定理

Major results, such as the Sz.-Nagy Dilation Theorem, the Weyl-von Neumann-Berg Theorem and the classification of von Neumann algebras, are covered, as is a treatment of Fredholm theory.

主要成果，如Sz。，纳吉扩张定理，外尔，冯诺依曼，伯格定理与冯诺伊曼代数的分类，覆盖，就像一个Fredholm算子理论的待遇。

Theorem 1 (Boundedness and max-min theorem) If is a continuous function on a closed interval, then has an absolute maximum and an absolute minimum on the interval.

定理 1 (有界性与最大值最小值定理)在闭区间上连续的函数在该区间上有界且一定能取得它的最大值和最小值。

A general communication system, channel coding theorem and source-channel coding theorem.

通信系统的一般模型，信道编码定理和信源信道编码定理。

Information theory and coding, right Shannon source coding theorem simulation, verification of the Shannon coding theorem.

信息论与编码中，对香农信源编码定理的仿真，验证了香农编码定理的可行性。

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）。

We've found that on symplectic manifolds there exists a series of Euler-Lagrange cohomology groups different from both de Rham and harmonic cohomology in general and proposed a set of general volume-preserving equations that contain the Hamiltonian equations as a special case.

中文摘要：我们发现在作为经典力学中的相空间的辛流形上有可能存在不同于de Rham上同调和调和形式的上同调，称之为Euler-Lagrange上同调；提出相空间上保体积的一般方程，通常的正则方程是其特殊形式；进而推广了经典力学中著名的刘维定理；同时把Noether定理与上同调联系起来。

As applications of the imbedding theorem, a fuzzy version of the well-known Urysohn metrizable theorem and the general theory of the fuzzy Stone-Cech compactification are given.

最后作为嵌入定理的应用，得到了不分明Urysohn度量化定理并完成了不分明Stone-Cech紧化的一般理论。

As a particular of Rado's theorem and the compactness theorem one obtains the following result.

作为Rado定理和紧致性定理的一种特殊情形，我们得到下面的结果。

First,we show a compactness theorem in SBH,then byusing this compactness theorem,we discuss variational problems for two different func-tionals.

首先给出了SBH空间的一个紧性定理，然后利用这个定理讨论了两个不同泛函的变分问题。

Figueiredo (2002) condition, using above compactness theorem we prove that the functional corresponding to a class of quasilinear system of elliptic equations satisfies condition.

建立了一个抽象的紧性定理，然后借此定理证明了对应于一类拟线性椭圆型方程组的泛函在比Boccardo和De。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。