基本解释：隐函数定理
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By using the implicit function theorem, the condition of flexible workspace boundary of a plane closed loop five bar mechanism was derived.应用隐函数定理 ,推导出平面闭链五杆机构柔性工作空间边界的条件 ,即输出杆与相连的连架杆共线及另一连架杆与相连的连杆共线 。
The existence of classical solutions to non-divergence quasilinear parabolic equation of second order has been proved by basic knowledge of non-linear functional analysis and implicit function theorem in banach spaces.用非线性泛涵分析的基本知识和Banach空间上的隐函数定理证明了非散度型拟线性抛物型方程古典解的存在性。
In this paper, the necessary optimality conditions for vector extremum problems with equality constraint in product of Banach spaces are obtained by using a implicit function theorem in Banach spaces and a theorem of the alternative for subconvexlike vector-valued maps in ordered linear topological spaces.本文利用Banach空间中的隐函数定理和序线性拓扑空间中对于次似凸向量值映射的择一定理,得出了乘积Banach空间中具有等式约束向量极值问题的若干最优性必要条件。
Then,the system is linearized by variational approach,the local null controllability is proved by applying a generalized implicit function theorem and combining the property of the solution mapping.首先得到了系统的逼近能控性;然后采用变分方法对系统线性化,再结合解映射的性质,应用推广的隐函数定理,证明系统的局部零能控性;最后给出系统零能控的结论。
Then, the system is linearized by variational approach, the local null controllability is proved by applying a generalized implicit function theorem and combining the good property of the solution mapping.首先通过对系统线性化,构造泛函,利用对偶方程,给出控制函数具体形式的办法得到系统的逼近能控性;然后采用变分方法对系统线性化,再结合解映射好的性质,应用推广的隐函数定理,证明系统的局部零能控性;最后利用局部零能控性和逼近能控性结合给出系统零能控的结论。
Furthermore, utilizing the Lagrange method of multipliers and the implicit theorem to work out the critical value which makes one of those inequality locally inverted.然后利用拉格朗日乘数法与隐函数定理,求出了使其中一不等式局部反向的临界值。
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。
existence theorem of implicit function隐函数的存在性定理
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
implicit differentiation隐函数微分，隐微分法
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
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
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
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
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
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
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
A judging theorem about function sequence uniformly convergent;关于函数列一致收敛的一个判定定理
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
About decision theory of function′s uniformly continuous关于可导函数一致连续性的判定定理
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。
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
Liouville Theorem and Green Function for Degenerate Elliptic Equations;退化椭圆型方程的Liouville定理及Green函数
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
