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排序方式: 共有38条查询结果,搜索用时 62 毫秒
1.
Order statistics applications to queueing and scheduling problems   总被引:1,自引:0,他引:1  
We prove several basic combinatorial identities and use them in two applications: the queue inference engine (QIE) and earliest due date rule (EDD) scheduling. Larson (1990) introduced the QIE. His objective was to deduce the behavior of a multiserver queueing system without observing the queue. With only a Poisson arrival assumption, he analyzed the performance during a busy period. Such a period starts once all servers are busy with the queue empty, and it ends as soon as a server becomes idle. We generalize the standard order statistics result for Poisson processes, and show how to sample a busy period in the M/M/c system. We derive simple expressions for the variance of the total waiting time in the M/M/c and M/D/1 queues given that n Poisson arrivals and departures occur during a busy period. We also perform a probabilistic analysis of the EDD for a one-machine scheduling problem with earliness and tardiness penalties. The schedule is without preemption and with no inserted idle time. The jobs are independent and each may have a different due date. For large n, we show that the variance of the total penalty costs of the EDD is linear in n. The mean of the total penalty costs of the EDD is known to be proportional to the square root of n (see Harel (1993)). This revised version was published online in June 2006 with corrections to the Cover Date.  相似文献
2.
Applications of residues to combinatorial identities   总被引:1,自引:0,他引:1  
A concrete aspect of Grothendieck Duality is used to give local cohomology proofs of combinatorial identities including MacMahon's master theorem, Grosswald identity, identity of Shoo, Tepper identity, and others.

  相似文献

3.
新型组合恒等式(一)   总被引:1,自引:0,他引:1  
新型组合恒等式是研讨别开生面的几类组合孪生恒等式组的问题.本要主要研讨互逆类的组合孪生恒等式组,该类可分为多项式型、二项式定理型、指数函数型以及三角函数(或双曲函数)型等四型,一批成双出现的新结果。与许多著名数列(Fibonacci数列、Bernoulli数、Euler数以及二项式定理系数数列等)有着密切关系.此外,本人还研讨了一类特殊行列式的性质及其应用。  相似文献
4.
一个组合恒等式的推广   总被引:1,自引:0,他引:1       下载免费PDF全文
本文推广了文[1]中的一个组合恒等式.  相似文献
5.
Identities on Bell polynomials and Sheffer sequences   总被引:1,自引:0,他引:1  
In this paper, we study exponential partial Bell polynomials and Sheffer sequences. Two new characterizations of Sheffer sequences are presented, which indicate the relations between Sheffer sequences and Riordan arrays. Several general identities involving Bell polynomials and Sheffer sequences are established, which reduce to some elegant identities for associated sequences and cross sequences.  相似文献
6.
By modifying Beukers' proof of Apéry's theorem that is irrational, we derive criteria for irrationality of Euler's constant, . For 0$">, we define a double integral and a positive integer , and prove that with the following are equivalent:

1. The fractional part of is given by for some .

2. The formula holds for all sufficiently large .

3. Euler's constant is a rational number.

A corollary is that if infinitely often, then is irrational. Indeed, if the inequality holds for a given (we present numerical evidence for and is rational, then its denominator does not divide . We prove a new combinatorial identity in order to show that a certain linear form in logarithms is in fact . A by-product is a rapidly converging asymptotic formula for , used by P. Sebah to compute correct to 18063 decimals.

  相似文献

7.
组合恒等式     
本文利用函数1f(x)展开式定理,导出一批新的组合恒等式.  相似文献
8.
The multidimensional sum with polynomial coefficients is computed with the help of the method of integral representation and computation of combinatorial sums. This sum was obtained in the attempt to prove the well known Jacobian conjecture (two-dimensional case). Supported in part by the Natural Sciences and Engineering Research Council of Canada on Grant NSERC-108343 and the Russian Fund of Fundamental Researches.Mathematics Subject Classifications (2000) combinatorics, algebra.  相似文献
9.
徐利治 《数学研究》1995,28(1):11-13
本文给出了含有调和数的一类组合和的求和公式.该公式有二熟知特例.  相似文献
10.
孙平 《数学学报》2007,50(2):373-384
利用概率论与组合数学的方法,研究了与Riemann-zeta函数ξ(k)的部分和ξ_n(k)有关的一些级数,计算出了一些重要的和式.特别的,Euler的著名结果5ξ(4)= 2ξ~2(2)能够从四阶和式直接推出.因此,通过计算全部的11个六阶和式,研究它们之间的非平凡关系,就有可能得到ξ(3)的数值.  相似文献
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