The Further Results of the Chromatic Uniqueness of Certain Bipartite Graphs K （m,n）- A

With its comprehensive application in network information engineering （e. g. dynamic spectrum allocation under different distance constraints ） and in network combination optimization （e. g. safe storage of deleterious materials）, the graphs＇ cloring theory and chromatic uniqueness theory have been the forward position of graph theory research. The later concerns the equivalent classification of graphs with their color polynomials and the determination of uniqueness of some equivalent classification under isomorphism. In this paper, by introducing the concept of chromatic normality and comparing the number of partitions of two chromatically equivalent graphs, a general numerical condition guarenteeing that bipartite graphs K （ m, n） - A （A belong to E（K （m, n） ） and ｜ A ｜≥ 2） is chromatically unique was obtained and a lot of chromatic uniqueness graphs of bipartite graphs K（m, n） - A were determined. The results obtained in this paper were general. And the results cover and extend the majority of the relevant results obtained within the world.     

图的圈长分布和圈长分布唯一的图

阶为ｎ的图Ｇ的圈长分布是指序列（ｃ１，ｃ２，…，ｃｎ），其中ｃｉ是Ｇ中长为ｉ的圈数．若不存在，使Ｇ’与Ｇ有相同的圈长分布，则称图Ｇ是圈长分布唯一图．本文确定了Ｋｎ－Ａ（｜Ａ｜＝ｊ，ｎ≥｜Ａ｜＋３）的最小、最大的４圈和５圈数．证明了当ｎ≥９时，Ｋｎ－Ａ（｜Ａ｜＝４）以及当ｎ≥１４时，Ｋｎ－Ａ（｜Ａ｜＝５）都是圈长分布唯一图．     

股票的投资价值、投资理念与投资分析方法

在时股票的投资价值和投资理念进行讨论的基础上，时股票投资的基本分析方法和行为分析方法进行了较深入的探讨，时证券市场风险预警指标体系进行了设计，介绍了股市风险顸警信号界限的确定方法，建立了基于市场风险信号顸警的投资决策模型。     

The Chromatic Uniqueness of Bipartite Graphs K （ m, n ） - A with ｜ A ｜ = 2

The chromatically uniqueness of bipartite graphs K （m, n） - A（]A] = 2） was studied. With comparing the numbers of partitions into r color classes of two chromatically equivalent graphs, one general numerical condition guaranteeing that K（ m, n） - A （ I A ] = 2） is chromatically unique were obtained. This covers and improves the former correlative results.     

围长为r的圈布图最大边数的新下界

降为n的图G的圈长分布为序列{C1,C2…,Cn},其中Ci是G中长为i的圈的数目,若图G的圈长分布满足C1＝C2＝…＝Cr-2＝0,Cr＝1,且对i＝r 1,…,n,有Ci≤1,则称图G是围长为r的圈分布图,用fr(n)表示阶为n的围长为r的圈分布图最大可能的边数,本文证明：对每个整数n≥R0（其中：r＝3时,R0=17,r≥4时,R＝3r-[r/2] 5,有fr(n)≥n-r ek t 4 η。     

完全三部图K（m,n,r）的色唯一性的进一步结果

设G是简单图,用P（G,λ）表示图G的色多项式,若对任意简单图H使P（H,λ）,都有H与G 同构,则称G是色唯一图,令K（m,n,r)表示完全三部图。     

The Information Efficiency and Functionality Efficiency of Stock Markets

The efficiency of a stock market is principally measured by its information efficiency and functionality efficiency.Both metrics are closely related to the information of stock markets.However,there is no uniform definition of information in the economy field since researchers may have various opinions on the information of stock markets.In this research,a comparatively strict definition of information in sense of economy is presented.Based on this definition,the optimal conditions to reach the maximum information efficiency and functionality efficiency of stock markets are derived.The conclusion is,only when the market's operation and information transmission mechanisms are fully effective,its information completeness degree is optimal,all investors take optimal equilibrium actions,and the information efficiency and functionality efficiency of stock markets will be optimal.Based on the conclusions,the information efficiency and functionality efficiency of reality stock markets in China are studied and the corresponding supervision countermeasures are suggested.     

资本市场中代表风险资产的选择问题

针对资本资产定价模型中关于所有资产都市场化的假设的不足，探讨资本市场中代表风险资产的选择问题。给出选择代表风险资产的原则。通过选取s个代表风险资产，得出类似于资本资产定价模型的资本资产定价关系式，并对两种资产有效前沿的相切关系给出新的较完整的证明。从而使资本资产定价模型的实证检验可建立在此基础上。     

Model of Risk Forewarn and Investment Decision in Stock Markets and Its Realization

IntroductionChinese stock market is an emerging stock market.Like all emerging stock markets in other region orcountries, there are many problems in the development ofChinese stock market for insufficient experience andirregular criterion. One of the most serious problems isfrequentparoxysmal volatilityof stockprices, which resultsin a great deal of damage to investors. Table.1 lists someof large scale of volatility in shanghai stock market.Table 1　Fou…     

关于完全三部图K(n-k,n,n+k)的色性

设Ｇ为简单图,Ｐ（Ｇ,λ）的色多项式,若对任意简单图Ｈ满足Ｐ（Ｈ,λ）＝Ｐ（Ｇ,λ）,都有Ｈ与Ｇ同构,则称Ｇ是色唯一图,设Ｋ（ｍ,ｎ,ｒ）表示完全三部图,证明了：（１）对任意非负整数ｋ,若ｎ≥２√－３ｋ／３＋ｋ＾２,则Ｋ（ｎ－ｋ,ｎ,ｎ＋ｋ）是色唯一图。（２）若ｎ≥９,则Ｋ（ｎ－３,ｎ,ｎ＋３）是色唯一图。