查询词典 implicit function theorem

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

When the nonlinearity is an odd function, multiple positive solutions for the sec-ond order self-adjoint difference equation with the Neumann boundary conditionΔu(0)= 0,Δu = 0 are obtained by applying Clark's theorem.

另一方面，当非线性项非负且在0~+和+∞是渐近线性的情况下，应用山路引理研究了方程在混合边值条件u(0)= 0，Δu = 0下正解的存在性。

In this paper the transfer function of noulinear control system is defined over a noncommutative polynomial ring, which can be extended into its quotient ring by Ore Theorem.

本文定义了非线控制系统的传递函数，这种传递函数定义在由一个非交换多项式环扩张而成的商环上用传递函数描述了非线性控制系统的三种基本联接：串联、并联与反馈。

One is for Green's function in elements by using linear integrals; the other is for its normal derivative by the divergence theorem.

作法是仅需对原有的奇异性核函数加入一项使其异性消除，同时再将函数的解析积分值减去原方程式。

Theorem 7:For j=1,2,〓,we have〓and for any 〓 and 〓,the function family〓is an orthogonal basis of 〓.

定理7对每个j=1，2，…有〓13而且，对于每个〓和k=1，〓，函数族〓14是〓的一个标准正交基。

Fourier's theorem : any periodic function can be expressed as a sum of sinusoids of appropriate amplitudes and frequencies.

付氏理论：任何周期函数均可以表示为一组正弦函数的和，正弦函数具有合适的大小和频率

The basic idea of the method is as follows: an algebraic theorem is used to avoid computing the composition and multiplication of B-spline basis function by Blossom and Polar form, and to reduce the computation by solving linear equations.

基本思想是：运用代数基本定理避免通常B样条基函数复合所采用的极形式以及非常烦琐复杂的开花运算，把B样条基函数的复合、乘积运算转化为求解线性方程组。

There isn't maximum principle for polyharmonic equation,so this paper first established a super-sub-sulution theorem via low semi-continuity and changed assistant function.

因为多重调和方程没有极值原理，所以首先利用泛函弱半连续性和适当变换辅助函数的方法建立起多重调和方程的上下解定理。

Difference equations; Green's function; Fixed point theorem; Fixed point index; Positive solutions; Cone

基础科学，数学，数学分析差分方程； Green函数；不动点定理；不动点指数；正解；锥

So-called first-order theorem proving may be restricted to a propositional calculus with terms (constants, function names, and free variables) added, making it impossible to express mathematical induction.

所谓一阶定理证明可限于命题演算的条款（常数，函数名，并免费变量）说，无法表达数学归纳法。

Don not attempt to do something which you can not to do.

不要企图做那些办不到的事情。

The expression of CTGF and TNF-αweredetected by immunochemistry and the number of Clara Cells was calculated.

光镜下观察肺组织的病理变化，采用免疫组化染色观察肺组织中结缔组织生长因子和肿瘤坏死因子-α的表达和Clara细胞的数量。