关于Shannon－McMillan定理的若干研究

设｛Ｘｎ，ｎ≥１｝是字母集为Ｓ＝｛１，２，…，Ｎ｝上的任意信源，其分布为ｐ｛ｘ１，…，ｘｎ｝，（ｐｋ（１），ｐｋ（２），…，ｐｋ（Ｎ），ｋ＝１，２，…，是Ｓ上的一列分布　称为｛Ｘｋ，１≤ｋ≤ｎ｝相对于乘积分布　的熵密度偏差，本文利用这个概念研究任意信源的极限性质，其中包括在没有平稳性和遍历性假设情况下对ＳｈａｎｎｏｎＭｃＭｉｌｌａｎ定理的某些讨论．     

Shannon信息最优编码论的数学问题

概述信息最优编码的数学理论的现代状况。指出若干迫切的问题1.近十年来十分流行的术语“信息论”直到如今还没有获得一致的解释。在技术文献和控制论文献中,通常把信息论了解为数学方法在信息的给予、加工、储存和传输问题上的应用的总和。从数学的观点上说,这些应用很少共同性,因为它们是基于十分不同的数学部门的方法之上的。按照这种了解,应当把全部数理统计、随机过程的很多部分、最近数年来开展的关于e-网在泛函空间中的势(可解释为这空间的元所给出的     

关于有向网络容量扩充问题

提出了有向网络最大容量的两种计算方法,将杨超等人（1998）的无向网络容量扩充问题,扩展到约束条件含固定费用的有向网络的扩充,并给出了强多项式算法。     

容量中的问题

今天的数学课上,我学到了一个新的知识——“容量”.容量就是指一个容器的容积大小,常见的容量计量单位是升和毫升.光听老师在课堂上讲,脑海里对一些常见容器的容量大小还是有点模糊.于是,放学一回到家,我便迫不及待要亲自操作一下,这样才能加深对容量的认识.     

关于Shannon—Mcmillan定理的若干研究（Ⅱ）

该文通过概率空间上的任意分布列与独立分布列比较，研究任意随机变量序列相对熵密度用不等式给出的强极限定理，即小偏差定理，并由此得出若干Shannon－Mcmillan定理，将作者已有的关于离散信源的结果加以推广.     

关于Shannon熵的统计计算及其在分布检验中的应用

本文利用顺序统计量给出了一个关于经验分布的定义,由这个定义可以给出关于连续型分布的Shannon熵的估计量,我们证明了它们的一系列收敛性,利用Shannon熵的统计量及最大熵原理,我们给出了一个关于正态分布,指数分布,均匀分布的新检验法,这个检验法称为《分布的熵-矩检验法》。     

Properties of two Shannon’s ciphers

In 1949 Shannon published the famous paper “Communication theory of secrecy systems” where he briefly described two ciphers, but did not investigate their properties. In this note we carry out information-theoretical analysis of these ciphers. In particular, we propose estimations of the cipher equivocation and the probability of correct deciphering without key.     

关于辛流形的辛容量的一点注记

本文证明辛流形 M×R~(2n)中的开辛圆柱 M×Z(r)的 Gromov 辛容量 C_G 是有限的,由此得到 Gromov 辛挤压定理的一点推广.最后,举例说明 Gromov 辛容量不同于 Hofer-Zehnder 辛容量.     

Shannon定理中信息准則成立的充要条件

<正> 本文是在胡国定先生的[1]文基础上写出的,主要討論了信源序列的結构性貭,信息准則(B)成立的充要条件及准則(B)与概率准則(A)的关系. 准則(A),(B)实际上就是Shannon第一定理及第二定理.本文主要推广了在一般条件下及临界条件下的第二定理,并且給出了微弱条件下二种反定理的証明;根据上述定     

双向小波子空间上的Shannon采样定理

本文将讨论双向小波子空间上的Shannon型采样定理.根据双向多分辨分析的Riesz基,构造出双向小波子空间上的Shannon均匀与非均匀采样公式.     

On the m-capacitated peripatetic salesman problem with capacity restrictions

We consider a special case of the problem of finding m Hamiltonian cycles with capacity restrictions on the number of usages of the edges (m-Capacitated Peripatetic Salesman Problem or m-CPSP): the minimization and maximization 2-CPSP with edge weights chosen from an integer segment {1, q} with the edges capacities given as independent identically distributed random variables equal to 2 with probability p and 1 with probability (1 ? p). Some polynomial algorithms are proposed for 2-CPSP_min and 2-CPSP_max with average performance guarantees. In particular, when the edge weights are equal to 1 and 2, the algorithms have approximation ratios (19 ? 5p)/12 and (25 + 7p)/36 for the minimization and the maximization problem correspondingly.     

The capacity problem

We consider a type of infinite-dimensional linear program posed over a measure space and called a capacity problem. This problem is related to that of finding the electrostatic capacity of a conducting body, and arises in certain types of two-person zero-sum games. The duality theory for this problem is discussed, and conditions are given under which the optimal solution is a measure with finite support. When solutions are restricted to be measures with finite support, a characterization of the extreme points of the feasible region is possible. This has implications for algorithms to solve the capacity problem.     

On the inverse problem of simultaneous determination of thermal conductivity and specific heat capacity

Translated from Sibirskii Matematicheskii, Vol. 35, No. 3, pp. 612–621, May–June, 1994.     

On the optimum capacity of capacity expansion problems

In this paper we consider problems of the following type: Let E = { e ₁, e ₂,..., e _n } be a finite set and be a family of subsets of E. For each element e _i in E, c _i is a given capacity and _i is the cost of increasing capacity c _i by one unit. It is assumed that we can expand the capacity of each element in E so that the capacity of family can be expanded to a level r. For each r, let f (r) be the efficient function with respect to the capacity r of family , and be the cost function for expanding the capacity of family to r. The goal is to find the optimum capacity value r ^* and the corresponding expansion strategy so that the pure efficency function is the largest. Firstly, we show that this problem can be solved efficiently by figuring out a series of bottleneck capacity expansion problem defined by paper (Yang and Chen, Acta Math Sci 22:207–212, 2002) if f (r) is a piecewise linear function. Then we consider two variations and prove that these problems can be solved in polynomial time under some conditions. Finally the optimum capacity for maximum flow expansion problem is discussed. We tackle it by constructing an auxiliary network and transforming the problem into a maximum cost circulation problem on the auxiliary network.