hypersurface

简明释义

英[/ˈhaɪpərˌsɜr.fɪs/]美[/ˈhaɪpərˌsɜr.fɪs/]

n. [数] 超曲面

英英释义

单词用法

同义词

反义词

例句

1.At last the complete hypersurface with constant mean curvature in the quasi constant curvature space is investigated, some characterization of totally umbilical hypersurfaces are obtained.

最后研究了常平均曲率完备超曲面，得到了这类超曲面全脐的一个结果。

2.At last the complete hypersurface with constant mean curvature in the quasi constant curvature space is investigated, some characterization of totally umbilical hypersurfaces are obtained.

最后研究了常平均曲率完备超曲面，得到了这类超曲面全脐的一个结果。

3.Finally, it gives an example that generating regular 3d spatial dataset based on the interpolation of hypersurface spline, it testifies the feasibility and veracity of this method.

最后以插值形成三维空间规则数据场为例，证明利用超曲面样条函数法进行三维空间插值的可行性和准确性。

4.Four reasonable geometries on the potential energy hypersurface of glycine and water system are considered with the global minimum being a cyclic double-hydrogen bonded structure.

在这个体系中，我们找到了甘氨酸和水作用的四种稳定构型，其中最稳定的构型是一个环状的双氢键结构。

5.B-spline inference rule was established and B-spline inference system was constructed, and then the final result of the system was calculated as a B-spline hypersurface.

建立B样条推理规则，构造实现了B样条推理系统，并求出该系统的最终结果为B样条超曲面。

6.The contributions in the first part are as follows:1) The existence of separating hypersurface and the geometric construction of separating hypersurface is studied.

研究了分类超曲面的存在性与几何构造法，并提出了基于几何超曲面的分类方法。

7.Using the principal curvature formula, we prove an existence theorem of Weingarten hypersurface.

并利用主曲率计算公式证明了W-超曲面的一个存在性定理。

8.It is essential to study the principal curvature of hypersurface in the hypersurface geometry.

在超曲面几何学中，对主曲率的研究是至关重要的。

9.The general event horizon formula of black hole is given from null hypersurface equation.

从零曲面方程出发，导出了黑洞视界面的普遍公式。

10.Study on hypersurface with constant mean curvature in sphere;

介绍了具有常数平均曲率的超曲面的稳定性概念。

11.In the study of algebraic geometry, a hypersurface 超曲面 is defined as a high-dimensional generalization of surfaces.

在代数几何的研究中，hypersurface 超曲面 被定义为表面的高维推广。

12.The concept of a hypersurface 超曲面 is crucial in the theory of relativity, where it can represent the boundary of spacetime.

在相对论理论中，hypersurface 超曲面 的概念是至关重要的，它可以表示时空的边界。

13.Researchers often use hypersurfaces 超曲面 to model complex systems in physics and engineering.

研究人员经常使用 hypersurfaces 超曲面 来建模物理和工程中的复杂系统。

14.In machine learning, the decision boundary can be viewed as a hypersurface 超曲面 in a high-dimensional space.

在机器学习中，决策边界可以被视为高维空间中的 hypersurface 超曲面。

15.A hypersurface 超曲面 can be defined by a polynomial equation in multiple variables.

一个 hypersurface 超曲面 可以通过多变量的多项式方程来定义。

作文

In the realm of mathematics and physics, the concept of a hypersurface (超曲面) plays a crucial role in understanding higher-dimensional spaces. A hypersurface can be defined as a high-dimensional analogue of a surface. While a surface exists in three-dimensional space, a hypersurface exists in four or more dimensions. This notion may seem abstract, but it has profound implications in various fields, including geometry, topology, and theoretical physics. To grasp the significance of a hypersurface, one must first understand its relation to lower-dimensional surfaces. For example, consider a two-dimensional surface like a sphere. The surface of the sphere is a two-dimensional manifold embedded in three-dimensional space. Similarly, a hypersurface can be viewed as a manifold that separates regions in a higher-dimensional space. In mathematical terms, a hypersurface can be described by an equation that relates its coordinates, often taking the form of a polynomial equation. One of the most fascinating aspects of hypersurfaces is their applications in the field of algebraic geometry. Here, mathematicians study the properties and behaviors of these entities to gain insights into complex geometric structures. For instance, the intersection of multiple hypersurfaces can reveal significant information about the solutions to systems of equations. This interplay between algebra and geometry is a central theme in modern mathematics. In physics, hypersurfaces are instrumental in the formulation of theories that describe the universe. For example, in general relativity, the fabric of spacetime is modeled using hypersurfaces. These hypersurfaces can represent moments in time, allowing physicists to analyze the dynamics of objects moving through spacetime. The curvature of these hypersurfaces is directly related to the gravitational effects experienced by matter, illustrating how deeply intertwined geometry and physics truly are. Moreover, hypersurfaces also find applications in computer science, particularly in machine learning and data analysis. In high-dimensional data spaces, hypersurfaces can act as decision boundaries that separate different classes of data points. Understanding the geometry of these hypersurfaces enables algorithms to make better predictions and classifications, showcasing the practical importance of this mathematical concept. In conclusion, the study of hypersurfaces (超曲面) transcends mere abstraction; it is a vital component of various scientific disciplines. From shaping our understanding of the universe to enhancing technological advancements, hypersurfaces serve as a bridge connecting mathematics, physics, and computer science. As we continue to explore the intricacies of higher-dimensional spaces, the relevance of hypersurfaces will undoubtedly grow, inspiring future generations of mathematicians and scientists to delve deeper into this captivating subject.

在数学和物理的领域中，hypersurface（超曲面）的概念在理解高维空间方面起着至关重要的作用。hypersurface可以定义为表面的高维类比。虽然表面存在于三维空间中，但hypersurface存在于四维或更多维度中。这个概念可能看起来抽象，但在几何、拓扑和理论物理等多个领域都有深远的影响。 为了理解hypersurface的重要性，首先必须了解它与低维表面之间的关系。例如，考虑一个二维表面，如球体。球体的表面是嵌入三维空间的二维流形。同样，hypersurface可以被视为一个流形，它将高维空间中的区域分开。在数学术语中，hypersurface可以通过一个方程来描述，该方程涉及其坐标，通常采用多项式方程的形式。 Hypersurfaces最迷人的方面之一是它们在代数几何领域的应用。在这里，数学家研究这些实体的属性和行为，以深入了解复杂的几何结构。例如，多条hypersurfaces的交集可以揭示关于方程组解的重要信息。这种代数与几何之间的相互作用是现代数学的中心主题。 在物理学中，hypersurfaces在描述宇宙的理论中起着重要作用。例如，在广义相对论中，时空的结构使用hypersurfaces进行建模。这些hypersurfaces可以表示时间中的时刻，使物理学家能够分析在时空中移动的物体的动态。这些hypersurfaces的曲率与物质所经历的引力效应直接相关，说明几何和物理是多么紧密相连。 此外，hypersurfaces还在计算机科学中找到了应用，特别是在机器学习和数据分析中。在高维数据空间中，hypersurfaces可以作为决策边界，分隔不同类别的数据点。理解这些hypersurfaces的几何特性使算法能够做出更好的预测和分类，展示了这个数学概念的实际重要性。 总之，hypersurfaces（超曲面）的研究超越了单纯的抽象；它是多个科学学科的重要组成部分。从塑造我们对宇宙的理解到促进技术进步，hypersurfaces作为连接数学、物理和计算机科学的桥梁。随着我们继续探索高维空间的复杂性，hypersurfaces的相关性无疑会增长，激励未来一代数学家和科学家深入研究这一迷人的主题。