流形上分别给出了伪不变凸函数和弱向量似变分不等式的概念。

2.The HPM Series is a group of CMOS, microprocessor-based control units designed to monitor and control gas delivery manifolds.

HPM系列是一组CMOS，采用微型处理器控制装置，设计用于检测和控制天然气运输通道。

3.In the steady flow in manifolds, there exist a number of stable flow states in the branches for the same main duct flow rate.

在稳定的多分支管道流动中，对于相同的主管道流量，各分支管道中可以有不同的稳定流动状况与之对应。

4.This paper proposed an accurate calculation discrete model for the flow distribution in manifolds for heat exchangers.

本文通过实验研究和理论分析，提出准确计算换热器集箱管组中流量分配的离散模型。

5.The condition for the reduction of a three time scale power system model is studied by using the concepts of fast and slow manifolds.

利用慢流形和快流形的概念，研究了电力系统三时间尺度动态模型降阶的条件。

6.Here are photographs of both the forward (bottom) and aft (top) deck manifolds.

这里的照片都向前(底部)和尾部(顶部)甲板流形。

7.The engineer designed a new system with multiple manifolds to improve fluid distribution.

工程师设计了一个新的系统，采用多个歧管以改善流体分配。

8.In automotive engineering, air intake manifolds play a crucial role in engine performance.

在汽车工程中，空气进气歧管在发动机性能中起着至关重要的作用。

9.The hydraulic system uses manifolds to connect various components efficiently.

液压系统使用歧管高效连接各种组件。

10.Different types of manifolds are used in plumbing to manage water flow.

在管道中使用不同类型的歧管来管理水流。

11.The laboratory setup included several manifolds for gas distribution during experiments.

实验室设置包括几个用于实验期间气体分配的歧管。

作文

In the realm of mathematics and physics, the concept of manifolds (流形) plays a crucial role in understanding complex structures. A manifold is essentially a topological space that resembles Euclidean space on small scales. This means that locally, around any point, a manifold can be treated as if it were flat, even though it may have a curved or complicated global structure. For example, the surface of a sphere is a two-dimensional manifold, as it can be described by two coordinates, but it does not resemble a flat plane globally. Understanding manifolds is vital in various fields, including physics, where they are used to describe the fabric of spacetime in general relativity. In this theory, the universe is modeled as a four-dimensional manifold, integrating both space and time into a single continuum. The curvature of this manifold is influenced by mass and energy, leading to the gravitational effects we observe. This profound connection between geometry and physics illustrates how manifolds serve as a bridge between abstract mathematical concepts and tangible physical phenomena. In addition to physics, manifolds are also significant in the field of computer graphics and data analysis. In machine learning, for instance, high-dimensional data can often be represented more efficiently on a lower-dimensional manifold. This technique allows for better visualization and understanding of complex datasets, enabling algorithms to perform more effectively. By recognizing the underlying manifold structure of the data, researchers can develop models that capture essential patterns without being overwhelmed by noise. Moreover, the study of manifolds has led to the development of numerous mathematical tools and theories. Differential geometry, for example, focuses on the properties and applications of manifolds equipped with additional structures, such as metrics that allow for the measurement of distances and angles. These tools have profound implications in various scientific fields, from robotics, where they help in motion planning, to economics, where they assist in understanding complex systems through optimization techniques. As we delve deeper into the world of manifolds, it becomes evident that they are not just abstract constructs, but rather foundational elements that enhance our understanding of the universe. They provide a framework for exploring the relationships between different dimensions and spaces, allowing us to model phenomena that would otherwise be too complex to comprehend. The versatility of manifolds underscores their importance across disciplines, making them a vital area of study for anyone interested in the mathematical sciences. In conclusion, manifolds (流形) are an essential concept that transcends the boundaries of pure mathematics, finding applications in physics, computer science, and beyond. Their ability to represent complex structures in a manageable way makes them indispensable tools for researchers and practitioners alike. As we continue to explore the intricacies of manifolds, we unlock new possibilities for understanding the world around us, paving the way for future innovations and discoveries.

在数学和物理的领域中，manifolds（流形）的概念在理解复杂结构方面发挥着至关重要的作用。流形本质上是一个拓扑空间，在小尺度上类似于欧几里得空间。这意味着在任何点附近，流形可以被视为平坦的，尽管它可能具有弯曲或复杂的全局结构。例如，球体的表面是一个二维的流形，因为它可以用两个坐标来描述，但在全局上并不类似于平面。 理解流形在各个领域中都是至关重要的，包括物理学，在这里它们用于描述广义相对论中的时空结构。在这个理论中，宇宙被建模为一个四维的流形，将空间和时间整合为一个单一的连续体。这个流形的曲率受到质量和能量的影响，从而导致我们观察到的引力效应。这种几何与物理之间的深刻联系说明了流形如何作为抽象数学概念与具体物理现象之间的桥梁。 除了物理学，流形在计算机图形学和数据分析领域也很重要。在机器学习中，例如，高维数据通常可以更有效地表示在低维流形上。这种技术使得复杂数据集的可视化和理解变得更加容易，使算法能够更有效地执行。通过识别数据的潜在流形结构，研究人员可以开发出捕捉重要模式的模型，而不被噪声所淹没。 此外，对流形的研究还催生了许多数学工具和理论的发展。例如，微分几何专注于具有附加结构的流形的性质和应用，例如允许测量距离和角度的度量。这些工具在各个科学领域都有深远的影响，从机器人技术中的运动规划到经济学中通过优化技术理解复杂系统。 当我们深入探讨流形的世界时，显而易见的是，它们不仅仅是抽象构造，而是增强我们对宇宙理解的基础元素。它们提供了探索不同维度和空间之间关系的框架，使我们能够建模那些否则过于复杂而无法理解的现象。流形的多功能性强调了它们在各个学科中的重要性，使其成为任何对数学科学感兴趣的人必不可少的研究领域。 总之，manifolds（流形）是一个基本概念，超越了纯数学的界限，在物理学、计算机科学等领域找到了应用。它们以可管理的方式表示复杂结构的能力使其成为研究人员和从业者不可或缺的工具。随着我们继续探索流形的复杂性，我们开启了理解周围世界的新可能性，为未来的创新和发现铺平了道路。