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其在分析中的应用就是自守函数理论的研究。The application of group theory in analysis is the study of automorphic function.

研究得最早的自导函数是椭圆模函数。The earliest automorphic functions to be studied were the elliptic modular functions.

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研究得最早的自导函数是椭圆模函数。The earliest automorphic functions to be studied were the elliptic modular functions.

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

本文给出任何有限群的一个顶点着色图，而这个群的每一个子群是同构于该有色图诱导出的自同构子群。The paper gives a vertex chromatic graph for any infinite group , each of whose subgroup is automorphic subgroup conducted by the chromatic graph.

矿石多具白形、半自形、他形粒状结构，以脉状、浸染状构造为主。The automorphic , hypidiomorphic and xenomorphic granular textures are the main ore textures and vein and disseminated structures are the main ore structure.

然后利用这个不动点定理，我们得到概自守正解的存在性定理。A new fixed point theorem for mixed monotone operator in a cone is presented, and with its help we establish existence theorems of positive almost automorphic solutions.

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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。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.

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

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

第二章是预备知识，主要包括概周期函数、拟概周期函数及概自守函数的概念和基本性质。Chapter 2 is preliminaries, mainly including some definitions and basic properties about almost periodic functions, pseudo almost periodic functions and almost automorphic functions.