查询词典 existence theorem of implicit function

First, a switching function is designed to guarantee that the movement of the system is asymptotically stable in the switching manifold. And the equation of the switching surface is given based on pole assignment theorem; Then a discrete robust adaptive quasi-sliding-mode tracking controller is presented by constructing the two adaptive gains, and the globally asymptotically stability of the system is proved based on the Lyapunov-Razumikhin stability theorem.

首先，利用广义系统的概念给出了系数矩阵为能控标准型的滑模面方程，并利用极点配置定理给出了能使系统稳定的滑模面；其次，构造了含有自适应律的离散趋近律，设计了能够使系统达到同步的变结构控制器，并利用Lyapunov稳定性定理，证明了系统的趋近运动的稳定性。

Using the method of analysis to study strong limit theorem proposed by professor Liu Wen, and a plying Legbesuge theoremon differentiability of monotone function, a new proof of the theorem of strong law of large numbers for the sequence of random variables of the product distribution of Poisson is forwarded.

利用文献[1]刘文教授提出的研究强极限的纯分析方法，通过构造适当的辅助函数，然后利用单调函数异数存在定理，给出具有乘积泊松分布的随机变量序列的一个强大数定理的新证明。

When proving the differential mid-value theorem,"Higher Mathematics" does know to make the auxiliary function ф in order to apply Rolle Theorem.

在证明微分中值定理时，《高等数学》作辅助函数ф的目的是为了应用罗尔定理。

The new methodof defining spline function will generalize the concept to the more universal Hilbert space. Hence, we take into consideration the interpolation spline function, general linear differential operater in semi- open interval and the Green function defined accordingly, and the reproducing kernel to produce the Green function and prove the existence of the reproducing kernel.

采用了一种新的样条函数的定义方法，把样条函数的概念推广到更一般的Hilbert空间上，再考虑半开闭区间a，+∞上的插值样条函数，一般线性微分算子及其定义的Green函数和再生核，构造出Green函数并且证明了再生核的存在性。

From the theory, the algorithm for determination of the degree of implicit polynomials is followed: detecting the stationary points in the object boundary based on its features, and then calculating the minimum degree according to the formula derived from the theorem. In addition, the theory can be extended to three-dimensional object.

该方法首先由给定物体边界的轮廓检测出其驻点数，然后根据驻点数得到拟合隐含多项式曲线方程次数的下界，进而推广到三维物体的隐含多项式曲面拟合次数的确定。

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。

Since the solutions of this problem are the critical points of the associated energy function. One generally needs some compactness such as PScondition or C-condition to prove the existence of critical points of the energy func-tion, but when we study the elliptic equation in R~N, the compactness condition does not always hold since the imbedding of the Sobolev space H_0~(1,2)into L~(2*) is not compact. In this chapter, based on the nonsmooth critical point theory, and by using the approximation technique with periodic function, the existence of nontrivial solution is obtained.

由于该方程的解就是其所对应的能量泛函的临界点，通常都要在一些紧型条件的基础上来证明其所对应的能量泛函临界点的存在性，但当我们在无界域上考虑该椭圆方程解的存在性时，Sobolev空间H_0~(1，2)到L~(2*)的嵌入非紧，从而导致所对应的能量泛函失去紧性，本章在非光滑临界点理论的基础上，应用周期逼近的方法证明该问题非平凡解的存在性。

By constructing a different piecewise linear supply function, the existence of piecewise linear supply function equilibria in electricity market is proved. From the theoretical point of view, new results regarding existence of these equilibria are presented.

在这种电力市场环境下构造了一类分段线性供应函数，证明了分段线性供应函数纳什均衡解的存在性，从理论上获得了相关新结论，为电力市场供应函数均衡近似数值求解算法设计提供理论基础。

This curriculum primary coverage includes: Function and limit, a circular function derivative and differential, theorem of mean and derivative application, indefinite integral, definite integral, definite integral application, space analytic geometry and vector algebra, function of many variables differential method and application, multiple integral, curvilinear integral and surface integral, infinite series, differential equation.

该课程的主要内容有：函数与极限，一元函数的导数与微分，中值定理与导数的应用，不定积分，定积分，定积分的应用，空间解析几何和向量代数，多元函数微分法及其应用，重积分，曲线积分与曲面积分，无穷级数，微分方程。

On the basis of analyzing detailedly the correlative conclusions of the extreme value problem of two variable Function , this paper extends the essential condition and sufficient condition to multi-variable function by using the Taylor Formula 、Quadratic Form 、Hesse Matrix and so on,and gives a method to judge the extreme value of point whose vice-derivative doesn't exist by utilizing Lagranges theorem ,so that compensates for the blank above ,which turns idea that solve the extreme value of multi-variable function problem one by one into realities.

摘要本文在对二元函数极值问题的相关结论进行分析的基础上，用泰勒公式、二次型、海赛矩阵作为工具，将二元函数极值的必要条件和充分条件推广到多元函数的情形，而且还利用拉格朗日中值定理找到了一个判别不可导点处极值的方法，从而弥补了多元函数不可导点处极值无法判断的空缺。因而，使得用穷举判断的方法来解决多元函数的极值问题这一思路成为现实。

"The operators will suffer a temporary decrease in the number of consumers and short message services as people may not like having to provide their ID cards for a phone number," Xu Junqi, vice-dean with the Policy-Making Institute of the Telecommunications Research Centre under MII, said yesterday.

信息产业部下属的通信决策研究院副主任徐俊其昨天说：&实行手机实名制后，人们可能不太情愿用身份证注册手机号，所以通信运营商会暂时面临用户减少和短信用户减少的问题。&

I don't believe in make-believe!

我不相信这些虚构的故事。