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4 因子分解和解析数论我们再简单介绍一下解析数论,它的起源可以上溯到欧拉对无限求和以及无穷乘积的收敛性研究;每个学过微积分的人都知道,当s是大于1的实数时,级数ζ(s)=1+12s+13s+…+1ns+…=∑∞n=1n-s是收敛的,而s=1时,此级数发散(即其和1+12+13+…+1n+…为正无穷大);对于s>1,欧拉于1737年把这个级数写成无穷乘积的形式:∑∞1n-s=Πp11-p-s=Πp1+1ps+1p2s+…+1pms+…,其中p过所有素数,这个等式的正确性是基于算术基本定理:将上式右… 相似文献
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随机条件概率的一个极限性质与条件矩母函数方法 总被引:7,自引:0,他引:7
设Xn,n〉0是在s=1,2,…,N中取值的一列随机变量,pk(xk↓x0,…xk-1)=p(Xk=xk↓X0=xk-1=xk-1)。本文得到随机概率{pk(Xk↓X0,…Xk-1),1〈k〈n↓)的调和平均a.e.收敛的一个定理.证明中提出了将关开网的微分法和条件矩母函数的工具应用于强极限定理的研究的一种途径。 相似文献
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qq±1(q=pn)的Aurifeuilian分解孙琦洪绍方(四川大学数学系)摘要设素数p≡ε(mod4),其中ε=1,-1,n为正整数,q=pn,q1=qq/p,η=ηq=exp(2πi/q).Φm(x)表示m阶分圆多项式.记Sε=Φq(εq),本... 相似文献
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§1. IntroductionLet:H:Rn×Rn→RbeasmoothHamiltonfunction(q,p)→H(q,p)G:Rn×Rn→R2nbesmoothoperator(q,p)→G(q,p)=(g1(q,p),…,g2n(q,p)). Wedefinetwospaces:L=span{gi,{H,gi},{H,{H,gi}},…,i=1,2,…,2n}dL(z)={df(z)|f∈L} z∈Rn×Rn.Here{,}ispoissonbracket.Throughoutth… 相似文献
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笔者在文[1]对于初等对称函数Ek(x)=Ek(x1,…,xn)=∑1≤i1<…<ik≤nΠkj=1xij,k=1,2,…,n建立了定理1设xi>0,i=1,2,…,n且∑ni=1xi=1,则对于k=1,2,…,n,有0≤Ek(1-x)-Ek(x)≤... 相似文献
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我们看两类函数(1){af(n)} (n=1,2,…)(2){f(an)} (n=1,2,…)如果数列(1)、(2)是等差(比)数列,那么我们把它们称为复合等差(比)数列.于是,af(n)=af(1)+(n-1)d或af(n)=af(1)qn-1.例1 数列{an}满足2S2n=2anSn-an(n≥2),a1=2,求an及Sn.解 将an=Sn-Sn-1(n≥1)代入等式,得 2SnSn-1=Sn-1-Sn.因为a1=2≠0,故Sn≠0,上式可变为1Sn-1Sn-1=2,∴ 数列{1Sn… 相似文献
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关于Gross问题的一个注记 总被引:6,自引:0,他引:6
本文研究亚纯函数的唯一性,得到了如下结果.设S={z:z3-z2-1=0},f(z)与g(z)是满足Θ(∞,f)>12,Θ(∞,g)>12,的两个非常数亚纯函数.若E(0,f)=E(0,g),E(S,f)=E(S,g)以及E(∞,f)=E(∞,g),则f(z)≡g(z).这个结果彻底解决了Gross[3]于1976年提出的一个问题 相似文献
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拟合隐函数曲线的GNL法 总被引:5,自引:1,他引:4
朱珉仁 《高等学校计算数学学报》1999,21(3):269-276
1参数可线性化的曲线拟合问题假设我们已经获得n组独立观测值(xi,yi),其中是精确观测值,i=1,2,…,n,下同.现欲在最小二乘意义下,拟合非线性模型并假设观测点都分布在模型函数曲线附近.其中为连续可导函数g(y)的反函数,且在我们所研究的y变化范围内恒有g’(y)≠0,(j=1,2.....下同)为p(<n)个待定参数.(x)为区间X内p个线性无关的已知连续函数.随机变量,即为也就是要求求解残差平方和Q()的无条件极值问题其中参数向量,残差向量,而残差都是微量.对这类常见问题,有以下几种算法.… 相似文献
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Nicholas C Yannelis 《Journal of Mathematical Analysis and Applications》1985,108(2):595-599
A direct proof is given of the market equilibrium theorem of Gale, Nikaido and Debreu for an infinite-dimensional commodity space. The theorem is closely related to a recent result of Aliprantis and Brown, but allows for excess demand correspondences rather than excess demand functions. 相似文献
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We consider an algebraic method for reconstruction of a function satisfying the Poisson equation with a polynomial right-hand side in the unit disk. The given data, besides the right-hand side, is assumed to be in the form of a finite number of values of Radon projections of the unknown function. We first homogenize the problem by finding a polynomial which satisfies the given Poisson equation. This leads to an interpolation problem for a harmonic function, which we solve in the space of harmonic polynomials using a previously established method. For the special case where the Radon projections are taken along chords that form a regular convex polygon, we extend the error estimates from the harmonic case to this Poisson problem. Finally we give some numerical examples. 相似文献
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Norman Biggs 《Journal of Algebraic Combinatorics》1999,10(2):115-133
The 'dollar game' represents a kind of diffusion process on a graph. Under the rules of the game some cofigurations are both stable and recurrent, and these are known as critical cofigurations. The set of critical configurations can be given the structure of an abelian group, and it turns out that the order of the group is the tree-number of the graph. Each critical configuration can be assigned a positive weight, and the generating function that enumerates critical configurations according to weight is a partial evaluation of the Tutte polynomial of the graph. It is shown that the weight enumerator can also be interpreted as a growth function, which leads to the conclusion that the (partial) Tutte polynomial itself is a growth function. 相似文献
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Maw Lin Lee 《Mathematical Social Sciences》1984,7(2):167-175
This paper develops a conceptual framework for including demographic variables in economic analysis of the demand for medical care, given the demand for health. The individual's need for medical care is defined and the process of satisfying the need is recognized. Thus, demographic factors are used to restrict the consumption space to a relevant subset in the commodity space. The restriction of the consumption space enables demographic variables to be included in a theoretical analysis of utility maximization. The inclusion of demographic variables in turn implies the dependency of income and price elasticities on nonbudgetary factors. 相似文献
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假设函数f(z)是亚纯函数,H(z,f)是关于f(z)的差分多项式,s(z)是关于f(z)的小函数,考察了差分多项式f(z)~nH(z,f)-s(z)的零点分布问题.首先得到了差分多项式f(z)~nH(z,f)-s(z)的零点计数函数和函数f(z)的特征函数以及极点计数函数之间的一些不等式估计,再根据这些不等式,建立了Hayman关于亚纯函数的一个经典结果的差分模拟. 相似文献
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In this paper we prove that if a function of a certain smoothness class is represented by a sum of r arbitrarily behaved ridge functions, then, under suitable conditions, it can be represented by a sum of ridge functions of the same smoothness class and some polynomial of a certain degree. 相似文献
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《European Journal of Operational Research》2001,131(1):162-170
Situations abound in the real world, where aggregate demand for a commodity exceeds aggregate supply. When such situations of excess demand occur, what is required is some kind of rationing. The literature on rationing problems has an interesting origin in the Babylonian Talmud. The purpose of this paper is to characterize axiomatically and analyze the constrained equal award solution for rationing problems. 相似文献
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Nasser-eddine Tatar 《Mathematical Methods in the Applied Sciences》2008,31(15):1874-1886
We consider a linear viscoelastic problem and prove polynomial asymptotic stability of the steady state. This work improves previous works where it is proved that polynomial decay of solutions to the equilibrium state occurs provided that the relaxation function itself is polynomially decaying to zero. In this paper we will not assume any decay rate of the relaxation function. In case the kernel has some flat zones then we prove polynomial decay of solutions provided that these flat zones are not too big. If the kernel is strictly decreasing then there is no need for this assumption. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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In this article, we provide estimates for the degree of V bilipschitz determinacy of weighted homogeneous function germs defined on weighted homogeneous analytic variety V satisfying a convenient Lojasiewicz condition.The result gives an explicit order such that the geometrical structure of a weighted homogeneous polynomial function germs is preserved after higher order perturbations. 相似文献