A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time

This paper deals with the optimal control of a finite capacity G/M/1 queueing system combined the F-policy and an exponential startup time before start allowing customers in the system. The F-policy queueing problem investigates the most common issue of controlling arrival to a queueing system. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distribution of the number of customers in the system. We illustrate a recursive method by presenting three simple examples for exponential, 3-stage Erlang, and deterministic interarrival time distributions, respectively. A cost model is developed to determine the optimal management F-policy at minimum cost. We use an efficient Maple computer program to determine the optimal operating F-policy and some system performance measures. Sensitivity analysis is also studied.     

A recursive algorithm for nonlinear least-squares problems

The solution of nonlinear least-squares problems is investigated. The asymptotic behavior is studied and conditions for convergence are derived. To deal with such problems in a recursive and efficient way, it is proposed an algorithm that is based on a modified extended Kalman filter (MEKF). The error of the MEKF algorithm is proved to be exponentially bounded. Batch and iterated versions of the algorithm are given, too. As an application, the algorithm is used to optimize the parameters in certain nonlinear input–output mappings. Simulation results on interpolation of real data and prediction of chaotic time series are shown. A. Alessandri and M. Cuneo were partially supported by the EU and the Regione Liguria through the Regional Programmes of Innovative Action (PRAI) of the European Regional Development Fund (ERDF). M. Sanguineti was partially supported by a grant from the PRIN project ‘New Techniques for the Identification and Adaptive Control of Industrial Systems’ of the Italian Ministry of University and Research.     

逐步聚合反应统计理论进展—递归计算法

本文介绍和评述了 Maeosko 等提出的聚合反应的新统计理论——递归计算法。该理论是基于逐步聚合过程的一级 Markov 统计特性以及这种链的递归性质。运用这种方法可以直接计算复杂的线性共聚体系的分子量、链长和序列分布等平均值,与其它统计方法相比,具有简单、通用性的优点。     

用~1H-和~(13)C-NMR方法研究聚对苯二甲酸乙二酯/聚一氧基苯甲酸酯共聚酯的序列分布

测定了PET/30PHB和PET/60PHB共聚酯的高分辨~1H和~(13)C谱,并采用INEPT方法和部分弛豫FT技术确定了季碳吸收峰,对NMR谱进行了归属.应用我们先前提出的方法对共聚酯的序列分布进行了表征.结果表明,两种共聚酯的无规度B_q值均小于1,序列分布不象Jackson等认为的那样为完全无规的.此外,文中还指出,某些研究者套用Flory公式判别PET/PHB共聚酯是否为无规的不妥之处.     

The Halting Probability Omega: Irreducible Complexity in Pure Mathematics

Some G?del centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. Enriques Lecture held on October 30, 2006 Received: November 2006     

找约束方程组最佳解的递推算法

本文利用关于Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆的Ｇｒｅｖｉｌｌｅ算法及其有关参数的性质，导出了找约束方程组Ａｘ＝ｂ，ｘ∈Ｔ最佳解的两类递推算法，其中后者是与求解通常线性方程组的ＡＢＳ算法类似的。     

Anharmonic resonances with recursive delay feedback

We consider application of time-delayed feedback with infinite recursion for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, recursive delay feedback exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Remarkably, these small-anharmonicity induced resonances can be stronger than the harmonic ones. Analytical results are confirmed numerically for van der Pol and van der Pol-Duffing oscillators.     

Recursive Marginal Quantization of the Euler Scheme of a Diffusion Process

Abstract

We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method raises several questions like the analysis of the induced quadratic quantization error between the marginals of the Euler process and the proposed quantizations. We show in particular that at every discretization step t_k of the Euler scheme, this error is bounded by the cumulative quantization errors induced by the Euler operator, from times t₀ = 0 to time t_k. For numerics, we restrict our analysis to the one-dimensional setting and show how to compute the optimal grids using a Newton–Raphson algorithm. We then propose a closed formula for the companion weights and the transition probabilities associated to the proposed quantizations. This allows us to quantize in particular diffusion processes in local volatility models by reducing dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to the algorithms commonly proposed in this framework. Numerical tests are carried out for the Brownian motion and for the pricing of European options in a local volatility model. A comparison with the Monte Carlo simulations shows that the proposed method may sometimes be more efficient (w.r.t. both computational precision and time complexity) than the Monte Carlo method.     

Survival probability for a two-dimensional risk model

In this paper, we consider the survival probability for a two-dimensional risk model. We derive a partial integro-differential equation satisfied by the survival probability and prove its differentiability. We obtain explicit expressions for recursively calculating the survival probability by applying the partial integro-differential equation when claims are exponentially distributed.