定理的

Applying the techniques of real radical ideal, P-radical ideal , decomposition of semi-algebraic set in ( [72] ), affine Hilbert polynomial and B-net form of polynomials on simplex, this paper obtains two theorems of real C〓 piecewise algebraic variety dimensions and the real Nullstellensatz in C〓 spline ring.

4：应用多项式在单纯形上的B-网形式以及文献（[72]）中的实根理想，锥根理想，半代数簇分解定理，本文得出了实C〓分片代数簇的二个维数定理和C〓样条空间的实零点定理。

The content of this course is divided into four chapter, the normed linear space and bounded linear operator on the normed space; the character of finite dimensional linear space; the basic theorems on Banach space.

本课程主要分为四章，赋范线性空间与内积空间；赋范线性空间上的有界线性算子，有限维赋范线性空间的特征。Banach空间中的基本定理：泛函存在定理，一致有原理，开映象，闭图象、逆算子定理。

The key concepts are "isomorphism" and "symmetric isomorphism" which are used to describe the relation between two search domains, the key results are "Structure Theorem","Isomorphism Theorem" and "Isomorphism Classification Theorem".

核心的概念是非常重要的用于描述搜索域之间相互关系的"同构"与"对称同构"，核心结果是"结构定理"，"同构定理"和"同构类定理"。

All notions and results in Section 2 of reference [1] are generalized and a counterexample is given to illustrate that Theorem 2.6 of [1] is incorrect.

摘要推广了文[1]第二部分中的所有概念和所有定理（即定理2.2、2.4、2.5、2.7、2.9、2.11和2.12），并通过举反例说明文[1]中的定理2.6是错误的。

Chapter 7 gives the H-stability of the eqilibrium point set first (theorem7.1), and the other two theorems (theorem7.2-7.3) provide an estimation result for the attractive region of different eqilibrium points.

首先给出了非凸梯度神经网络平衡点集合的H—稳(来源：AB29e6C论文网www.abclunwen.com)定性结果(定理7.1)，另外的两个定理(定理7.2—7.3)给出了不同平稳点的吸引域估计。

For example, basic tools from calculus such as Fermat theorem, Rolle theorem and the intermediate value theorem may not necessarily hold and fundamental concepts such as chain and product rules and certain smoothness properties all need to be modified.

例如，微积分中的基本工具诸如Fermat定理、Rolle定理以及介值定理不再成立，一些基本的概念诸如链式法则、乘积公式以及某些光滑性都需要做适当的修正。

We obtain these theorems on the isometry groupsof pinched Hadamard manifolds under Condition A.

特别是在三维双曲情形，条件A等是自然满足的，因此我们所得到的代数收敛性定理、极限定理和收敛性定理与平面上的经典情形一致。

This paper has further extended these conclusions on the foundations of them and obtained some new results with the method of Hulwize Theorem, Schauder Fixpoint Theorem and Tapered Fixpoint Theorem.

本文主要是在这些结果的基础上将已有的结论作了进一步的推广，利用了霍维茨定理、Schaudr不动点定理、锥上不动点定理等得到一些新的理论。

Weil's theorem on character sums is an important theorem in number theory.

1.Weil定理关于特征和的Weil定理是一个重要的数论定理。

In chapter 2, first, the index of random fixed point for random semiclosed 1-set contractive operator is investigated.

其次 讨论了随机半闭1-集压缩算子随机不动点的存在性，所获结果推广了著名的Rothe定理、 Petryshyn定理和Altman定理。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。