meromorphic

简明释义

英[/ˌmɛrəˈmɔrfɪk/]美[/ˌmɛrəˈmɔrfɪk/]

adj. [数] 亚纯的

英英释义

单词用法

同义词

反义词

例句

1.Entire function, Meromorphic function, Exceptional set, Deficiency, Differential polynomial.

整函数，亚纯函数，例外集，亏量，进分多项式。

2.Concerning normal families of meromorphic functions, normal families with sharing values has mainly discussed. And some results are obtained which generalize and improve the present result.

在正规族方面，主要探讨了分担一函数的亚纯函数族的正规性，得到了相应的正规定则，推广了当前的结果。

3.Using the idea of weighted sharing, deal with the uniqueness problems on meromorphic functions that sharing three sets.

采用权分担值的思想讨论了亚纯函数关于微分多项式分担值的唯一性问题。

4.We will give reduce demonstration for a lemma in four values theorem of meromorphic function.

给出了亚纯函数四值定理中一个引理的简化证明。

5.In this paper Argument principle is extended to the case in which meromorphic function has limited number of zeros and poles at the boundary of reg - ion.

本文将复变函数中的幅角原理推广到亚纯函数在区域的边界上有零点和极点的情况。

6.The dynamics of composite transcendental meromorphic functions is investigated in this paper, and some known results was extended to this case.

讨论了两个超越亚纯函数复合的动力学性质，推广了若干已知结果。

7.Abstract Some theorems on systems of meromophic functions are proved. As an application of the theorems, a unicity theorem of meromorphic functions is proved. Some previous results given by F.

摘要证明了关于亚纯函数组的几个定理，推广和改进了笔者先前的几个结果。应用这些定理证明了一个亚纯函数唯一性定理，它是F。

8.The concept of meromorphic 有理的 functions is crucial in the study of algebraic curves.

在代数曲线的研究中，meromorphic 有理的函数的概念至关重要。

9.A function is called meromorphic 有理的 if it is holomorphic except for isolated poles.

如果一个函数除了孤立的极点外都是全纯的，那么它被称为meromorphic 有理的。

10.Many physical models use meromorphic 有理的 functions to describe wave behavior in quantum mechanics.

许多物理模型使用meromorphic 有理的函数来描述量子力学中的波动行为。

11.The Riemann zeta function is an example of a meromorphic 有理的 function with a well-known pole at s = 1.

黎曼ζ函数是一个著名的meromorphic 有理的函数，其在s = 1处有一个众所周知的极点。

12.In complex analysis, a meromorphic 有理的 function can be represented as the ratio of two holomorphic functions.

在复分析中，一个meromorphic 有理的函数可以表示为两个全纯函数的比率。

作文

In the realm of complex analysis, the concept of meromorphic functions plays a crucial role in understanding the behavior of complex variables. A function is considered meromorphic if it is holomorphic (complex differentiable) on an open set except for a discrete set of isolated points, where it can have poles. This characteristic makes meromorphic functions particularly interesting, as they can be seen as a generalization of rational functions, which are defined as the ratio of two polynomials. The study of meromorphic functions not only enriches our knowledge of complex analysis but also has profound implications in various fields such as number theory, algebraic geometry, and mathematical physics.To illustrate the significance of meromorphic functions, consider the Riemann zeta function, which is a classic example of a meromorphic function. The Riemann zeta function is defined for complex numbers and has a deep connection to the distribution of prime numbers. It is holomorphic in the entire complex plane except for a simple pole at s = 1. The zeros of the Riemann zeta function, especially those that lie on the critical line, are central to the famous Riemann Hypothesis, one of the most important unsolved problems in mathematics. This highlights how meromorphic functions can bridge different areas of mathematics, illustrating their importance beyond mere definitions.Moreover, the concept of meromorphic functions is not confined to theoretical mathematics; it also finds applications in physics, particularly in the study of quantum field theory and string theory. In these contexts, meromorphic functions help describe the behavior of certain physical systems, providing insights into the nature of singularities and the analytic structure of physical theories. For instance, in string theory, the scattering amplitudes can often be expressed in terms of meromorphic functions, revealing the underlying symmetries and interactions of particles.Understanding meromorphic functions requires a solid foundation in complex analysis, including knowledge of contour integration, residues, and the argument principle. Students and researchers must grasp these concepts to appreciate the full depth of meromorphic functions and their applications. As they delve deeper into this subject, they will discover a rich tapestry of connections between meromorphic functions and other mathematical constructs, reinforcing the idea that mathematics is an interconnected discipline.In conclusion, the study of meromorphic functions offers a fascinating glimpse into the intricate world of complex analysis and its applications. Whether it is through exploring the properties of the Riemann zeta function or applying these concepts in theoretical physics, meromorphic functions serve as a vital tool in advancing our understanding of both mathematics and the natural world. As we continue to explore and uncover the mysteries of meromorphic functions, we not only deepen our mathematical knowledge but also expand the horizons of science and its many disciplines.

在复分析的领域中，meromorphic 函数的概念在理解复变量的行为方面发挥着至关重要的作用。如果一个函数在一个开集上是全纯的（复可微），但在某些孤立点处可以有极点，那么这个函数就被认为是 meromorphic 的。这一特性使得 meromorphic 函数特别有趣，因为它们可以被视为有理函数的推广，有理函数被定义为两个多项式的比率。对 meromorphic 函数的研究不仅丰富了我们对复分析的理解，而且在数论、代数几何和数学物理等多个领域都有深远的影响。为了说明 meromorphic 函数的重要性，可以考虑黎曼ζ函数，这是一个经典的 meromorphic 函数示例。黎曼ζ函数是为复数定义的，与素数的分布有着深刻的联系。它在整个复平面上是全纯的，除了在 s = 1 处有一个简单极点。黎曼ζ函数的零点，尤其是那些位于临界线上的零点，是著名的黎曼假设的核心，这个问题是数学中最重要的未解问题之一。这突显了 meromorphic 函数如何桥接不同的数学领域，展示了它们超越单纯定义的重要性。此外，meromorphic 函数的概念并不仅限于理论数学；它还在物理学中找到了应用，特别是在量子场论和弦理论的研究中。在这些背景下，meromorphic 函数帮助描述某些物理系统的行为，为奇点的性质和物理理论的解析结构提供了洞见。例如，在弦理论中，散射振幅通常可以用 meromorphic 函数来表示，揭示了粒子之间的基本对称性和相互作用。理解 meromorphic 函数需要扎实的复分析基础，包括对轮廓积分、留数和论证原理的知识。学生和研究人员必须掌握这些概念，以欣赏 meromorphic 函数及其应用的全部深度。当他们深入研究这一主题时，将发现 meromorphic 函数与其他数学结构之间的丰富联系，强化了数学是一个相互关联的学科这一观点。总之，meromorphic 函数的研究为我们提供了一个迷人的视角，深入探索复分析及其应用。无论是通过探索黎曼ζ函数的性质，还是在理论物理中应用这些概念，meromorphic 函数作为推进我们对数学和自然世界理解的重要工具。随着我们继续探索和揭示 meromorphic 函数的奥秘，我们不仅加深了数学知识，也拓展了科学及其许多学科的视野。