Jordan函数r次方Jk^r（n）的误差项的进一步性质

设k，r分别是自然数和非零整数，Jk(n)是Jordan函数．以E(x；k，r)表示和式∑n≤xJk^r(n)的渐近公式中的误差项，本文研究了E(x；k，r)的某种加权平方积分均值．     

广义的Landau误差项研究

设ψ（n)是Euler函数,r是正整数,以E（x,r)表示和式∑n≤x(n/ψ(n))^r的渐近公式中的误差项,本文研究了E(x;r)算子均值和积分均值。     

广义Dedekind函数误差项的加权平方积分均值

研究了和式∑↑n≤x（n/ψ（n））^r的渐近公式中的误差项E（x;r）的加权平方积分均值。其中，r是正整数，ψ(n)是Dedekind函数。     

一道Lebesgue积分题目的注记

设E为n维欧氏空间Rn的可测子集,m E+∞,f(x)为E上的非负可测函数,并记Ek=E{x|k≤f(x)k+1}(k=0,1,2,…),利用Lebesgue积分的性质,通过构造反例,指出"级数∑k km Ek收敛"并不是f(x)在E上Lebesgue可积的充分条件.进一步,通过增加条件"f在E上a.e.有限",得到相应的充分必要条件.     

（mg＋k,mf—k）—图中正交于r个不相交子图的边不变的（g,f）—因子

设m,k和r为正整数,且使l≤k＜m.设G是一个具有顶点集合V(G)和边集合E(G)的图,并设g和f是定义在V(G)上的使对每个x∈V(G)有r≤g(x)≤f(x)的整数值函数.设H1,H2,…,Hr是G的r个顶点不相交的子图且|E(Hi)|=k,1≤i≤r.本文证明了每个(mg+k,mf-k)-图有k个边不相交的(g,f)-因子正交于Hi,1≤i≤r.     

广义Carmichael数

设n是一个合数,Z_n表示模n的剩余类环,r(x)∈Z_n[x]是一个首一的k(>0)次不可约多项式。本文引入n是k阶摸r(x)的Carmichael数的定义,全体这样的数记为集C_(k,r)(x),由此给出k阶Carmichael数集:C_k={∪C_(k,r)(x)|r(x)过全体Z_n上的首一k次不可约多项式}。显然C_1表示通常的Carmichael数集。作者得到了n∈C_(k,r(x))的一个充要条件,进而得到n∈C_k的一个充要条件及n∈C_2的一个更易计算的充要条件,还证明了C_1(?)C_2以及|C_2|=∞。     

关于积分∫f(x,{Nx})dx带准确余项的渐近展开式的一种新证明

本文对于积分from n=0 to 1 f(x,{Nx})dx带准确余项的渐近展开式from n=0 to 1 f(x,{Nx})dx=from n=0 to 1 from n=0 to 1f(x,y)dxdy+sum from k=1 to r 1/(k!) (1/N)~k from n=0 to 1[f~((k-1,0))(1,y)(?)_k(y-N)-f~((k-1,0))(O,y)B_k(y)]dy-1/(r|)(1/N)~r from n=0 to 1 from n=0 to 1 f~((r,O))(x,y)(?)_r(y-Nx)dxdy给出了一种简捷的推导,这种推导只需普通的分析知识,无需用到Euler-Maclaurin求和公式及Bernoulli多项式的Raabe乘积定理。     

用Newman型有理算子对|x|的逼近的渐近性质

设p(x)=∏k=1n=1((k/n)r z),0相似文献   

关于图中子图的（n,k）—正交因子分解

设G是一个具有顶点集V(G)和边集E(G)的图. 设g和f是定义在V(G)上的两个整数值函数,使得g(x)f(x)对所有的点x∈V(G)都成立.如果G是一个(mg+n,mf-n)-图,1n<m2k,且g(x)2k-1对所有的点x∈V(G)都成立,则对任意给定具有|E(H)|=nk边的G的子图H,存在G的一个子图G′使G′有一个(g,f)-因子分解(n,k)-正交H.     

q-差分内积中的小q-Jacobi-Sobolev多项式

本文讨论了关于以下内积的正交多项式 :〈p(x) ,r(x)〉( u0 ,u(α,β) ) =∑∞k=0p(qk) r(qk) (qk-c) ak(b) k(q) k +λ∑∞k=0(Dqp) (qk) (Dqr) (qk) (aq) k(bq) k(q) k给出了它的一些代数性质以及和小 q-Jacobi多项式的关系 ,得到了在 C\([0 ,1 ]∪ H )的紧子集上Qn(x)P(α- 1,β- 1)n (x) n和 Pn(x)P(α- 1,β- 1)n (x) n的相对渐近性质 .其中 Qn(x)是 n次的小 q -Jacobi-Sobolev正交多项式 ,P(α- 1,β- 1)n (x)和 Pn(x)分别是关于线性泛函 u(α- 1,β- 1)和 u0 的首一的 n次正交多项式 .     

On the distributions of the ratios of the extreme roots to the trace of the Wishart matrix

In this paper, the authors cosider the derivation of the exact distributions of the ratios of the extreme roots to the trace of the Wishart matrix. Also, exact percentage points of these distributions are given and their applications are discussed.     

On the comparison between the APV and the NPV computed via the WACC

The valuation of levered investment in the practice is made with the WACC approach, even if the superior technique of the APV is available. The paper shows that the APV can be interpreted as the arbitrage free value of the portfolio made by an investment and a supporting loan. Therefore the WACC evaluation, generally different from the APV, allows for arbitrage. We provide various conditions which completely characterize the sign of the error as a functions of all the variables entering the model.     

用常微分方程模型分析预防和隔离措施对SARS发病率的影响

通过建立常微分方程模型 ,分析了预防和隔离措施对 SARS发病率的影响 ,并把计算结果与实际统计数据进行了比较 ,结果表明 ,及时高效的预防和隔离措施能够有效地控制 SARS的传播 .     

On the Gap in the Spectrum of the Translations

The spectrum of the translations in local quantum field theory will be analyzed in order to show that in a positive energy representation without vacuum vector and with lowest mass m₁ there is no gap in the spectrum which is larger than 2m₁. In particular in a zero mass representation there is no hole at all. These results are obtained with methods of analytic functions of several complex variables.     

From the subalgebras of the square to the discriminator

Presented by A. F. Pixley.     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

On the depth of the tangent cone and the growth of the Hilbert function

For a dimensional Cohen-Macaulay local ring we study the depth of the associated graded ring of with respect to an -primary ideal in terms of the Vallabrega-Valla conditions and the length of , where is a minimal reduction of and . As a corollary we generalize Sally's conjecture on the depth of the associated graded ring with respect to a maximal ideal to -primary ideals. We also study the growth of the Hilbert function.