查询词典 approximation theorem

First we give some necessary and sufficient conditions for the oscillation of(1) by Lebesguge s dominated convergence theorem and Schauder — Tychonoff fixed point theorem.

这篇文章中，我们首先利用Lebesgue控制收敛定理，以及Schauder-Tychonoff不动点定理给出了方程(1)振动的若干充分必要条件。

And extended codes of quadratic residue codes over Z〓(Definition 3. 4) also are discussed, which have good dual properties (Theorem 3. 9 and Theorem 3. 10). At last, two kinds of Gray map from Z〓 to Z〓 are defined (Definition 3. 5 and Definition 3. 6), and they are compared with each other, and we find the second Gray map is better than first by an example.

最后，以两种方式定义从Z〓到Z〓的Gray映射并相应的有两种码字的Lee重量定义（定义3.5与定义3.6），并以一实例计算比较了这两种Lee重量定义，指出第二种方式定义的Gray映射更好，因为其相应的Lee重量定义使得相应所得到的最小Lee重量更大。

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。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。