基于分形维数的分析信号自适应中值滤波

提出一种面向分析仪器谱图信号处理的分形维自适应中值波方法（AMeFFD）。该法延拓运用分形理论，定义了相对点盒维数概念，由此建立建立判定脉冲型噪声的特异性指标，从而可自动调节中值滤波窗口宽度，有效地滤除脉冲型噪声及其它类噪声。对仿真色谱信号及实测色谱图的处理结果表明：AMeFFD法克服了经典中值滤波算法的缺陷，无论在信号的均方根偏差还是谱峰差等指标上，均明显优于后者，能在确保谱峰不畸变的同时更有效地滤除脉冲型常见噪声，是处理化学谱图信号的有力工具。     

A discrete problem on d-dimensional symmetric weighted median filters

Using a tool-energy of d-dimensional signal sequences taking values 1 or -1, we have completely solved an interesting discrete mathematical problem on d-dimensional symmetric weighted median filters, i.e., when a d-dimensional symmetric weighted median filter is applied iteratively to a real signal sequence, then the limit of the iterates with even index as well as the limit of the iterates with odd index both converge.     

小波分析在信号去噪声中的应用

小波分析是近年来发展起来的一种数学方法,在信号与图象处理中有重要的应用.中值滤波是信号处理中常用的一种非线性滤波器,它能够有效地消除瞬时脉冲干扰,并且能够很好地保持信号的边缘信息,在信号和图象处理中得到广泛应用.对中值滤波器与小波变换的结合进行了比较系统的研究.通过实例说明中值滤波器与小波变换相结合具有比单一滤波器更好的效果.     

盒子型区域上变分不等式的一个光滑牛顿法(英文)

The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator.In this paper,we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function.The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.     

Postoptimal analysis of the multicriteria combinatorial median location problem

We consider a multicriteria variant of the well-known combinatorial minisum facility location problem (median problem) with Pareto and lexicographic optimality principles. Necessary and sufficient conditions of a solution stability to the initial data perturbations in such problems are formulated in terms of binary relations. Numerical examples are given.     

Presenting mathematics in a first‐year engineering course at university

The approach used to teach mathematics to first‐year engineering students at the University of Warwick is described. The instruction is programmed, with weekly assignments and tutorials, so that the learning is self‐paced within each week. Our experiences with this method of teaching are discussed.     

Nonparametric regression under dependent errors with infinite variance

We consider local least absolute deviation (LLAD) estimation for trend functions of time series with heavy tails which are characterised via a symmetric stable law distribution. The setting includes both causal stable ARMA model and fractional stable ARIMA model as special cases. The asymptotic limit of the estimator is established under the assumption that the process has either short or long memory autocorrelation. For a short memory process, the estimator admits the same convergence rate as if the process has the finite variance. The optimal rate of convergencen ^−2/5 is obtainable by using appropriate bandwidths. This is distinctly different from local least squares estimation, of which the convergence is slowed down due to the existence of heavy tails. On the other hand, the rate of convergence of the LLAD estimator for a long memory process is always slower thann ^−2/5 and the limit is no longer normal.     

选址问题研究的若干进展

中值问题、覆盖问题、中心问题是选址研究中的三个经典问题，它们的应用非常广泛，也是迄今为止大多数选址理论研究的坚实基础。本文综述了近年来它们的研究进展，包括模型、求解方法以及相关问题，最后，指出这一领域未来研究的一些问题与方向。     

单形深度中位数在封闭式基金排名中的应用

本文介绍了单形深度函数理论,通过改进夏普指数公式,利用单形深度函数中位数稳健性的特点,将单形深度函数中位数应用于改进的夏普指数公式,对国内的封闭式基金进行了排名与评级,并将其与中信星级和样本星级进行了对比.最后,通过定义基金业绩偏离度提出将其用于评价基金捕捉市场机遇的能力的观点.     

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??When the data has heavy tail feature or contains outliers, conventional variable selection methods based on penalized least squares or likelihood functions perform poorly. Based on Bayesian inference method, we study the Bayesian variable selection problem for median linear models. The Bayesian estimation method is proposed by using Bayesian model selection theory and Bayesian estimation method through selecting the Spike and Slab prior for regression coefficients, and the effective posterior Gibbs sampling procedure is also given. Extensive numerical simulations and Boston house price data analysis are used to illustrate the effectiveness of the proposed method.