查询词典 theorem of implicit functions

Based on the segmented unstructured model of Nosiheptide fermentation process, the secondary variables are selected according to the implicit function existence theorem. The on-line identification of fermentation phases is accomplished by using an indicator variable which is gained by mathematical inference, and for each phase, a local soft sensor model is developed.

首先以分阶段的诺西肽发酵过程非结构模型为基础，根据隐函数存在定理进行辅助变量的合理选择；然后利用经数学推导得到的指示变量"伪比生长率"完成发酵阶段的在线辨识，并采用神经网络构建出对应于各阶段的局部软测量模型。

In this project, we intend to combine the above mathematical ideas. First, we consider a wild family of dynamical systems which can be derived into a family of difference equations. Then using a generalized version of the implicit function theorem which we will establish, we want to show that for any dynamical systems near 「singular limit」, there exists a horseshoe structure and hence chaotic phenomena occur.

在此研究计画中，我们打算结合上述的数学结论与想法，进一步考虑一类能够转化成差分方程的动态系统函数族，使用即将建立的推广性隐函数定理，我们希望证明当参数接近奇异极限时，动态函数会具有马蹄结构所以有混沌现象。

According to the estimation of biomass in Nosiheptide fermentation process, the secondary variables are selected according to the implicit function existence theorem, and then a soft sensor model of biomass is developed by using the IBPNN. The testing result shows the effectiveness of the presented approach.

最后针对诺西肽发酵过程中菌体浓度的估计问题，根据隐函数定理选取辅助变量，应用IBPNN建立菌体浓度软测量模型，实验结果验证了所提方法的有效性。

A kind of one parameter planar singular perturbation equation is studied by the qualitative theory of ordinary differential equations, asymptotic analysis methods, implicit function theorem and fixed point methods.

本文应用微分方程定性理论、渐进分析方法、隐函数定理以及不动点理论的方法研究一类单参数二维奇异摄动系统。

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。

Based on approximation capability of neural networks and mean value theorem, a stable adaptive control scheme is proposed to control the implicit dynamic system with an uncertain nonlinearity.

针对一类隐含控制输入的非线性系统，引用中值定理并利用径向基神经网络的逼近能力，提出了一种稳定自适应神经网络控制方案，以实现对一类隐含控制输入未确定非线性系统的控制。

In order to expand half space Green's functions with addition theorem, a high order approximation method is proposed for evaluation of reflection term of half-space Green's functions with far interactions.

采用高阶拟合方法将远区相互作用单元的半空间空域格林函数用级数表示，对高阶拟合项作加法定理展开，进而应用多层快速多极子算法。

Functions, relations and graphs; inverse functions; inequalities; theory of equations; introduction to matrices; determinants; binomial theorem; sequences and series.

函数， 图表，曲线。反函数，不等公式，等式，矩阵的介绍，定列式，序列和系列等。

By the perturbation theorem of cosine operator functions,one perturbation result for C-cosine operator functions is obtained.

而对于扰动问题的研究向来是十分重要的，因为这类研究是获得丰富理论的基本途径之一。

Power system ; Harmonic analysis ; Artificial neural network ; Convergence theorem ; Fast Fourier transformation ; Triangle base functions ; Window functions

电力系统；谐波分析；人工神经网络；收敛定理；快速傅立叶变换；三角基函数；窗函数

He tendered his resignation to the Prime Minister.

他向首相递了辞呈。不适合

International economy and trade,Nanking 210044

国际经济与贸易，南京 210044