查询词典 existence theorem of implicit function

In this paper,we generalize that Polya Theorem for composite of the entire function f is finite order to the form composite and the entire and meromorphic function f is finite order .

将Polya.G关于整函数的复合函数f为有穷级的定理推广到整函数与亚纯函数的复合函数f为有穷级，并得到f为有穷级的一些充分条件

However,To prove Inequality with elementary method,we often create complex computational process. The second ,we will take full advantage of the knowledge of calculus Inquiry Testimony of inequality,and concluded the higher mathematics to prove Inequality several main method and its application conditions.Constructors in the context of the use of the monotone function,Calculus value theorem,function and the most extreme value,integral, it can be a very effective solution to the inequality problem proof. At last,we summed up several convenient and simple way to prove Inequality.It will be play a great role in our problem Solving.

但是用初等方法证明往往会造成复杂的运算过程，本文接着充分利用微积分的知识探究不等式的证明方法，并指出微分学和积分学在不等式的证明的具体应用，那就是在构造函数的背景下运用函数的单调性、微积分中值定理、函数的极值和最值、定积分，那么就可以十分有效地解决不等式中的证明问题，从而归纳出几种方便而又简捷的方法，这样对我们解题将会起到很大的作用。

To reduce the error between the interpolation function regaining the sampled signal and interpolation function ha by Shannon sampling theorem, this paper suggests that the common linear interpolation is replaced by a second order approximation of the parabolic interpolation.

为减小恢复被采信号所用的内插函数与山农采样定理要求的内插函数ha之间的误差，提出了用抛物线内插--ha的二阶近似代替常规的线性内插。

As the inversion and compression attack includes the question relating to solving thepreimage from image of function, a subdivision algorithm for solving preimage of function withbounded derivative based on Lagrange mean value theorem is proposed firstly.

由于逆推压缩攻击方法涉及混沌映射的求逆，针对复杂混沌映射求逆困难的问题，运用拉格朗日中值定理，我们提出了求解导函数有界的函数原象的分割算法，给出了使分割算法计算复杂性上界达到最小的充分条件。

A theorem for the summation of series expressed by function terms derived from function identities is established.

摘要建立了由函数恒等式所导出的函数项级数的求和定理，并给出了具体应用的实例。

Firstly,based on the generalized function,φ-mapping topological currentare rigorously proved to be of delta-function formδand can be labelledby the nodal indices of the vector field,namely by Hopf indices and Brouwerdegrees of this vector field,which reveals the inner relationships between ourtheory and the topology of vector bundle.A singular divergence theorem isalso presented.

论文首先以广函数为基础严格证明了，φ-映射拓扑流具有δ函数形式，并且可以向量场的零点指标表征，即以其Hopf数和Brouwer度拓扑量子化，从而揭示了它与向量丛的拓扑学之间的内在联系。

Distribution function ; characteristic function ; the uniqueness theorem

分布函数；特征函数；唯一性定理

A new kinematically admissible velocity field is constructed. On operating with a linear failure criterion that exceeds the actual nonlinear failure criterion, the objective function formulation of the upper bound theorem leads to a classical nonlinear programming problem where the objective function, which is to be minimized, corresponds to the dissipated power.

本论文在上限定理的基础上，首次提出&切线法&与非线性&序列二次规划&优化相结合的计算方法，使在非线性屈服下求解岩土承载力或稳定性问题成为可能，为上限定理的广泛应用开辟了新的途径。

In the fourth chapter, we build the model of coefficient on one dimension partial differential equation and adopt finite element method to discrete partial differential equation and in the fifth chapter, we employ GP to identify and build the model of right-side function and adopt over-relaxation or alternating direction implicit method to solute difference equation.

在求解这些偏微分方程连续系数反演或右端连一一一~武卫1里鱼立二大一至」夔里匕崖匕位止透二立一一一一续函数的适应值评价中，我们都采用H'一范数正则化来解决连续参数的识别问题。

The definition and stability criterion of resonant operating points in a CPT system have been described. A Poincarémapping model has been built up and its Jacobian matrix has been derived with the implicit function derivative rule and chain rule. Then the stability of the fixed points can be determined according to the eigenvalues of the the Jacobian matrix. It has been used to study an example push-pull CPT system with three resonant operating points.

文中给出了CPT系统中谐振点的定义及判断条件，建立了系统的庞加莱映射模型，并根据隐函数及复合函数求导法则，推导出了系统庞加莱映射周期不动点的雅可比矩阵，根据雅可比矩阵的特征值分布情况，即可判断各不动点的自治振荡稳定性。

The studies on the developing of new media are very important to the increasing of the area density of HDD and to the implementation of hybrid recoding technology.

光磁混合记录方法，是一种可以突破超顺磁极限的限制，并进一步提高硬盘记录密度和读写速率的一种新型超高密度信息存储方式。

In io, mTOR inhibition promotes T cell anergy under conditions that would normally induce priming.

体内研究中，在正常可激发免疫反应的条件下，抑制mTOR可促使T细胞无能。