1.
A complete analysis must build on the implicit function theorem.
完整的分析必须建立在隐函数定理的基础上。
2.
existence theorem of implicit function
隐函数的存在性定理
3.
The Constant Theorem of Analytic Function in Complex Function;
关于复变函数中解析函数的常数定理
4.
implicit differentiation
隐函数微分，隐微分法
5.
Hesse Matrix of Sufficient Condition for Extrema of n-variable implicit function;
判定n元隐函数取极值的充分条件Hesse矩阵
6.
THE SECOND FUNDAMENTAL THEOREM OF ALGEBROIDAI FUNCTION
涉及小函数的代数体函数的第二基本定理
7.
Several Immovable Point Theorems about One-Variable Real Function and Complex Function;
有关一元实函数和复函数不动点的几个定理
8.
The Prime Number Theorem for Automorphic L-functions for GL(m);
关于GL（m）上自守L-函数的素数定理
9.
The Application of Complex Function in Algebraic Basic Theory Proof;
复函数在代数基本定理证明中的应用
10.
Some Improvement About Item-by-item Differential Theorem for Function Series;
关于函数项级数逐项微分定理的改进
11.
NOTE ON THE THEOREMS OF TERM BY TERM INTEGRATION FOR FUNCTION SERIES;
关于函数项级数逐项积分定理的注记
12.
A judging theorem about function sequence uniformly convergent;
关于函数列一致收敛的一个判定定理
13.
SOME THEORIES ABOUT FUNCTION LIMITE ON THE DEFINITE OF D--EXPRESSION;
在D—语言定义下函数极限的有关定理
14.
About decision theory of function′s uniformly continuous
关于可导函数一致连续性的判定定理
15.
Basic Concepts: mathematical induction; functions and inverse functions; elementary functions, trigonometric functions; complex numbers; De Moivre's Theorem; roots of a complex number.
一些基础概念：数学归纳法、数及反函数、等函数、角函数、数、莫弗定理、数(角形式)次方根。
16.
Some Uniqueness Theories about Meromorphic Functions and Algebroid Functions;
涉及公共值的亚纯函数和代数体函数的几个唯一性定理
17.
Liouville Theorem and Green Function for Degenerate Elliptic Equations;
退化椭圆型方程的Liouville定理及Green函数
18.
The Other Proof of Existence Theorem of Expected Utility Function;
期望效用函数存在定理的另一种证明