The Two-Dimensional,Linear Orthotropic Plate

We First define a continuous extension of the Laquerre polynomials and give some properties of this continuous extension. Then we define a continuous Laguerre transform for square integrable functions, give some properties of this transform and give a sampling theorem that is similar to the well known Shannon-Whittaker Sampling Theorem for Fourier transform. The inverse of this transform is also given.     

A Markov Chain Monte Carlo comparison of variance estimators for the sampling of particulate mixtures

During the sampling of particulate mixtures, samples taken are analyzed for their mass concentration, which generally has non‐zero sample‐to‐sample variance. Bias, variance, and mean squared error (MSE) of a number of variance estimators, derived by Geelhoed, were studied in this article. The Monte Carlo simulation was applied using an observable first‐order Markov Chain with transition probabilities that served as a model for the sample drawing process. Because the bias and variance of a variance estimator could depend on the specific circumstances under which it is applied, Monte Carlo simulation was performed for a wide range of practically relevant scenarios. Using the ‘smallest mean squared error’ as a criterion, an adaptation of an estimator based on a first‐order Taylor linearization of the sample concentration is the best. An estimator based on the Horvitz–Thompson estimator is not practically applicable because of the potentially high MSE for the cases studied. The results indicate that the Poisson estimator leads to a biased estimator for the variance of fundamental sampling error (up to 428% absolute value of relative bias) in case of low levels of grouping and segregation. The uncertainty of the results obtained by the simulations was also addressed and it was found that the results were not significantly affected. The potentials of a recently described other approach are discussed for extending the first‐order Markov Chain described here to account also for higher levels of grouping and segregation. Copyright © 2013 John Wiley & Sons, Ltd.     

The arithmetic fourier transform and the visual pathway

The Arithmetic Fourier Transform is an algorithm for the computation of Fourier coefficients. In this paper it is extended to the computation of double Fourier coefficients by a repeated sum. We discuss the relevance of the repeated sum algorithm to signal processing by neurons in the visual pathway.     

General decay for a porous thermoelastic system with a memory

In this paper, we consider a linear damped porous thermoelastic system of memory type where the heat conduction is given by Cattaneo’s Law . We establish a general decay results using an appropriate Lyapunov functional.     

Interval optimization based line sampling method for fuzzy and random reliability analysis

For structural system with fuzzy variables as well as random variables, a novel algorithm for obtaining membership function of fuzzy reliability is presented on interval optimization based Line Sampling (LS) method. In the presented algorithm, the value domain of the fuzzy variables under the given membership level is firstly obtained according to their membership functions. Then, in the value domain of the fuzzy variables, bounds of reliability of the structure are obtained by the nesting analysis of the interval optimization, which is performed by modern heuristic methods, and reliability analysis, which is achieved by the LS method in the reduced space of the random variables. In this way the uncertainties of the input variables are propagated to the safety measurement of the structure, and the membership function of the fuzzy reliability is obtained. The presented algorithm not only inherits the advantage of the direct Monte Carlo method in propagating and distinguishing the fuzzy and random uncertainties, but also can improve the computational efficiency tremendously in case of acceptable precision. Several examples are used to illustrate the advantages of the presented algorithm.     

Efficient Monte Carlo simulation for integral functionals of Brownian motion

In the paper, we develop a variance reduction technique for Monte Carlo simulations of integral functionals of a Brownian motion. The procedure is based on a new method of sampling the process, which combines the Brownian bridge construction with conditioning on integrals along paths of the process. The key element in our method is the identification of a low-dimensional vector of variables that reduces the dimension of the integration problem more effectively than the Brownian bridge. We illustrate the method by applying it in conjunction with low-discrepancy sequences to the problem of pricing Asian options.     

均匀设计抽样的一、二阶矩

（７）中给出并研究了均匀设计抽样（ＵＤＳ）及随机化均匀设计（ＲＵＤ）的一些优良性质,作者给出该设计和抽样的一、二阶矩。     

A health insurance pricing model based on prevalence rates: Application to critical illness insurance

The Italian health insurance market is currently undersized. The paucity of assured data and the discontinuous statistical surveys carried out by the National Institute of Statistics (ISTAT) represent one of the main obstacles to the insurance market development. The paper sets forth a parametric model to estimate technical basis for health insurance policies when data are limited and only aggregated information on mortality and morbidity is available. The probabilistic framework is based on a multiple state continuous and time inhomogeneous Markov model. We provide an estimate of transition intensities from the healthy state to the sickness state when only prevalence rates of sickness are available, according to an extension and modification of the methodology proposed in Olivieri (1996) for Long Term Care insurance. We assume that mortality intensity of both healthy and sick lives is modelled by two independent Gompertz–Makeham models.     

A New Approach to Source Conditions in Regularization with General Residual Term

This article addresses Tikhonov-like regularization methods with convex penalty functionals for solving nonlinear ill-posed operator equations formulated in Banach or, more general, topological spaces. We present an approach for proving convergence rates that combines advantages of approximate source conditions and variational inequalities. Precisely, our technique provides both a wide range of convergence rates and the capability to handle general and not necessarily convex residual terms as well as nonsmooth operators. Initially formulated for topological spaces, the approach is extensively discussed for Banach and Hilbert space situations, showing that it generalizes some well-known convergence rates results.