simplicial

简明释义

英[ˌsɪmˈplɪʃəl]美[ˌsɪmˈplɪʃəl]

adj. 单纯的；单体的

英英释义

单词用法

同义词

反义词

例句

1.Let G be a graph and let V(G) be the vertex set of G. Define the neighborhood complex N(G) as the simplicial complex whose simplices are those subsets of V(G) which have a common neighbor.

一个图G的邻域复形是以G的顶点为顶点，以G的具有公共邻接顶点的顶点子集为单形的抽象复形。

2.The model is based on a collection of a divisional terrain data defined as simplicial complexes arranged into a partially ordered set by time and space.

模型把子区域地形几何数据定义为单纯复合形集，按地形变化时间顺序和空间关系组织成一个偏序集。

3.Let G be a graph and let V(G) be the vertex set of G. Define the neighborhood complex N(G) as the simplicial complex whose simplices are those subsets of V(G) which have a common neighbor.

一个图G的邻域复形是以G的顶点为顶点，以G的具有公共邻接顶点的顶点子集为单形的抽象复形。

4.An algorithm for topology reconstruction is promoted that takes as input an unorganized set of points with known density and carries out as output simplicial surfaces.

提出了一种基于曲面局平特性的，以散乱点集及其密度指标作为输入，以三角形分片线性曲面作为输出的拓扑重建算法。

5.This paper presents for the first time a simplicial branch and bound algorithm for globally solving a class of nonlinear sum of ratios problem.

针对一类非线性比式和问题首次提出一种求其全局最优解的单纯形分枝定界算法。

6.The concept of simplicial 单纯的 complexes is fundamental in algebraic topology.

在代数拓扑中，simplicial 单纯的 复形的概念是基础。

7.The simplicial 单纯的 structure of the data allows for easier computation.

数据的 simplicial 单纯的 结构使得计算更为简单。

8.In topology, a simplicial 单纯的 complex is a set of points connected by simplices.

在拓扑学中，simplicial 单纯的 复形是一组由单纯形连接的点。

9.Researchers used a simplicial 单纯的 model to analyze the network's connectivity.

研究人员使用了一个 simplicial 单纯的 模型来分析网络的连通性。

10.A simplicial 单纯的 set can be visualized as a collection of vertices, edges, and faces.

一个 simplicial 单纯的 集合可以被可视化为顶点、边和面的集合。

作文

In the realm of mathematics, particularly in topology and geometry, the concept of a simplicial complex plays a crucial role. A simplicial complex is a set formed by points, line segments, triangles, and their higher-dimensional counterparts, which are called simplices. These structures provide a framework for understanding more complex shapes and spaces. The study of simplicial complexes allows mathematicians to explore properties of spaces that are not immediately apparent when looking at them in traditional Euclidean terms.For example, consider a triangle. It consists of three vertices connected by three edges, forming a two-dimensional shape. When we extend this idea into three dimensions, we can create a tetrahedron, which is a three-dimensional simplicial complex made up of four triangular faces. Each face of the tetrahedron is itself a simplicial shape, and together they define the volume of the tetrahedron. This ability to build complex shapes from simple building blocks is one of the key features of simplicial complexes.The beauty of simplicial complexes lies in their versatility. They can be used to model various phenomena in different fields, including physics, computer science, and biology. In computer graphics, for instance, simplicial complexes are used to represent 3D models. By breaking down complex surfaces into simpler triangular facets, rendering becomes more efficient and manageable. This simplification process is vital for real-time rendering applications, such as video games and simulations.Moreover, simplicial complexes are essential in the field of algebraic topology, where they help in studying topological spaces through algebraic methods. Researchers utilize tools such as homology and cohomology theories to derive important invariants of simplicial complexes, which provide insights into the structure and characteristics of the underlying spaces. For example, the Euler characteristic, a fundamental property of a simplicial complex, can reveal whether a space is connected or how many holes it contains.In addition to their mathematical significance, simplicial complexes also have practical applications. In data analysis, for instance, persistent homology, a method derived from simplicial topology, is used to study the shape of data. By constructing simplicial complexes from point cloud data, analysts can extract meaningful features and patterns that may not be evident in the raw data. This approach has been particularly useful in fields like machine learning and image recognition, where understanding the underlying structure of data is crucial for improving algorithms.In conclusion, the term simplicial encapsulates a fundamental concept in mathematics that extends beyond mere theoretical interest. Whether in pure mathematics or applied sciences, simplicial complexes serve as powerful tools for modeling, analyzing, and understanding complex systems. Their ability to simplify the intricate nature of shapes and spaces makes them indispensable in both academic research and practical applications. As we continue to explore the depths of mathematics and its connections to other disciplines, the importance of simplicial structures will undoubtedly remain prominent, inspiring future generations of mathematicians and scientists to delve deeper into the fascinating world of topology and geometry.

在数学的领域，特别是在拓扑学和几何学中，simplicial复合体的概念发挥着至关重要的作用。simplicial复合体是由点、线段、三角形及其更高维的对应物（称为单纯形）构成的一组。这些结构提供了一个框架，用于理解更复杂的形状和空间。对simplicial复合体的研究使数学家能够探索在传统欧几里得视角下不易显现的空间特性。例如，考虑一个三角形。它由三个顶点和三条边连接而成，形成一个二维形状。当我们将这个思想扩展到三维时，可以创建一个四面体，它是一个由四个三角形面构成的三维simplicial复合体。四面体的每个面本身都是一个simplicial形状，所有这些面共同定义了四面体的体积。这种通过简单构件构建复杂形状的能力是simplicial复合体的关键特征之一。simplicial复合体的美在于它们的多功能性。它们可以用于建模不同领域中的各种现象，包括物理学、计算机科学和生物学。在计算机图形学中，例如，simplicial复合体用于表示3D模型。通过将复杂表面分解为更简单的三角形面片，渲染变得更加高效和可管理。这种简化过程对于实时渲染应用程序（如视频游戏和模拟）至关重要。此外，simplicial复合体在代数拓扑学领域也至关重要，它们通过代数方法帮助研究拓扑空间。研究人员利用同调和上同调理论等工具推导出simplicial复合体的重要不变量，这些不变量提供了对基础空间的结构和特性的洞察。例如，欧拉示性数，一个simplicial复合体的基本属性，可以揭示一个空间是否连通或包含多少个孔。除了其数学意义外，simplicial复合体还有实际应用。在数据分析中，例如，持久同调——一种源自simplicial拓扑的方法，用于研究数据的形状。通过从点云数据构建simplicial复合体，分析人员可以提取出可能在原始数据中不明显的有意义特征和模式。这种方法在机器学习和图像识别等领域尤为有效，在这些领域中，理解数据的基础结构对于改进算法至关重要。总之，simplicial这个术语概括了一个在数学中基本的概念，它超越了纯理论的兴趣。无论是在纯数学还是应用科学中，simplicial复合体都作为强大的工具，用于建模、分析和理解复杂系统。它们简化形状和空间复杂性质的能力使它们在学术研究和实际应用中不可或缺。随着我们继续探索数学的深度及其与其他学科的联系，simplicial结构的重要性无疑将保持突出，激励未来一代数学家和科学家深入探讨拓扑学和几何学的迷人世界。