Asymptotic analysis of a large closed queueing network with discriminatory processor sharing

In this paper the steady-state behavior of a closed queueing network with multiple classes and large populations is investigated. One of the two nodes of the network simply introduces random delays and the discipline in the other node is discriminatory processor sharing. The network is not product-form, so not even the steady-state behavior is known. We assume that the usage is moderately heavy, and obtain two-term asymptotic approximations to the mean number of jobs, and the mean sojourn time, of each class of jobs in the processor node. We also obtain the leading term in the asymptotic approximation to the joint distribution of the number of jobs in the processor node, which is a zero-mean multivariate Gaussian distribution around a line through the origin.     

“选择资费”的多重价格歧视特性

本文在分析电信业选择资费实例和价格结构的基础上 ,研究了选择资费中的三级和二级价格歧视 ,并提出了多重价格歧视的概念 .研究结果表明 ,电信公司在选择资费中综合运用了三级、二级价格歧视 ,且通过提供多个二部资费计费方案 ,达到双重二级价格歧视和优化二部资费的目的 .选择资费是电信公司应对市场竞争的一种定价策略 ,认识其经济特性有利于我国电信公司和电信管制部门进行科学决策     

应用逐步统计判别模型预报麦蚜复合种群动态

本文应用逐步统计判别原理 ,对山东省曲阜地区 1982～ 1994年共 13年麦蚜复合种群动态的系统调查资料进行了统计分析 ,建立了 4个统计判别数学模型 :dy1=0 .1 343x1- 0 .1 472x2 ;　　y2 =0 .740 9x1- 0 .1 1 85x2 ;y3=- 8.391 5x1- 1 .785 6x2 ;　y4=2 .32 40x1- 0 .30 82x2运用所建模型 ,对历史资料进行回代验证 ,其平均历史拟合率在 93%以上 ,并以 1 995年作为独立样本进行试报 ,结果与实际一致。     

High-power continuous-wave operation of a diode-pumped laser at

The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO₄ crystal operating at formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd³⁺-doped concentration of Nd:GdVO₄ crystals were studied.     

Studies on the conformation of α-arylcinnamic acids and their esters: Crystal structures of methyl (E)-2,3-bis(3,4-dimethoxyphenyl)propenoate and methyl (Z)-2,3-bis(3,4-dimethoxyphenyl)propenoate

The conformations of stereoisomers of -arylcinnamic acids and their esters are discussed based on crystal structures of the E and Z forms of 2,3-bis(3,4-dimethoxyphenyl)propenoic acid and its methyl ester. In the E forms of the cinnamic acid and the cinnamic acid ester, the plane of the -aryl substituent is approximately perpendicular to that of the rest of the molecule. In the Z forms the plane of the carboxyl or methoxycarbonyl group is approximately perpendicular to that of the ethylenic group, and both the aromatic group planes are significantly twisted out of the ethylenic group plane. Crystal structures of methyl (E)-2,3-bis(3,4-dimethoxyphenyl)propenoate (space group P2₁/n with a = 8.1697(5), b = 11.3882(9), c = 19.7766(9) Å, = 90.058(4)°, V = 1840.0(2) ų, and Z = 4), monoclinic methyl (Z)-2,3-bis(3,4-dimethoxyphenyl)propenoate (space group P2₁/n with a = 11.183(2), b = 5.640(2), c = 29.737(7) Å, = 99.19(2)°, V = 1851.4(9) ų, and Z = 4), and orthorhombic methyl (Z)-2,3-bis(3,4-dimethoxyphenyl)propenoate (space group P2₁2₁2₁ with a = 8.849(4), b = 24.288(9), c = 8.734(3) Å, V = 1877(1) ų, and Z = 4) are reported.     

Optimization and analysis of the profitability of tariff structures with two-part tariffs

Service providers often offer tariff structures with several two-part tariffs that consist of a fixed fee and a usage price, such that consumers may pick the tariff they prefer. Prices of tariffs have significant impacts on service providers’ profit, because they simultaneously influence consumers’ tariff choices and their usage. The number of tariffs also plays an important role, because more tariffs segment the market better but also increase the administrative burden and require more marketing effort. This article presents a mixed-integer nonlinear programming optimization problem to determine profit-maximizing tariffs; compares several heuristic search methods, in particular, the gradient method, stochastic search, and simulated annealing, to solve this problem; analyses the profitability of different tariff structures; and outlines the factors that drive differences in profitability across various tariff structures. The results show that especially for large samples of more than 100 consumers, simulated annealing performs best and deviates only 0.2% from the optimum. Structures with fewer two-part tariffs are generally sufficient, because additional two-part tariffs only negligibly increase service providers’ profit.     

σ-多项式的根

§ 1　IntroductionAll graphs considered are finite and simple.Undefined notation and terminology willconform to those in[1 ] .Let V(G) ,E(G) and Gdenote the vertex set,edge set and complement of a graph G,respectively. Let P(G,x) andσ(G,x) denote the chromatic polynomial andσ-polynomialof G,respectively.The log-concavity property of the chromatic polynomial andσ-polyno-mial of G has a close relation to their roots,which were well studied in[2 ,3] .Results onthe study of the roots of…     

用逐步二级分辨数学模型预测农业害虫种群动态

文章应用基本Ｆｉｓｈｅｒ准则下逐步二级分辨原理，对山东省临沂市１９６５～１９８６年（１９８０年除外）共２１年的第二代玉米螟虫株率的历史观测数据进行了数量分析，建立了３个逐步二级分辨数学模型。经对历史资料的回报验证，其历史符合率分别为９５．２４％、９２．３１％、１００％。将１９８７年、１９８８年观测数据作为独立样本进行试报，其预报结果与实际一致。     

两阶段双寡头垄断市场Hotelling定价模型

激烈的双寡头垄断市场竞争环境下,单一定价和歧视定价成为厂商选择的两大定价策略.考虑到网络外部效用的广泛存在性与对称性,对传统的Hotelling模型加以改进,分价格竞争和策略选择两个阶段,对双寡头垄断厂商的定价策略进行了博弈分析,指出了各种均衡情况及需满足的条件,并验证了歧视定价相对单一定价的边际成本、网络外部效应、消费者对产品的忠诚度等因素对厂商进行定价策略选择的重要影响,为其制定最优定价策略提供了指导.     

An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.