Optimal packings of two to four equal circles on any flat torus

We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent vectors. We prove the optimality of the arrangements using techniques from rigidity theory and topological graph theory.     

近红外光谱的古筝面板用木材等级识别研究

目前民族乐器古筝面板用板材的等级主要依靠乐器技师凭借个人经验进行判断，此方法受限于有丰富经验的技师且容易受其主观判断影响。针对此现状，以用于制作古筝面板的泡桐木材为实验样本，提出了一种利用近红外光谱结合改进的BP神经网络方法，实现快速识别古筝面板用板材的不同等级。近红外光谱可以表征丰富的物质结构与组成信息，并且测量仪器成本较低，附件形式多样化，所以针对泡桐板材的近红外光谱实验分析有实用意义首先进行光谱去噪，消除系统误差等以提高光谱分辨率，根据均方根误差与信号平方和作为多种预处理方法评价指标，选取一阶导数为本实验最终预处理方式，15为合适的滤波去噪窗口大小，然后通过主成分分析法压缩数据以及马氏距离法剔除建模集异常样本，从而建立更具代表性的建模集。然后通过聚类分析无监督学习方法进行板材等级分析，证明板材分级的可行性。由于H₂O在近红外光谱区域具有较大吸收，根据实验光谱分析结果，不考虑其基频振动波段5 396.0～4 978.0 cm-1区域和第一泛音振动波段6 800～7 000 cm-1区域，仅考虑剩余近红外光谱波段信息，将不同光谱信息波段组合，共七种组合波段区域作为神经网络模型的输入，进行面板板材等级识别模型实验。对传统的BP神经网络模型作改进。BP神经网络中学习率的设置采用自适应学习率优化策略，弥补传统神经网络训练速率慢等劣势。同时采用交叉熵函数作为代价函数，从而加快权重的更新速度。选取Relu函数作为输入层与隐藏层之间的传递函数，提高了模型训练速度，有效防止过拟合的发生。选取Softmax函数作为最后一层的传递函数，以此减少复杂计算，构成该研究最终BP神经网络模型。选取不同数量的主成分变量所能提取的光谱信息量不同，通过不断增加主成分个数和调整参与模型的光谱波段区间，调整BP神经网络模型的输入，当主成分个数为11和光谱区间为10 000～7 000和4 976～4 000 cm-1时，未知样本识别率达到99.7%，所选光谱区间涵盖C-H等基团全部特征信息。研究结果表明，近红外光谱结合神经网络可以对不同等级的泡桐木材进行有效的识别，降低人工检测误差，缩短板材分级时间，更好地满足乐器市场需求。     

Vortex shedding around a near-wall circular cylinder induced by a solitary wave

This study developed a two-dimensional generalized vortex method to analyze the shedding of vortices and the hydrodynamic forces resulting from a solitary wave passing over a submerged circular cylinder placed near a flat seabed. Numerical results for validation are compared with other numerical and experimental results, and satisfactory agreement is found. A series of simulations were performed to study the effects of gap-to-diameter ratio and incident wave height on vorticity pattern as well as the forces exerted on the cylinder. The range of the heights of incident waves is from 0.3h to 0.7h, where h is the still water depth. The range of the gap-to-diameter ratios is from 0.1 to 0.8. The results indicate that the flow pattern and the pressure distribution change significantly because of the close proximity of the seabed where the vorticity flux on the seabed-side surface of the cylinder is suppressed. Placing the cylinder nearer the seabed increases the drag and the positive lift on the cylinder. When the gap-to-diameter ratio increases, the pattern of vortices changes because of the interaction between the main recirculation zone and the shear layers separated from the gap. The maxima of drag, lift and total force increase linearly with the height of the incident wave.     

Estimation of partially specified spatial panel data models with random-effects

In this article, we study estimation of a partially specified spatial panel data linear regression with random-effects. Under the conditions of exogenous spatial weighting matrix and exogenous regressors, we give an instrumental variable estimation. Under certain sufficient assumptions, we show that the proposed estimator for the finite dimensional parameter is root-N consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and asymptotically distributed. Consistent estimators for the asymptotic variance-covariance matrices of both the parametric and unknown components are provided. The Monte Carlo simulation results verify our theory and suggest that the approach has some practical value.     

爆炸荷载作用下方形夹芯板动力学响应与优化设计数值分析

为研究方形蜂窝铝板在爆炸荷载作用下的动力学响应,基于LS-DYNA非线性有限元软件,建立了TNT炸药-前后面板-蜂窝夹芯-空气的三维有限元模型。采用ALE(任意的拉格朗日欧拉)多物质流固耦合算法分析了蜂窝铝板在冲击荷载作用下的变形机理、塑性变形、能量吸收以及结构的优化。数值模拟结果表明:随着面板厚度、核心高度的增加,蜂窝铝板在冲击荷载作用下的塑性变形明显减小,抵抗变形的能力增强;随着爆轰入射角度的增加,结构的破坏程度有所减小,入射角越大这种效果越发明显。对结构给定边长和受冲击面积以及面板厚度配合比、夹芯量纲为一的高度进行了局部的优化分析,为设计优质铝蜂窝板提供参考。     

半导体电极的平带电位

平带电位(E_(fb))是半导体/电解质溶液体系的重要概念,是半导体电极在平带状态时的电极电位,它是半导体电极特有的可以实验测定的物理量。利用Mott-Schottky曲线以及光电化学等方法可以测定平带电位,判断半导体的类型以及估算半导体的载流子浓度,其数值可用于推测半导体的能级结构,确定半导体材料的价带或导带能级位置。这对于与太阳能开发利用相关的半导体光催化和光电化学研究都是非常重要的。本文分析了半导体电极的能带弯曲及影响因素,首次提出半导体界面层内费米能级弯曲,阐明半导体电极平带电位的物理意义及其测定方法,以帮助初学者理解和应用平带电位。     

一种面板数据分位数回归模型的工具变量方法

本文将工具变量分位数回归模型(IVQR)应用到面板数据中,结合Canay对面板分位数回归的两步估计法以及Chernozhukov对IVQR模型的估计方法,提出了两步面板分位数工具变量估计法(2S-IVFEQR),并给出相应的参数估计。本文提出的方法较已有的方法计算复杂度低,蒙特卡洛模拟结果显示在数据量不大或者处理长面板数据时,2S-IVFEQR方法要优于传统的IVFEQR方法,且运算时间短。     

基于面板模型的商品房价格影响因素的实证研究

选取了我国30个省市2006~2015年的面板数据,应用面板数据计量模型回归的方法,基于R语言对影响商品房价格的因素进行实证研究.首先,经过Hausman检验与F检验确定面板数据的模型为混合估计模型;模型可以通过十折交叉验证法、残差正太性的检验、Q-Q图检验、变量间共线性的检验;最后经过逐步回归分析,结果表明土地价格、商品房销售面积、居民可支配收入、人均国内总产值财政收入占地区生产总值比重、汇率这6个指标对商品房价格都有显著性的影响.其中,土地价格和居民可支配收入对商品房价格的影响最为突出.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.