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61.
It is shown that the residue expansion of an elliptic Selberg integral gives rise to an integral representation for a multiple modular hypergeometric series. A conjectural evaluation formula for the integral then implies a closed summation formula for the series, generalizing both the multiple basic hypergeometric 87 sum of Milne-Gustafson type and the (one-dimensional) modular hypergeometric 87 sum of Frenkel and Turaev. Independently, the modular invariance ensures the asymptotic correctness of our multiple modular hypergeometric summation formula for low orders in a modular parameter. 相似文献
62.
We obtain upper bounds for mixed exponential sums of the type
where pm is a prime power with m⩾ 2 and X is a multiplicative character (mod pm). If X is primitive or p⫮(a, b) then we obtain |S(χ,f,p
m)| ⩽2np
2/3 m. If X is of conductor p and p⫮( a, b) then we get the stronger bound |S(χ,f,p
m)|⩽np
m/2.
This paper is dedicated to Prof. Wang Yuan on the occasion of his 70th birthday. 相似文献
63.
Joel M. Wisdom 《Compositio Mathematica》2000,121(1):55-78
Let R
k
(n) denote the number of representations of a natural number n as the sum of three cubes and a kth power. In this paper, we show that R
3
(n) n
5/9+, and that R
4
(n) n
47/90+, where > 0 is arbitrary. This extends work of Hooley concerning sums of four cubes, to the case of sums of mixed powers. To achieve these bounds, we use a variant of the Selberg sieve method introduced by Hooley to study sums of two kth powers, and we also use various exponential sum estimates. 相似文献
64.
Jeannette Van Iseghem 《Acta Appl Math》2000,61(1-3):351-365
The aim of this paper is the expansion of a matrix function in terms of a matrix-continued fraction as defined by Sorokin and Van Iseghem. The function under study is the Weyl function or resolvent function of an operator, given in the standard basis by a bi-infinite band matrix, with p subdiagonals and q superdiagonals, where the p + q – 1 intermediate diagonals are zero. The main goal of this paper is to find, for the moments, an explicit form in terms of the coefficients of the continued fraction, called genetic sums, which lead to a generalization of the notion of a Stieltjes continued fraction. These results are extension of some results already found for the vector case (p = 1) and are a step in the direction towards the solution of the direct and inverse spectral problem. The actual computation of the approximants of the given function as the convergents of the continued fraction is shown to be effective. Some possible extensions are considered. 相似文献
65.
M. G. Charalambous 《Applied Categorical Structures》2000,8(4):639-648
We prove results establishing sufficient conditions for the sum of two nearness frames to have enough Cauchy filters. From these results and the fact that, in the category of strong nearness frames having enough Cauchy filters and uniform frame maps, complete spatial frames form a coreflective subcategory, follow a variety of results where the open-sets contravariant functor from topological spaces to frames transforms products into sums and inverse limits into direct limits. 相似文献
66.
采用乘积近似法计算了氧化亚氮分子的总配分函数,其中转动配分函数考虑了离心扭曲修正,振动配分函数采用谐振子近似. 利用计算所得的配分函数和实验振动跃迁矩平方及Herman-Wallis因子系数,计算了氧化亚氮3000—0200和1001—0110跃迁带在常温和高温下的线强度. 结果显示,当温度高达3000K时,计算所得线强度与实验值及HITRAN数据库提供的结果仍符合较好. 这表明高温下的分子配分函数和线强度的计算是可靠的. 还进一步计算了氧化亚氮3000—0200和1001—0110跃迁带在更高温度(40
关键词:
氧化亚氮
配分函数
线强度
高温 相似文献
67.
Tian Ping ZHANG Wen Peng ZHANG 《数学学报(英文版)》2008,24(2):215-222
The main purpose of this paper is to use the properties of the Gauss sums, primitive characters and the mean value of Dirichlet L-functions to study the hybrid mean value of the error term E(n, l, c, q) and the hyper-Kloosterman sums K(h,n+1,q), the asymptotic property of the mean square value ∑^p c=1 E^2(n, 1, c, p), and give two interesting mean value formulae. 相似文献
68.
We address the probability that k or more Consecutive Customer Losses take place during a busy period of a queue, the so-called k-CCL probability, for oscillating GI
X
/M//n systems with state dependent services rates, also denoted as GI
X
/M(m)−M(m)//n systems, in which the service rates oscillate between two forms according to the evolution of the number of customers in
the system. We derive an efficient algorithm to compute k-CCL probabilities in these systems starting with an arbitrary number of customers in the system that involves solving a linear
system of equations. The results derived are illustrated for specific sets of parameters. 相似文献
69.
We derive fast recursions to compute the probability that k or more consecutive customer losses take place during a busy period of a queue, the so called k-CCL probability, for regular and oscillating M
X
/G/1/n systems. 相似文献
70.
Central limit theorem and almost sure central limit theorem for the product of some partial sums 总被引:1,自引:0,他引:1
Miao Yu 《Proceedings Mathematical Sciences》2008,118(2):289-294
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of
independent identically distributed random variables. 相似文献