用顶点的平均K-度表示图的谱半径的上、下界

设图G=(V,E)是简单连通图,顶点集V(G)={v1,v2,…vn},度序列d1,d2,…dn。对于顶点vi∈V(G,记N(vi)={v∈V∣viv E}的邻点集,则顶点vi的度di=|N(vi)|。顶点vi的k-度记为d(k)i=Σvj∈N(vi)d(k-1)j,顶点vi的平均k-度定义为d(k)i=d(k)id(k-1)i,这里k是正整数并且d(0)i=1,d(1)i=di=d(1)i设ρ(G)是G的谱半径。在本文中,我们用d(k)i表示ρ(G)的上、下界。从我们的结果可以得出一些已知的结果,并且我们的结果通常比其他结果好。     

关于积分integral (t~λφ(t+α)dt) from t=0 to z的一种计算方法

本文应用引理1中所提到的Ramanujan的公式和引理2给出的公式,使用解析数论中的方法得到了定积分integral (t~λφ(t+α)dt) from t=0 to z一种计算方法,该结果使得积分integral (t~λφ(t+α)dt) from t=0 to z的计算问题得到彻底解决。     

个人所得税对社会公平的影响

<正>一、模型和数据本文尝试建立一个简单的模型来分析个人所得税和社会公平的相关关系:模型一:distcpiit=β0+β1inctotit+β2wthit+β3fetccpiit+β4ratioapit+β5eduit+μit在模型一中,下标i和t(t=1998,…,2006)分别代表第i个省份和第t年,样本包括了全国31个内地省、直辖市和自治区,μ是残差项。     

黎卡提方程的两种变换

将黎卡提方程dy/dx+ay2=bxmm=0,-2,-4k/2k+1,-k4/2k-1,(k=1,2,…),通过适当的变换化为变量分离的方程;将黎卡提方程dy/dx=p(x)y2+q(x)y+r(x),通过适当的变换化为u'=r2+f(x)的形式。     

财务风险度量方法评析

财务风险的度量是用一系列财务指标分析财务风险,认识、判断企业财务风险大小的活动过程。围绕财务风险的不确定性与风险损失有三种风险度量方法,即均值-方差法、Downside-Risk法和风险资产度量法(ValueatRisk)法。一、均值-方差法马柯维茨的“均值-方差”法是在未来投资报酬的随机结果服从正态分布的条件下,用平均值和方差两个参数度量平均报酬的总体离差,来判断风险的程度。风险计量模型为:E(R)=R=ni=1∑RiPiK=Var[E(R)]=Var(R)其中,R i表示投资报酬各种可能的结果,Pi表示第i种投资报酬结果出现的概率,R表示投资报酬的平均值,K表…     

基于组合预测的营业活动现金流量分析

一、营业活动现金流组合预测模型构建 设对同一预测对象的某个指标序列{xt，t=1,2…n}存在m种可行单项预测方法对其进行预测，设第i种单项预测方法在第t时刻的预测值为xit,i=1，2，…m；t=1，2，…，n；设l1，l2，…，lm分别为m种单项预测方法的加权系数，加权系数应该满足∑i=1 ^m li=1,li≥0，i=1，2，…，m。     

无截距项的经济计量模型的最小二乘法估计

在经济计量学中,一般的单方程线性经济计量模型(简称为模型)形如:Y_i=β_0+β_1X_(1i)+β_2X_(2i)+…+β_kX_(ki)+u_i (i=1,2,…,N,下同) (1)式中:Y为应变量;x_1、x_2……x_k为K个解释变量;u为随机扰动项;β_0、β_1……β_k为参数,β_0亦称为截距项,β_1,…,β_k亦称为偏回归系数;N为观察值数。     

论价格指数与增加价值指数的关系：—兼与宋佰谦同志商榷

由价值型投入产出(纵向)模型可知 (1) (2)其中V是增加价值行向量;E=(1,1,…,1)是每个分量都等于1的n维行向量;I是单位矩阵;A是价值型投入系数矩阵;X是总产值行向量,X=diag(X_1,X_2,…,X_n)是以X的分量为主对角线元素的对角矩阵(下文类似);P是价格指数行向量;变量的上标0和1分别表示价格变动前和变动后。由(1)和(2)式显然有     

盈余反应系数及其研究动因初探

一、盈余反应系数的含义 "盈余反应系数"(ERC) 是实证会计领域的一个专有名词.对其的一般理解来自如下线性模型: CARit=Pit-1+bUXit+eit (1) 其中:CARit表示对证券i在时期t的累计风险调整报酬率;UXit表示市场对证券i在时期t的未预期盈余;Pit-1表示证券i期初股票价格,作为平减因子;eit为随机分布项[服从N(0,σe2)分布];斜率(b)就是ERC.     

浅谈功能评价值的确定

<正> 功能评价有两种方法。一种是对功能评分的办法,称“功能评价系数法”,表达式为: V_i=(f_i/sum from i=1 to n(f_i))/(C_i/sum from i=1 to n(C_i)式中:V_i——第i项功能的价值系数; f_i——第i项功能的得分; C_i——第i项功能的成本; n——功能个数(或项数)。 另一种是对功能采用货币计算的办法,称“功能成本法”,国外应用较广,用下式表示:     

Inequalities relating maximal moments to other measures of dispersion

Let X , X ₁, ..., X_k be i.i.d. random variables, and for k ∈ N let D_k ( X ) = E ( X ₁ V ... V X _{k +1}) − EX be the k th centralized maximal moment. A sharp lower bound is given for D ₁( X ) in terms of the Lévy concentration Q_l ( X ) = sup _{x ∈ R} P ( X ∈[ x , x + l ]). This inequality, which is analogous to P. Levy's concentration-variance inequality, illustrates the fact that maximal moments are a gauge of how much spread out the underlying distribution is. It is also shown that the centralized maximal moments are increased under convolution.     

一类有理型时滞差分方程的稳定性研究

在这篇文章中,我们研究如下形式的有理型时滞方程xn+1=(β4xn-4/A+B4xn-4)+Cxn-k-4,n=0,1,2,…的稳定性,得到了上述方程零解渐近稳定的充分条件,其中A,C,β4,B4是实常数,且A≠0,C≠0,k>1正整数。     

On a crossroad of resampling plans: bootstrapping elementary symmetric polynomials

We investigate the validity of the bootstrap method for the elementary symmetric polynomials S ^{( k )} _n =( ⁿ _k )⁻¹Σ_{1≤ i 1}< ... < i _k ≤ n X _{i 1} ... X _{i k} of i.i.d. random variables X ₁, ..., X _n . For both fixed and increasing order k , as n→∞ the cases where μ=E X ₁[moe2]0, the nondegenerate case, and where μ=E X ₁=0, the degenerate case, are considered.     

s=4的完全多部图K_(a_1n_1,a_2n_2,…,a_sn_s)的无符号Laplace特征多项式

文中计算得到了完全多部图K(n1,n2,…,n)t=Ka1n1,a2n2,…,asns当s=4时的无符号Laplace特征多项式。     

On characterizations of distributions by regression of adjacent generalized order statistics

Let , r ≥ 1, denote generalized order statistics, with arbitrary parameters , based on distribution function F. In this paper we characterize continuous distributions F by the regression of adjacent generalized order statistics, i.e. where are continuous and increasing functions and ψ is strictly increasing. Further we investigate in detail the case when ψ(x) = x and g is a linear function of the form g(x) = cx + d for some .     

Banach代数上的Jordan kth偏导子的稳定性

设A1,A2,…,An是复数域上的赋范代数,B是复数域上的Banach代数,本文刻画了Jordan kth偏导子δk:A1×…×An在一定条件下的稳定性。     

A note on minimum variance

Summary Minimizing is discussed under the unbiasedness condition: and the condition (A):f _i (x) (i=1, ..., p) are linearly independent , and .     

Een model voor discreet verdeelde grootheden met negatieve correlatie

Summary
A model for negatively correlated variables.
A mathematical model is described with which a bivariate distribution of two negatively correlated binomially distributed variables can be constructed. Let be given a vase with W white, Z black and R red balls; N = W + Z + R; P1= W: N;P2 = Z: N.
Let be drawn a random sample with replacement of n balls. Let be w = number of white en z = number of black balls; w + z < n. Then and are binomially distributed variates, correlated according to (1).
At the end of the paper the author formulates the following statistical problem: let be drawn a finite number of times () such random samples of n balls. The pairs w, z furnish a correlation coefficient r, which itself is a stochastical variable. How is the distribution of? In particular what are the expectation (, N) and the standard deviation (k, n, N)     

Een Monte-Carlo-bepaling van overschrijdingskansen, in verband met een keuzetest

A Monte-Carlo method for a test of significance, applied to points on a lattice, in connection with a vocational preference test, by C. A. G, Nass.
Appendix by Constance van Eeden.
A periodical rectangular lattice, with a period of k.m, is considered. Thus there are N = k.m points on the lattice, repeated in the two perpendicular directions. Two points are said to be "connected" if they are adjacent in a straight or diagonal way. Thus, if k and m 3, every point is connected with 8 other pooints. Out of the N points of the lattice, n points are selected and the total number of connections x, of all possible pairs of those n points is considered for a vocational preference test with k = m = 9, N = 81, n = 10. The problem is to test whether the sum y = x₁+…+ x*** from a sample of h values of x, is significantly small, under the hypothesis that in the h cases the n points are selected at random with equal chance. A Monte-Carlo sample of 100 values of x was taken, using random numbers. For h = 1, the problem was solved by the determination of P( y x₁), assuming that y is taken at random from the 101 values of x, supplied by the Monte-Carlo sample and x₁ for fixed values of x₁. For h - 2, a similar solution is given. For greater values of h, Student's two-sample test, with correction for continuity is suggested. For h = 2 the results of Student's test are compared with those of the solution mentioned above.
In the appendix a summary is given of results found by P.A.P Moran and P. V. Krishna Iyer for some closely related problems. Further some results concerning exact distributions, moments and asymptotic distributions for C. A. G. Nass' problem are given. The proofs of these results may be found in a paper by C. van Eeden and A. R. Bloemena (1959).