Production control of an unreliable manufacturing system under the assumption of no backlog

This paper deals with an unreliable manufacturing system in which no backlog is allowed. The hedging point policy is used to control production. This paper's objective is to find the optimum hedging point so as to minimize the average inventory cost. Firstly, for a tentative hedging point, we derive the limiting distribution of the inventory level. This derivation is accomplished by comparison between this system and a finite storage-production system. Based on it we calculate the average inventory cost and find the optimum hedging point.This research was supported in part by the National Natural Science Foundation of China. Bin Liu was partially supported by ITDC, contract No. 105-82150.     

Guest Editors' Foreword

This issue of Discrete & Computational Geometry contains the detailed proof by T. Hales and S.P. Ferguson of the Kepler conjecture that the densest packing of three-dimensional Euclidean space by equal spheres is attained by "cannonball" packing. This is a landmark result. This conjecture, formulated by Kepler in 1611, was stated in Hilbert's formulation of his 18th problem [8]. The proof consists of mathematical arguments and a massive computer verification of many inequalities.     

A sheaf model for intuitionistic quantum mechanics

We analyze the passing of a single particle through a double-slit apparatus. This is done using a sheaf model of intuitionistic logic. We develop an algebra of slits and study the non-classical behaviour of quantum slits. A specific interference formula is obtained by averaging. This formula extends the usual one.This work was partially supported by an Australian Research Council program grant and by theDeutsche Forschungsgemeinschaft.     

2-Minimality,jump classes and a note on natural definability

We show that there is a generalized high degree which is a minimal cover of a minimal degree. This is the highest jump class one can reach by finite iterations of minimality. This result also answers an old question by Lerman.     

An improved class of estimators of a finite population quantile in sample surveys

This work proposes a general class of estimators for a finite population quantile using auxiliary information. This information is provided by the population means of auxiliary variables. The optimum estimator in this class is derived. This result is supported with a numerical example.     

Piecewise linear paths to minimize convex functions may not be monotonic

The exact homotopy path when seeking the minimum of a convex function is monotonic in the homotopy parameter. This monotonicity is not inherited by the piecewise linear approximations to such paths produced by fixed-point algorithms.This research was partially supported by National Science Foundation Grant ENG76-08749.     

流过多孔介质的流体研究

研究流过密集的具二次变化渗透性的重叠理想聚合体的流体．流体流由达西定律的布林克曼扩展及连续方程来刻画,通过引入流函数,求出上述方程在适当边界条件下的解析解,并将结果与一些已知的结果进行了比较．     

A nonsmooth version of Newton's method

Newton's method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized Jacobian instead of the derivative. This extension includes the B-derivative version of Newton's method as a special case. Convergence theorems are proved under the condition of semismoothness. It is shown that the gradient function of the augmented Lagrangian forC ²-nonlinear programming is semismooth. Thus, the extended Newton's method can be used in the augmented Lagrangian method for solving nonlinear programs.This author's work is supported in part by the Australian Research Council.This author's work is supported in part by the National Science Foundation under grant DDM-8721709.     

A minimum principle for a population equation

A minimum principle for the Verhulst-Pearl population equation is given in terms of the integral of the inverse of population. This principle is contrasted with one given earlier by Volterra in terms of the integral of population.This research was supported by NSF under Grant No. GP-2405.     

Exponential decay of solutions of Maxwell's equations coupled with a first-order ordinary differential equation for the polarization

This paper is concerned with Maxwell's equations involving a first-order ordinary differential equation for the dielectric polarization. The main goal is the exponential convergence of the electromagnetic field to an asymptotic state which is determined by the initial data. This is achieved by the construction of a suitable energy functional involving a vector potential which provides an additional dissipative term for the magnetic field.     

Decision analysis with indeterminate or incoherent probabilities

This paper presents a new method of modeling indeterminate and incoherent probability judgments in decision analysis problems. The decision maker's degree of beliefs in the occurrence of an event is represented by a unimodal (in fact, concave) function on the unit interval, whose parameters are elicited in terms of lower and upper probabilities with attached confidence weights. This is shown to provide a unified framework for performing sensitivity analysis, reconciling incoherence, and combining expert judgments.This material is based upon work supported by the National Science Foundation under grant SES-85-11675, and by the Business Associates Fund at the Fuqua School of Business.     

Finite Gröbner basis algebra with unsolvable problem of zero divisors

This work presents a sample construction of an algebra with the ideal of relations defined by a finite Gröbner basis for which the question whether this element is a zero divisor is algorithmically unsolvable. This gives the negative answer to a question raised by V. N. Latyshev.     

An auxiliary result in the theory of transcendental numbers

This is an improvement on some estimates of exponential polynomials proved by Gelfond, Mahler, and Baker. This type of estimate is useful in the theory of transcendental numbers.     

Bayesian analysis of herding behaviour: an application to Spanish equity mutual funds

This paper proposes a dynamic Bayesian rolling window estimation procedure applied to the three‐factor model of Fama and French to analyse herding behaviour in the style exposures of mutual funds. This procedure allows a user to dynamically select the length of the estimation window by means of weighted likelihood functions that discount the loss of information because of time. This method is very flexible and allows us to consider different approaches of detecting herding behaviour by taking into account the uncertainty associated in the estimation of the style coefficients. In particular, the paper first determines the convergence behaviour following the traditional LSV herding measure and then refines this method by removing the influence exerted by market conditions, such as market volatility and returns, on this convergence. This process is empirically illustrated by an application to Spanish equity mutual funds. Copyright © 2014 John Wiley & Sons, Ltd.     

A nonlocal problem for singular linear systems of ordinary differential equations

A system of linear ordinary differential equations is examined on an infinite half-interval. This system is supplemented by the boundedness condition for solutions and a nonlocal linear condition specified by the Stieltjes integral. A method for approximating the resulting problem by a problem posed on a finite interval is proposed, and the properties of the latter are investigated. A numerically stable method for solving this problem is examined. This method uses an auxiliary boundary value problem with separated boundary conditions.     

On the weighting of the mean-absolute-deviation cost minimization model

The mean-absolute-deviation cost minimization model, which aims to minimize sum of the mean value and the absolute deviation (AD) of the total cost multiplied by a given non-negative weighting, is one of a number of typical robust optimization models. This paper first uses a straightforward example to show that the solution obtained by this model with some weightings is not actually an optimal decision. This example also illustrates that the mean-absolute-deviation cost minimization model cannot be regarded as the conventional weighted transformation of the relevant multiobjective minimization model aiming to simultaneously minimize the mean value and AD. This paper further proves that the optimal solution obtained by the mean-absolute-deviation cost minimization model with the weighting not exceeding 0.5 will not be absolutely dominated by any other solution. This tight upper bound provides a useful guideline for practical applications.     

The efficient solution of electromagnetic scattering for inhomogeneous media

We consider an electromagnetic scattering problem for inhomogeneous media. In particular, we focus on the numerical computation of the electromagnetic scattered wave generated by the interaction of an electromagnetic plane wave and an inhomogeneity in the corresponding propagation medium. This problem is studied in the VV polarization case, where some special symmetry requirements for the incident wave and for the inhomogeneity are assumed. This problem is reformulated as a Fredholm integral equation of second kind, which is discretized by a linear system having a special form. This allows to compute efficiently an approximate solution of the scattering problem by using iterative techniques for linear systems. Some numerical examples are reported.     

Optimal Control of Non-well-posed Heat Equations

This work is concerned with Pontryagin＇s maximum principle of optimal control problems governed by some non-well-posed semilinear heat equations. A type of approach to the non-well-posed optimal control problem is given.     

Wavelet transform associated to the affine group AG m p

This paper considers wavelet transforms associated to the affine group, which is more general than the paper given by R. Murenzi, and it seems more important in mathematical theory and more natural to be used to analyze signals in more than 1-dimension. This work is supported by National Natural Science Foundation of China.     

数学期望型水平值逼近全局最小值的方法

郑权在1978年提出的一种积分水平集算法概念性算法.由于水平集一般情况下难以求出,此算法通过Monte-Carlo随机取点来实现.本文提出了数学期望型水平值逼近全局最小值的概念性算法,它利用了相对熵主要思想,通过改变重要样本密度函数,克服了郑权算法水平集不易求得而难以求出水平值的困难.本文还给出了求全局最小值的收敛准则并证明了它的渐进收敛性.