定理的

In Chapter 2, some new convergence and stability theorems of the Ishikawa iterative procedures with errors for solutions to variational inclusions involving accretive mappings in real reflexive Banach space are proved.

第二章在实自反Banach空间中，证明了增生型变分包含解的具误差项的Ishikawa迭代程序的一些新的收敛性定理和稳定性定理。

In this paper, we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence, uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations.

利用混合单调凝聚算子的耦合不动点定理，给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。

To cousider the least,we have to establish these facts under some comparablystrong but not the most proper conditions.From [12] and [13],if we suppose thatfis Lipschitz continuous in t,then all the above conditions(H1)-(H3) canbe established to a class of approximating problems of (1)(2).So the followingtheorem can be proved by theorem 5 through approximation process.

这时，我们只好"退而求其次"，在较强的"看来不是最适当的条件"下，来建立这些事实，从[12]和[13]中我们看到，只要加上"〓对t为Lipschitz连续"，则对（1）（2）的逼近问题族，上述条件（H1）-（H3）都可建立起来，从而，通过逼近过程，用定理5就可得到如下的定理。

In this paper we use pointwise modulus of smoothness to study approximation direct theorem and equivalent theorem for some linear operators and quasi-interpolant operators; Using pointwise modulus we discuss the strong converse inequality on K-functional; and using a modified weighted K-functional and weighted modulus of smoothness we study approximation with Jacobi weight on operator with non-zero first order moments.

本文利用点态光滑模ω_~(2r)来研究某些线性算子及逆中插式逼近正定理和等价定理；利用点态光滑模讨论其关于K-泛函的强逆不等式；同时利用一种改变的带权K-泛函和带权光滑模研究一阶矩不为零的算子的点态带Jacobi权逼近。

If the power series ∑anxn an ∑anxn and ∑bnxn satisfy the condition r =∑bn xn, we obtain the twin combinatorial identity theorem between the sequences {an} and bn}.We also obtain some specific twin combinatorial identities by using the expansion on the binomial expression formula, including two expansions of combinatorial number(rsn and ...

如果幂级数∑anxn与∑bnxn满足条件r＝∑bnxn 时，获得数列｛an｝与｛bn｝之间孪生组合恒等式的定理，应用在二项式定理等展开式上得出具体的多组孪生组合恒等式，其中包含组合数的两种展开法，Bernoulli数直接表达式的新证等结果。

This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included.

通过Hilbert空间中的Riesz表示定理，首先将变分不等式问题的迭代过程转化为一种不动点形式，再利用Schauder不动点定理构造了一个高效率的数值证明过程，即通过数值计算产生一个包含近似解的有界闭凸子集。

The topics covered include the basic concepts of information theory--entropy, mutual information, channel capacity, information rate, Shannon's noiseless coding theorem and Shannon's fundamental coding theorem; modeling of information sources--zero-memory and Markov models; modeling of information channels--BSC and BEC channels, additivity of information and cascaded channels; construction of compact source codes--Kraft inequality, compact codes, Huffman and LZW compression codes; and analysis and design of error-control channel codes--Hamming distance, binary linear codes and the parity-check matrix, Hamming codes, checksum codes, cyclic codes and the generator polynomial and CRC codes.

课程的内容包括：信息论的基本概念（熵、交互信息、信道容量、信息率、 Shannon无噪声编码定理和Shannon基本编码定理）、信源模型（无记忆模型和Markov模型）、信息信道模型（BSC 和 BEC模型、信息的可加性和级联信道），紧致信源编码设计（Kraft不等式，紧致编码，Huffman 和LZW压缩编码）以及差错控制信道码的设计与分析（海明距离，二元线性码，奇偶校验矩阵，海明码，校验和，循环码，生成多项式和CRC码）。

In chapter four"The application of generalized sampling theorem to data compression", the qaulity of approximation coefficients is proved and a methodology of discrete cosine transformation combined with ununiform sampling is put forward.

第四章&广义采样定理在数据压缩中的应用&，对广义采样定理一中的展开式系数性质进行了证明，在此基础上提出了一种结合非均匀采样的离散余弦变换方法。

We can change nonlinear 2-D digital system into a linear system set with varying parameters by vector method.

定理2是用于检验多个非线性的2-D数字系统的极限环判断。定理1所获结果与Fahmy[4]的结果一致。

It proved that the intersection of hyperplanes corresponding to the edges of a clique in a simple graph is a modular...

并利用上面证明的定理及Stanley定理给出此类图构形的Poincaré多项式的一个因式分解。

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。