用WKB方法讨论透射系数和反射系数

本文用WKB近似方法讨论了势垒贯穿问题系数T和其透射反射系数R之和恒等为1,即满足恒等式T R=1,并进一步得出这一结论不仅适用于一般势垒贯穿而且在方势垒贯穿中也成立,最后讨论了势垒贯穿的几种极限情况,例如,h→0(即经典情况),势垒高度v→∞、v→0,势垒宽度a→∞、a→0,等几种特殊情况下的T及R的取值问题。     

Characterisation of mortar morphology in thin sections by digital image processing

A digital imaging approach was applied to investigate mortar morphology in thin sections; in particular, the binder/aggregate ratio and the grading curve of five mortar bars were attained by digital image processing (DIP), using the Image Pro Plus 4.1 software package. The imaging procedure employed image segmentation, to extract mortar aggregate, and image filtering, to fix grain boundaries. The results show that digital image processing may be considered as an alternative method to mechanical sieving for the characterisation of mortar morphology, as it appears to be quicker and more accurate than the traditional method. However, digital image processing exhibits limits, which are discussed in the text.     

全级配混凝土单轴疲劳特性细观数值模拟

为研究全级配混凝土在等幅、变幅及阶梯重复荷载作用下的疲劳特性,揭示材料特性与疲劳应力水平对其疲劳寿命的影响规律,通过自编程序建立二维随机骨料模型,运用有限元软件和耐久性疲劳分析软件进行联合仿真,对全级配混凝土细观结构进行应力分析和疲劳分析,探讨了不同骨料分布、骨料形状及疲劳应力水平对混凝土疲劳性能的影响,并估算了疲劳寿命。结果表明:在阶梯重复荷载作用下,骨料形状和分布对混凝土疲劳寿命影响较小,而疲劳应力水平对疲劳寿命影响较大;圆形和椭圆形骨料混凝土疲劳寿命较高,多边形骨料寿命较低;在疲劳加载破坏过程中,骨料界面先起裂,然后裂纹逐渐扩展贯通,最后导致整个试件完全破坏,可见骨料界面是混凝土中的薄弱部位,其寿命直接影响整个混凝土试件的寿命。研究成果为后续混凝土疲劳性能研究提供了参考。     

Single-machine parallel-batching scheduling with family jobs to minimize weighted number of tardy jobs

We consider the problem of scheduling n jobs in batches on a single parallel-batching machine, where the jobs are partitioned into jobs families and the jobs in each family have the same due date. The objective is to minimize the weighted number of tardy jobs. We first devise an efficient pseudo-polynomial time and a fully polynomial time approximation scheme for the weighted problem. Then we present $O(n^2)$-time and $O(n\log n)$-time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time, respectively.     

A stochastic Kaczmarz algorithm for network tomography

We develop a stochastic approximation version of the classical Kaczmarz algorithm that is incremental in nature and takes as input noisy real time data. Our analysis shows that with probability one it mimics the behavior of the original scheme: starting from the same initial point, our algorithm and the corresponding deterministic Kaczmarz algorithm converge to precisely the same point. The motivation for this work comes from network tomography where network parameters are to be estimated based upon end-to-end measurements. Numerical examples via Matlab based simulations demonstrate the efficacy of the algorithm.     

广义Mamdani模糊系统依K-积分模的泛逼近及其实现过程

首先,通过引入拟减法算子给出K-积分模定义,并针对广义Mamdani模糊系统实施等距剖分其输入空间. 其次,应用分片线性函数（Piecewise linear function,PLF）的性质构造性地证明了广义Mamdani模糊系统在K-积分模意义下具有泛逼近性,从而将该模糊系统对连续函数空间的逼近能力扩展到一类可积函数类空间上. 最后,通过模拟实例给出该广义Mamdani模糊系统对给定可积函数的泛逼近及实现过程.     

Nonlinear time series forecasting with Bayesian neural networks

The Bayesian learning provides a natural way to model the nonlinear structure as the artificial neural networks due to their capability to cope with the model complexity. In this paper, an evolutionary Monte Carlo (MC) algorithm is proposed to train the Bayesian neural networks (BNNs) for the time series forecasting. This approach called as Genetic MC is based on Gaussian approximation with recursive hyperparameter. Genetic MC integrates MC simulations with the genetic algorithms and the fuzzy membership functions. In the implementations, Genetic MC is compared with the traditional neural networks and time series techniques in terms of their forecasting performances over the weekly sales of a Finance Magazine.     

Computer Algebra Derivation of the Bias of Linear Estimators of Autoregressive Models

Abstract. A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large‐sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the Burg estimator's bias because this problem is too intractable without using computer algebra. The asymptotic bias coefficient to O(1/n) of Yule–Walker as well as least squares estimates is also derived in AR(3) models. Our asymptotic results show that for the AR(3), just as in the AR(2), the Yule–Walker estimates have a large bias when the parameters are near the nonstationary boundary. The least squares and Burg estimates are much better in this situation. Simulation results confirm our findings.