Approximations for Markovian multi-class queues with preemptive priorities

We discuss the approximation of performance measures in multi-class M/M/k queues with preemptive priorities for large problem instances (many classes and servers) using class aggregation and server reduction. We compared our approximations to exact and simulation results and found that our approach yields small-to-moderate approximation errors.     

Bayesian Prediction Analysis for Growth Curve Model Using Noninformative Priors

We apply a Bayesian approach to the problem of prediction in an unbalanced growth curve model using noninformative priors. Due to the complexity of the model, no analytic forms of the predictive densities are available. We propose both approximations and a prediction-oriented Metropolis-Hastings sampling algorithm for two types of prediction, namely the prediction of future observations for a new subject and the prediction of future values for a partially observed subject. They are illustrated and compared through real data and simulation studies. Two of the approximations compare favorably with the approximation in Fearn (1975, Biometrika, 62, 89–100) and are very comparable to the more accurate Rao-Blackwellization from Metropolis-Hastings sampling algorithm.     

Sufficient optimality conditions in nondifferentiable optimization ∗

The concept of local cone approximations, introduced in recent years by Ester and Thierfelder, is a powerful tool for establishing optimality conditions. In this paper we show how to use it for obtaining sufficient optimality conditions in nondifferentiable optimization     

Dynamic fracture model for acoustic emission

We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function q(x) is computed at high orders in powers of τ = T _c - T and H. We find that none of the Parisi-Toulouse scaling hypotheses on the q(x) behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the q(x). At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite τ. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field. Received 3 March 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: andrea.crisanti@phys.uniroma1.it RID="b" ID="b"e-mail: tommaso.rizzo@phys.uniroma1.it RID="c" ID="c"e-mail: temtam@helios.elte.hu     

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.     

Stability and approximations of eigenvalues and eigenfunctions for the Neumann Laplacian, Part 2

We extend the results obtained earlier in a joint paper with R. Banuelos, on the stability and approximations of the second Neumann eigenvalue and its corresponding eigenfunction, to the case when the second Neumann eigenvalue has multiplicity at least 2. We then show that our stability result can be applied to the Koch snowflake and the usual sequence of polygons approximating it from inside.     

Application de l'approximation polytropique à la Simulation Numérique Directe de gaz chaudsApplication of the polytropique approximation to Direct Numerical Simulation of heated gases

As alternative to the usual assumptions of Boussinesq, we propose, for heated gases, a new approximation called polytropic approximation. With this approximation the quantities of corresponding state are related by a polytropic law of exponent χ of which we neglect the variability in space-time derivations in the equations governing the flow considered. As application, we used this new proposition to solve numerically a heated gas flow in an annular cavity of rotor-stator type. We expose here the numerical method and some results of the polytropic approximation with comparison to results of Boussinesq approximations. To cite this article: S. Benjeddou et al., C. R. Mecanique 332 (2003).     

基于Nie-Tan算法的区间二型模糊集质心计算:改变主变量采样个数

计算区间二型模糊集的质心(也称降型)是区间二型模糊逻辑系统中的一个重要模块。Karnik-Mendel(KM)迭代算法通常被认为是计算区间二型模糊集质心的标准算法。尽管如此,KM算法涉及复杂的计算过程,不利于实时应用。在各种改进类算法中,非迭代的Nie-Tan(NT)算法可节省计算消耗。此外,连续版本NT(CNT,continuous version of NT)算法被证明是计算质心的准确算法。本文比较了离散版本NT算法中求和运算和连续版本NT算法中求积分运算,通过四个计算机仿真例子证实了当适度增加区间二型模糊集主变量采样个数时,NT算法的计算结果可以精确地逼近CNT算法。     

Local second-order approximations and applications in optimization

A new general abstract scheme for local second-order approximations and second-order generalized directional derivatives is presented. Applications to optimization are provided.