A queueing system with linear repeated attempts,bernoulli schedule and feedback

We analyse a single-server retrial queueing system with infinite buffer, Poisson arrivals, general distribution of service time and linear retrial policy. If an arriving customer finds the server occupied, he joins with probabilityp a retrial group (called orbit) and with complementary probabilityq a priority queue in order to be served. After the customer is served completely, he will decide either to return to the priority queue for another service with probability ϑ or to leave the system forever with probability =1−ϑ, where 0≤ϑ<1. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state regime. Moreover, we obtain the generating function of system size distribution, which generalizes the well-knownPollaczek-Khinchin formula. Also we obtain a stochastic decomposition law for our queueing system and as an application we study the asymptotic behaviour under high rate of retrials. The results agree with known special cases. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.     

Value‐Distribution of General Dirichlet Series. II

In the paper, a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved.     

Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution

In this paper the problem of estimating the ratio of variances, , in a bivariate normal distribution with unknown mean is considered from a decision-theoretic point of view. First, the UMVU estimator of is derived, and then it is shown to be inadmissible under two specific loss functions, namely, the squared error loss and the entropy loss. The derivation of the results is done by conditioning on an auxiliary negative binomial random variable.     

The Weight Distribution of C 5(1, n)

In [2] the codes C _q (r,n) over were introduced. These linear codes have parameters , can be viewed as analogues of the binary Reed-Muller codes and share several features in common with them. In [2], the weight distribution of C ₃(1,n) is completely determined.In this paper we compute the weight distribution of C ₅(1,n). To this end we transform a sum of a product of two binomial coefficients into an expression involving only exponentials an Lucas numbers. We prove an effective result on the set of Lucas numbers which are powers of two to arrive to the complete determination of the weight distribution of C ₅(1,n). The final result is stated as Theorem 2.     

矩阵损失下多维几何分布均值 的线性估计可容许性

本文在矩阵损失函数 (d - λ ) (d - λ )′下讨论多维几何分布均值参数 λ的线性估计在齐次线性 估计类中的可容许性 .     

Exchangeable Random Orders and Almost Uniform Distributions

Random orders on invariant under permutations are called exchangeable. The compact and convex set of all random total orders is shown to be a Bauer simplex whose set of extreme points, the socalled totally ordered paintbox processes, is homeomorphically parametrized by almost uniform distributions on the unit interval, i.e. by probability measures w on [0, 1] whose distribution functions are w-almost surely the identity.     

The symmetry energy in nuclei and in nuclear matter

We discuss to what extent information on ground-state properties of finite nuclei (energies and radii) can be used to obtain constraints on the symmetry energy in nuclear matter and its dependence on the density. The starting point is a generalized Weizs?cker formula for ground-state energies. In particular, effects from the Wigner energy and shell structure on the symmetry energy are investigated. Strong correlations in the parameter space prevent a clear isolation of the surface contribution. Use of neutron skin information improves the situation. The result of the analysis appears consistent with a rather soft density dependence of the symmetry energy in nuclear matter.     

基于shifrin变换反演粒度分布的理论分析

理论上验证了shifrin变换粒度反演算法。采用Fraunhofer衍射理论计算前向散射光强,并利用shifrin变换进行了粒径反演。模拟结果发现,shifrin变换算法能够反演出被测单一或多分散颗粒群的粒径峰值位置,且随着接收CCD像元总数的增加,反演的准确度也会增大,但是在被反演的峰值周围会存在一定数量的小峰。随着接收衍射角的增大,也能相应地增大反演的粒径范围。中心涂黑一定数目的CCD像元并不会对反演结果造成很大的影响。     

Marginal Distributions of Wigner Function in a Mesoscopic L-C Circuit at Finite Temperature and Thermal Wigner Operator

Wigner function in phase space has its physical meaning as marginal probability distribution in coordinate space and momentum space respectively, here we endow the Wigner function with a new physical meaning, i.e., its marginal distributions’ statistical average for q ²/(2C) and p ²/(2L) are the energy stored in capacity and in inductance of a mesoscopic L-C circuit at finite temperature, respectively. PACS numbers: 03.65.-w, 73.21.-b     

Planar Line Processes for Void and Density Statistics in Thin Stochastic Fibre Networks

Using results for the distribution of perimeters of random polygons arising from random lines in a plane, we obtain new analytic approximations to the distributions of areas and local line densities for random polygons and compute various limiting properties of random polygons. Using simulation, we show that the lengths of adjacent sides of polygons generated by random line processes in the plane are correlated with ρ=0.616±0.001.