查询词典 theorem of implicit functions

In this paper, we prove that if Ф is parallel and A+G+μB=0 for some functions λ,μ, then Ф=0, which gives the classification of the hypersurfaces in S(superscript n+1) with parallel Mbius form and A+G+μB=0 from the classification theorem in paper of Li H.

本文证明了如果x的Mbius形式Ф平行，并且A+λG+μB=0，其中λ，μ分别是定义在M上的光滑函数，那么Φ=0，由此及李海中、王长平（2003年）文献中的分类定理给出了S(上标 n+1)中具有平行的Mbius形式及满足A＋λG+μB=0的超曲面的分类。

Chapter one has introduced the background and classification of minimax theorems; Chapter two summarizes several proof method of minimax theorems, which are illustrated with examples; Chapter three has explained the development general situation of minimax theorems for a function and for two functions with chapter four respectively, and according to the classification of the theorem, has illustrated some important conclusionses in quantitative minimax theorems, topological minimax theorems and quantitative-topological minimax theorems separately.

第一章介绍了极大极小定理的背景及其分类；第二章总结了极大极小定理的几种证明方法，并举出例子进行说明；第三章和第四章分别阐述了单函数的极大极小定理和两个函数的极大极小定理的发展概况，在第三章中，按照极大极小定理的分类，分别对数量极大极小定理，拓扑极大极小定理和数量拓扑极大极小定理的一些重要结论作了介绍。

Theorem Let be continuous on a bounded closed region in the -plane.(1) If is given by and , where are continuous functions of on, then

定理 设在xy平面上的有界闭区域 D 上连续，(1)若区域由和所给出，其中是上的连续函数，则。

By using the compactness theorem of SBD space, Poincaréinequality onthe BD functions,we prove the existence for variational problems.

主要利用SBD函数空间的紧性定理，BD函数的Poincaré不等式等给出了变分问题的存在性。

Sometimes different combinations in the concavity and convexity of functions may construct a new theorem.

函数凹凸性的不同组合往往可以构成一个新的极大极小定理。

By using the group-chain, the wavefunctions of the 4f〓 configuration for RE ions are also expressed as linear combinations of group-chain basis functions in Butler's irreducible representation notation. The matrix elements of the CF Hamiltonian then are calculated by means of the Wigner-Eckart theorem and factorization lemma of the jm factors. Before the CF level fitting, a point-charge calculation of the conventional CF parameters B〓 has been performed by means of the lattice-sum technique from the known crystal structure data. The corresponding parameters in the group-chain are calculated by the conversion relationship between two schemes that proved identical in essence, which are usually used as initial values in the fit to the experimental levels. The ratios of the same k-value CF parameters are suggested as the constraint conditions in the fit, in order to utilize fully the symmetry distortion degree of the studied system.

利用群链理论，属稀土离子4f〓组态的波函数表示为以不可约表示标记的群链基波函数的线性组合；借助Wigner-Eckart定理和2jm和3jm因子的分解定律计算了晶场哈密顿的矩阵元；根据点电荷模型和已知晶体结构数据，利用点阵求和技术计算得到传统晶场参数B〓初值，相应的非传统形式的群链参数初值则由两种方案下的转换关系求得；这些初值通常作为非线性拟合晶场能级计算的初值，系统的对称性畸变信息则反映在以同阶晶场参数的比值作为能级拟合的约束条件。

By using the limits of functions and the exchange limit theorem,we considered the relationship between the double limit of function with two variables and its repeated limit s.

应用函数列的极限与函数的极限交换次序定理，研究了二元函数的二重极限与它的两个累次极限的关系定理，研究了二元函数的两个二阶混合偏导数可交换次序定理。

For example,a generalization of linear algebra is developed in which "convex bifunctions" are the analogues of linear transformations,and "inner products" of convex sets and functions are defined in terms of the extremal values in Fenchel's Duality Theorem.

例如，一类线性代数的推广形式在凸双重函数中发展起来，而凸双重函数是线性变换的类似情况，凸集和凸函数的内积是根据 Fenchel 对偶理论的极值定义的。

In part III by using capacity theory and extension theorem of Lip-schitz functions we first discuss the uniqueness of weak solution ofnonhomogeneous quasilinear elliptic equations〓in space〓,which is bigger then〓.

第三部分首先用容量理论、Lipschitz函数延拓定理讨论了一类非齐次拟线性椭圆型方程〓在比〓更大的空间〓中弱解的唯一性。

In Chapter 4,we obtain the optimality for the quasi-score function 〓in a more general class of estimation functions〓,where〓and〓or〓This result is a extension of Gauss-Markov theorem of the linear model to the nonlin-eaar model.

在本章中，我们得到拟得分函数〓在一种较大的估计函数类〓中的最优性，其中〓而〓或〓于是，我们得到类似于线性模型中的Gauss-Markov定理和拟得分函数的拟Fisher信息上界及达到上界的充要条件：〓，其中〓为真实未知的得分函数，〓为模型均值。

The second is to cut a mere 100 calories from your diet , which is the equivalent of a tablespoon of butter.

第二个就是从你的饮食中减少一百卡路里，只是相当于一大汤匙的黄油。

This is where the Rorschach test comes in.

现在，罗氏测试就出现了。