常数项无穷级数判别法综述

常数项无穷级数的审敛问题是伴随着无穷项数的和的问题而产生的一个问题。最初的问题可以追朔到公元前5世纪,而到了公元17、18世纪产生了真正的无穷级数理论,英国数学家Gregory J（1638～1675）给出了“收敛”和“发散”两个术语,由此引发了关于常数项无穷级数判别法的广泛而深入的研究,得到了一系列常数项无穷级数的判别法。时至今日,关于常数项无穷级数判别法的研究仍然比较活跃,特别是近十多年来,国内数学工作者从不同的角度或针对不同的类型提出了许多新的研究成果。为了呈现常数项无穷级数判别法的概貌,同时为进一步研究该问题提供些许素材,对常数项无穷级数的判别法进行了分类整理,并加以综述。     

Exploring the benefits of vertically staggered wind farms: Understanding the power generation mechanisms of turbines operating at different scales

Wind farms are known to modulate large scale structures in and around the wake regions of the turbines. The potential benefits of placing small hub height, small rotor turbines in between the large turbines in a wind farm to take advantage of such modulated large‐scale eddies are explored using large eddy simulation (LES). The study has been carried out in an infinite wind farm framework invoking an asymptotic limit, and the wind turbines are modeled using an actuator line model. The vertically staggered wind turbine arrangements that are studied in the present work consist of rows of large wind turbines, with rows of smaller wind turbines (ie, smaller rotor size and shorter hub height) placed in between the rows of large turbines. The influence of the hub height of the small turbines, in particular, how it affects the interactions between the large and small turbines and consequently their power, along with the multiscale dynamics involved, has been assessed in the current study. It was found that, in the multiscale layouts, the small turbines at lower hub heights operate more efficiently than their homogeneous single‐scale counterparts. In contrast, the small turbines with higher hub heights incur a loss of power compared with the corresponding single‐scale arrangements.     

正则周期矩阵对分离度的估计

正则周期矩阵对在分析和设计线性离散周期控制系统中有重要应用．正则周期矩阵对的分离度是测量周期矩阵对的周期收缩子空间敏感性的一个重要指标,因此,计算这个分离度显得非常重要．然而,这需要的太多的计算量．目前对单个矩阵和矩阵对的分离度的估计,常用的处理方法有二种：一种是利用矩阵的Schur分解,另一种则是利用矩阵的约当分解．本文应用正则周期矩阵对的周期Schur分解,给出这个分离度的上界和下界．这与计算精确的分离度相比较可大大减少运算量．另外,这些界可以看成是两正则矩阵对分离度的上、下界的推广．最后,数值例子验证了所给的下界和上界．     

基于深度学习的有遮挡人脸识别方法研究

针对传统CNN在有遮挡人脸识别中计算量大的问题,文中以L1-2DPCA为基础,提出了一种用于人脸识别的新型PCANet深度学习网络.该网络以L1-2DPCA学习多个卷积层的滤波器,在卷积层之后,通过二进制散列和逐块直方图进行池化.文中以CNN、PCANet、2DPCANet和L1-PCANet作为比较,在AR和RMFD...     

二维不可压缩Navier-Stokes方程的并行谱有限元法求解

针对不可压缩Navier-Stokes （N-S）方程求解过程中的有限元法存在计算网格量大、收敛速度慢的缺点,提出了基于面积坐标的三角网格剖分谱有限元法（TSFEM）并进一步给出了利用OpenMP对其并行化的方法。该算法结合谱方法和有限元法思想,选取具有无限光滑特性的指数函数取代传统有限元法中的多项式函数作为基函数,能够有效减少计算网格数量,提高算法的精度和收敛速度;利用面积坐标便于三角形单元计算的特点,选取三角单元作为计算单元,增强了适用性;在顶盖方腔驱动流问题上对该算法进行验证。实验结果表明,TSFEM较传统有限元法（FEM）无论是收敛速度还是计算效率都有了显著提高。     

基于ISTA算法的稀疏约束反演谱分解及应用

常规谱分解的分辨率难以满足地震解释的需求,稀疏约束反演谱分解可以很好地解决该问题。稀疏约束反演谱分解是把地震信号看成已知的子波矩阵库和伪反射系数的褶积,从而将谱分解问题转化为一个反问题来求解,其核心内容是如何快速获得最优解。采用L₁范数正则化的L₂范数作为稀疏约束反演谱分解的目标函数,并通过迭代阈值算法求解稀疏反问题。为了进一步提高计算速度,基于Ricker子波构建一种新的算子,并用ISTA算法进行计算。在此基础上,将稀疏约束反演谱分解用于模拟信号的数值试验,并与常规谱分解结果进行比较。结果表明,稀疏约束反演谱分解具有更好的时频聚集性和更高的时频分辨率;进一步应用于济阳坳陷沾化凹陷渤南洼陷义176井区地震资料,处理结果对油气响应十分敏感,可以较好地识别油气储集层。     

基于一阶范数的视频超分辨率重建

讨论了视频成像的基本模型,并在此基础上提出了一种基于一阶范数的视频图像重建算法,该方法同时对高分辨率图像和运动矢量进行迭代估计,并采用一阶范数和Robers算子对于当前普遍的采用二阶范数项作为视频数据逼近项和归整项的方式进行了改进。实验结果表明,该算法在原图像受到椒盐噪声影响的情况下,重建效果要优于二阶方法,并且该方法在重建图象的边缘保持上也有相对比较好的效果。     

自适应临床路径建模中语义与规范分析研究

文中运用语义分析与规范分析的方法表示临床路径知识,其中语义分析表示临床路径中的语义单元以及它们的关系与行为的方式,规范分析提取并描述决定这些行为如何发生的规范。论述了基于语义分析和规范分析建立临床路径本体模型的方法,通过定义可能的行为模式和根据病人的具体情况控制这些行为的规范,为自适应临床路径建模提供关键技术,从而为设计实现自适应临床路径奠定基础。     

DRYING OF SOLIDS: THE INFINITE SLAB CONDITION

ABSTRACT

Fourier's second law was solved using convective boundary conditions without considering the shrinkage of the solid. The solutions for a finite and an infinite slab were compared to determine the dimensions for a slab to be considered as infinite. The solutions obtained for Bi = 0.1 and Bi = 100 correspond to heat and mass transfer-controlled processes, respectively, during drying. The results show that the finite slab cannot be considered as infinite, even for R²/R¹ > 20. The relative error obtained when the finite slab was assumed to be infinite was not significant for small Fourier numbers, but it increased as the Fourier number increased; errors were also higher for higher Biot numbers. When the numerical solution of a drying model was obtained for finite and infinite slabs, significant differences in drying kinetics and temperature evolution were observed.     

Temporal Aggregation of Lognormal AR processes

We consider temporal aggregation of lognormal autoregressive (AR) processes. More specifically, we develop a novel moment‐matching approximation for temporally aggregated lognormal AR processes. In addition, we show that our approximation provides the closest lognormal AR process in terms of Kullback–Leibler divergence. Moreover, we perform a simulation study to compare our proposed approximation with two competing approximations. This study shows that in terms of L¹‐ and L²‐norm distances our approximation provides superior results. Our results have an important practical application and one main practical implication. In terms of practical application, our approximation can provide possible candidate solutions for simulation‐based algorithms such as the Metropolis–Hastings algorithm. The practical implication gives support to common practice: when the original fine‐level process follows a lognormal AR process but only aggregated data are available, then instead of assuming a Gaussian process it is better to assume a lognormal AR process at the aggregated level. Finally, we illustrate the utility of our results with two applications. The first example considers a simulated dataset whereas the second example examines the number of yearly sunspots in the period 1700–1984.