automorphic

简明释义

英[ˌɔːtəˈmɔːrfɪk]美[ˌɔːtəˈmɔːrfɪk]

adj. [岩] 自形的；自同构的；[数] 自守的

英英释义

单词用法

同义词

反义词

例句

1.Under certain condition, these systems are proved by fixed point method and mean value method to have almost-automorphic solution.

在某些条件下，利用不动点方法和平均值法证明了这类方程系具有概自守解。

2.The application of group theory in analysis is the study of automorphic function.

其在分析中的应用就是自守函数理论的研究。

3.In this thesis, we discuss mainly the existence of (pseudo) almost periodic solutions and (asymptotically) almost automorphic solutions for some nonlinear equations.

本文主要讨论几类非线性方程的(拟)概周期解和(渐近)概自守解的存在性。

4.Although automorphic or partial automorphic quartz cementation losses some intergranular pores in late diagenesis, the reservoir with relatively high porosity still can be formed.

虽然晚成岩期自形或半自形石英胶结损失了部分粒间孔隙，但仍能形成孔隙度相对较高的储层。

5.The theory of automorphic function is the result of the intersection of geometry, algebra, complex analysis and differential equation, which manifest the unity of mathematics.

这一理论是几何学、代数学、复分析、微分方程解析理论交叉的产物，体现了数学的统一性。

6.Chapter 2 is preliminaries, mainly including some definitions and basic properties on strongly continuous semigroups, integrated semigroups and pseudo al-most automorphic functions.

主要包括强连续半群、积分半群与拟概自守函数的定义与基本性质。

7.Chapter 2 is preliminaries, mainly including some definitions and basic properties on strongly continuous semigroups, integrated semigroups and pseudo al-most automorphic functions.

主要包括强连续半群、积分半群与拟概自守函数的定义与基本性质。

8.The earliest automorphic functions to be studied were the elliptic modular functions.

研究得最早的自导函数是椭圆模函数。

9.The theory of automorphic function is an intersection of many subjects, which manifests the unity of mathematics.

自守函数理论是多个数学分支交叉的产物，体现了数学的统一性。

10.Many students find automorphic numbers fascinating due to their unique properties.

许多学生发现自形数字由于其独特的性质而令人着迷。

11.In mathematics, a number is called automorphic if its square ends with the same digits as the number itself.

在数学中，如果一个数字的平方以与该数字相同的数字结尾，则称该数字为自形。

12.The smallest automorphic number is 5, since 5² = 25 ends with 5.

最小的自形数字是5，因为5² = 25以5结尾。

13.The concept of automorphic forms is important in number theory.

在数论中，自形形式的概念是非常重要的。

14.An automorphic number can be found by squaring it and checking the last digits.

通过将一个数字平方并检查最后的数字，可以找到一个自形数字。

作文

In the realm of mathematics, the term automorphic refers to certain types of functions or numbers that exhibit a fascinating property: they remain invariant under specific transformations. This concept is particularly intriguing when we consider automorphic numbers, which are integers whose square ends with the same digits as the number itself. For example, the number 5 is automorphic because when you square it, you get 25, and the last digit is indeed 5. Similarly, the number 76 is also automorphic because 76 squared is 5776, which ends with 76. The beauty of automorphic numbers lies not just in their mathematical properties but also in their rarity. While there are infinitely many integers, automorphic numbers are relatively few and far between. This rarity adds an element of excitement for mathematicians and enthusiasts alike, who often find joy in discovering new examples of these unique numbers. The study of automorphic numbers can lead to a deeper understanding of number theory and its various branches, including modular arithmetic and algebraic structures.Furthermore, the concept of automorphic can be expanded beyond mere numbers to include functions and other mathematical entities. For instance, in group theory, an automorphic function may refer to a function that preserves the structure of a group under a transformation. This idea is essential in many areas of mathematics, including cryptography, where the properties of automorphic functions can be utilized to create secure communication protocols.In addition to its mathematical significance, the notion of automorphic can also be metaphorically applied to various aspects of life. For example, one might consider individuals who display automorphic traits as those who remain true to themselves despite the transformations they undergo throughout their lives. Just as an automorphic number retains its identity through squaring, a person may maintain their core values and beliefs even when faced with challenges and changes.In literature, the theme of automorphic identities can be explored through characters who undergo significant transformations yet retain their essence. This duality can provide rich material for storytelling, allowing authors to delve into the complexities of human nature and the struggle for self-identity in a world that often demands conformity.In conclusion, the concept of automorphic encompasses a wide range of ideas, from the mathematical properties of numbers to philosophical reflections on identity. Whether in the pursuit of knowledge within the field of mathematics or in the exploration of personal growth and transformation, the principle of automorphic serves as a reminder of the beauty and complexity inherent in both numbers and human experience. As we continue to explore the depths of this concept, we uncover not only the wonders of mathematics but also the profound connections it has to our lives and identities.

在数学领域，术语automorphic指的是某些类型的函数或数字，它们展现出一种迷人的特性：在特定变换下保持不变。这个概念特别引人入胜，当我们考虑automorphic数字时，这些是平方后以相同数字结尾的整数。例如，数字5是automorphic的，因为当你将它平方时，你得到25，而最后一位确实是5。同样，数字76也是automorphic的，因为76的平方是5776，结尾是76。automorphic数字的美不仅在于它们的数学特性，还在于它们的稀有性。虽然整数是无限的，但automorphic数字相对较少。这种稀有性为数学家和爱好者增添了兴奋感，他们常常在发现这些独特数字的新例子中找到乐趣。研究automorphic数字可以深入理解数论及其各个分支，包括模算术和代数结构。此外，automorphic的概念可以扩展到数字之外，包括函数和其他数学实体。例如，在群论中，automorphic函数可能指的是在变换下保持群结构的函数。这个思想在数学的许多领域中都是至关重要的，包括密码学，其中automorphic函数的特性可以用于创建安全的通信协议。除了其数学意义外，automorphic的概念还可以隐喻性地应用于生活的各个方面。例如，人们可能会认为那些表现出automorphic特征的个体是那些尽管经历了变化，仍然忠于自我的人。正如automorphic数字通过平方保持其身份一样，一个人可能在面对挑战和变化时保持其核心价值观和信念。在文学中，automorphic身份的主题可以通过经历重大转变但仍保留其本质的角色进行探索。这种二重性可以为叙事提供丰富的素材，使作者能够深入探讨人性的复杂性以及在一个常常要求遵从的世界中自我认同的斗争。总之，automorphic的概念涵盖了广泛的思想，从数字的数学属性到对身份的哲学反思。无论是在数学领域追求知识，还是在探索个人成长和转变的过程中，automorphic的原则都提醒我们数字和人类经验中固有的美与复杂性。当我们继续探索这一概念的深度时，我们不仅揭示了数学的奇迹，也揭示了它与我们生活和身份之间的深刻联系。