查询词典 implicit function theorem

The Maschke's Theorem of group algebras is well known, and [Mo2] gives us a version of Maschke's and Dual Maschke's Theorem of finite-dimensional Hopf algebras.

半格分次弱Hopf代数是弱Hopf代数的一类特殊情况，而且又是Hopf代数的一种推广，在第1.3节中，我们将会给出半格分次弱Hopf代数的Maschke和对偶Maschke定理的结论及其应用。

After that, we discuss the weak duality theorem and the strong duality theorem concerning Benson efficient solutions.

接着讨论了Benson真有效解的强弱对偶性定理。

In the study of finiteness conjecture, there are two important conclusions, that is Revised Dulac"s Theorem and Il"yashenkos Theorem. But the discusses and demonstrations of these two theorems are very brief and simple in existing documents.

在有限性猜测的研究中有两个十分重要的结果，即修正的Dulac定理和Il'yashenko定理，现有的文献对这两个定理的讨论和证明非常简要。

In chapter 4, we state and prove Campanato type Theorem, Morrey type Theorem and some embedding Theorems for the maps.

在第四章，我们证明Campanato型和Morrey型不等式和一些嵌入定理。

For the homoclinics taking on values in the unbounded domain, in order to apply the usual "Mountain Pass " theorem, A compact embedding theorem is proved.

为克服同宿解取值于无界域而缺乏自然紧性，证明了一个紧嵌入定理，从而可以利用通常的山路引理与对称山路引理获得同宿解的存在性与多重性条件。

We discussed the coupled generalized BBM equations with pseudodifferential operator in Chapter three.In this chapter we get the global existence for the Cauchy problem by Banach-fixed point theorem ,a priori estimates and Sobolev embedding theorem.

第三章讨论了具拟微分算子的广义BBM方程组，通过Banach不动点定理、解的先验估计和Sobolev嵌入定理得到了解的整体存在性。

We analyse the Lewy theorem and the provement idea of the theorem, and find the equation (7)and (8)are not equivalent under the reversible transformation, this lead to the absurdity in the provement does not come into existence .

分析Lewy定理及定理的证明思想，发现在证明中所述的可逆变换下，方程（7）与（8）并不等价，导致Lewy定理证明中归谬不成立。

Under the locally uniform τ-Opial condition, using product topological net, a new convergence condition of X with locally uniform τ-Opial condition is obtained, and give the ergodic theorem and τ-convergence theorem of the almost-orbits for asympotically nonexpansive typesemigroups in Banach space X are given.

首先给出了局部一致τ-Opial条件的概念，运用乘积拓扑网技巧得到了具有局部一致τ-Opial条件下空间X的新的收敛条件。

Ruck, Hirano and Reich extended Baillon抯 theorem to a uniformly convex Banach space with a Frechet differentiable norm. Hirano-Kido-Takahashi, Oka, Park and Jenong proved the ergodic theorem for commutative semigroups of nonexpansive mappings and asymptotically nonexpansive mappings in the uniformly convex I3anach space with the Frechet differentiable nonn.

aillon的定理被Bruck，Hirano及Reich推广到具Frechet可微范数的一致凸Banach空间中，而当G是一般交换拓扑半群时，Hirano-Kido-Takahashi，Oka，Park及Jeong分别给出了具Frechet可微范数的一致凸Banach空间中非扩张半群及渐近非扩张半群的遍历压缩定理和遍历收敛定理。

The earliest such theorem is the Gauss-Bonnet theorem, which gives the Euler characteristic in terms of the integral of the Gaussian curvature.

这方面最早的结果是 Gauss-Bonnet定理，它表明曲面的Euler示性数能用Gauss曲率的积分表示。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。