analyticity

简明释义

英[ænəlɪˈtɪsəti]美[ænəlɪˈtɪsɪti]

n. 分析性，[数] 解析性

英英释义

单词用法

同义词

反义词

例句

1.The paper introduces integrated semi-groups and analytic families of integrated semi-groups, the relations among the three natural ways to understand "analyticity" of the family are clarified.

介绍了积分半群及积分半群的解析族，阐述了积分半群的无穷小生成元解析、积分半群解析和预解式解析三者之间的关系。

2.The time analyticity of solution is proved.

证明了该方程解的时间解析性。

3.Magnetohydrodynamics equations with periodic boundary conditions are considered in this note. The time analyticity of the solutions for the equations is proved and the backward uniqueness is obtained.

考查了周期边界条件下的磁流体方程，证明了它的解关于时间是解析的，由此得到了磁流体方程的解的向后惟一性。

4.This paper studies the causality and analyticity characteristics in harmonic oscillator, and from which drives Hilbert transform pair.

本文对谐振子的因果律和解析性质进行了研究，并由此推导出谐振子的希尔伯特变换对。

5.In this article we study the analyticity dependence on the parameter of solutions to the equation on pseudoconvex domains.

本文作者研究拟凸域上的-方程解关于参数的解析依赖性。

6.The uniqueness theorem of generalized quasi-analyticity of the infinitely differentiable functions in some closed angular domain is extehded to the functions of several complex variables.

摘要把无穷可微函数类在角形闭区域上的唯一性结果推广到了多维情形。

7.Besides this, discussion about simplicity and analyticity of Jost function is considered which is connected with scatterering.

此外，还讨论与散射有关的约斯特函数的全纯性和解析性；

8.Magnetohydrodynamics equations with periodic boundary conditions are considered in this note. The time analyticity of the solutions for the equations is proved and the backward uniqueness is obtained.

考查了周期边界条件下的磁流体方程，证明了它的解关于时间是解析的，由此得到了磁流体方程的解的向后惟一性。

9.In this paper, we extend the theorem on generalized quasi-analyticity of the infinitely differentiable functions in the closed angular domain to the functions of several complex variables.

摘要本文将关于角形闭区域中无穷可微函数类的广义准解析性的结果推广到了多维情形。

10.The analyticity of a function implies that it can be represented as a power series around any point in its domain.

函数的analyticity（解析性）意味着它可以在其定义域中的任何点附近表示为幂级数。

11.In physics, the analyticity of a wave function ensures that it behaves predictably under certain conditions.

在物理学中，波函数的analyticity（解析性）确保它在某些条件下表现出可预测的行为。

12.Mathematicians often test analyticity by checking the Cauchy-Riemann equations for a given function.

数学家通常通过检查给定函数的柯西-黎曼方程来测试analyticity（解析性）。

13.The concept of analyticity is crucial in complex analysis, as it defines functions that are differentiable in a neighborhood of every point in their domain.

概念analyticity（解析性）在复分析中至关重要，因为它定义了在其定义域每个点的邻域内可微的函数。

14.Understanding the analyticity of solutions to differential equations can lead to better predictions in engineering applications.

理解微分方程解的analyticity（解析性）可以在工程应用中带来更好的预测。

作文

In the realm of mathematics and logic, the concept of analyticity plays a crucial role in understanding various functions and their properties. Analyticity refers to the quality of a function being expressible as a power series in some neighborhood of every point in its domain. This characteristic is fundamental in complex analysis, where functions that are analytic exhibit remarkable behavior, such as being infinitely differentiable and equal to their Taylor series within their radius of convergence.To illustrate the importance of analyticity, consider the function f(z) = e^z, which is defined for all complex numbers z. This function is not only analytic everywhere in the complex plane, but it also has the remarkable property that its Taylor series converges to the function itself at every point. The ability to represent a function as a power series allows mathematicians to analyze and manipulate these functions more easily, facilitating deeper insights into their behavior and applications.The implications of analyticity extend beyond pure mathematics into fields such as physics and engineering. For instance, in quantum mechanics, wave functions must be analytic to ensure that physical observables can be derived from them consistently. In signal processing, analyticity is critical for the analysis of signals and systems, particularly when it comes to filtering and transforming data.Moreover, the study of analyticity leads to significant results like the Cauchy-Riemann equations, which provide necessary and sufficient conditions for a function to be analytic in a region. These equations connect the real and imaginary parts of complex functions, revealing the intricate relationship between geometry and analysis. Understanding this relationship is essential for mathematicians and scientists alike, as it opens up pathways to explore more complex phenomena.In conclusion, the notion of analyticity is not merely an abstract concept confined to the pages of textbooks; it is a vital aspect of mathematics that has far-reaching consequences across various disciplines. By grasping the principles of analyticity, one gains powerful tools to tackle problems in both theoretical and applied contexts. As we delve deeper into the world of analyticity, we uncover the beauty of mathematical structures and their profound connections to the natural world. Ultimately, analyticity enriches our understanding of functions and their behaviors, enabling us to apply these concepts in innovative and practical ways. Thus, mastering the idea of analyticity is essential for anyone aspiring to excel in mathematics and its applications.

在数学和逻辑的领域中，analyticity 的概念在理解各种函数及其性质方面扮演着至关重要的角色。Analyticity 指的是一个函数在其定义域内的每个点附近可以用幂级数表示的特性。这一特征在复分析中是基础，因为具有 analytic 性质的函数表现出显著的行为，例如在其收敛半径内是无限可微的，并且等于其泰勒级数。为了说明 analyticity 的重要性，考虑函数 f(z) = e^z，该函数在所有复数 z 上都有定义。这个函数不仅在复平面上处处 analytic，而且还有一个显著的特性，即它的泰勒级数在每个点上都收敛于该函数本身。能够将函数表示为幂级数使得数学家能够更轻松地分析和操作这些函数，从而促进对其行为和应用的更深入理解。Analyticity 的影响超越了纯数学，延伸到物理和工程等领域。例如，在量子力学中，波函数必须是 analytic 的，以确保可以一致地从中推导出物理可观测量。在信号处理领域，analyticity 对于信号和系统的分析至关重要，特别是在过滤和转换数据时。此外，analyticity 的研究导致了重要的结果，如柯西-黎曼方程，这些方程提供了函数在某一区域内为 analytic 的必要和充分条件。这些方程连接了复函数的实部和虚部，揭示了几何与分析之间的复杂关系。理解这种关系对于数学家和科学家来说至关重要，因为它开启了探索更复杂现象的路径。总之，analyticity 的概念不仅仅是局限于教科书页面的抽象概念；它是数学的一个重要方面，对各个学科有深远的影响。通过掌握 analyticity 的原理，人们获得了解决理论和应用问题的强大工具。当我们深入探讨 analyticity 的世界时，我们揭示了数学结构的美丽以及它们与自然界的深刻联系。最终，analyticity 丰富了我们对函数及其行为的理解，使我们能够以创新和实用的方式应用这些概念。因此，掌握 analyticity 的思想对于任何希望在数学及其应用中脱颖而出的人来说都是必不可少的。