A comparison of transformation methods for evaluating two‐dimensional weakly singular integrals

Accurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two‐dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one‐dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub‐regions are considered as well as non‐splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non‐linear transformation approach (GSSNT) is applied to various two‐dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two‐dimensional weakly singular integrals studied. Copyright © 2002 John Wiley & Sons, Ltd.     

弱导光纤的标量衍射光束特性分析

仿照罗兰圆光学系统构造罗兰球光学系统 ,在罗兰球中简化电磁波的瑞利 索末菲标量衍射积分公式 ,推导出折射率阶跃分布的弱导光纤LP模衍射场分布和空间频谱的计算公式。提出LP0 1模远场衍射分布存在类似于平面波圆孔夫琅禾费衍射艾里斑的中央亮斑概念 ,并给出中央亮斑角半宽度的计算公式。     

Recovery of pyruvic acid with weakly basic polymeric sorbents

BACKGROUND: Carboxylic acids are among the most important substances that can be manufactured from biomass. However, the recovery of carboxylic acids from fermentation broths presents a challenging separation problem. To avoid the production of waste salts and net consumption of chemicals in the calcium carboxylate salt process, the use of reversible chemical complexation with polymeric sorbents and extractants is attractive for carboxylic acid recovery. Pyruvic acid is widely used in the manufacture of medicines, pesticides and foodstuffs and can be produced by fermentation. Since the acidity of pyruvic acid (pK_a = 2.49) is stronger than that of normal carboxylic acids, and as few reports on the recovery of pyruvic acid are available, the sorption of pyruvic acid from aqueous solution on two types of weakly basic polymeric sorbent, tertiary amine D301R and primary amine D392, was investigated over a wide pH range and at various salt (MgSO₄) concentrations. RESULTS: Overloading adsorption of pyruvic acid on both weakly basic polymeric sorbents occurred, with the overloading of D392 being greater than that of D301R. The adsorption of pyruvic acid on both sorbents was greatly affected by the solution pH and the salt concentration in the aqueous phase. An overloading model was able to predict the experimental uptake data very well. CONCLUSION: Solution pH is one of the most important operating conditions, and both polymeric sorbents D392 and D301R can be used to recover pyruvic acid from dilute aqueous solution with high efficiency at a solution pH around 2. The uptake by D392 is greater than that by D301R owing to steric hindrance of the tertiary amine. Copyright © 2008 Society of Chemical Industry     

具有某种特性的向量优化问题的解的刻画

在有限维空间中,当目标函数凸下半连续时,向量优化问题一定有弱有效解,并且解集是紧的,但当目标函数非凸时,这不一定成立,文章讨论了把目标函数的凸性减弱之后,向量优化问题的解集是非空并且紧的,另外还得到一些等价的刻画。     

弱监督深度语义分割网络的多源遥感影像水体检测

目的 深度语义分割网络的优良性能高度依赖于大规模和高质量的像素级标签数据。在现实任务中,收集大规模、高质量的像素级水体标签数据将耗费大量人力物力。为了减少标注工作量,本文提出使用已有的公开水体覆盖产品来创建遥感影像对应的水体标签,然而已有的公开水体覆盖产品的空间分辨率低且存在一定错误。对此,提出采用弱监督深度学习方法训练深度语义分割网络。方法 在训练阶段,将原始数据集划分为多个互不重叠的子数据集,分别训练深度语义分割网络,并将训练得到的多个深度语义分割网络协同更新标签,然后利用更新后的标签重复前述过程,重新训练深度语义分割网络,多次迭代后可以获得好的深度语义分割网络。在测试阶段,多源遥感影像经多个代表不同视角的深度语义分割网络分别预测,然后投票产生最后的水体检测结果。结果 为了验证本文方法的有效性,基于原始多源遥感影像数据创建了一个面向水体检测的多源遥感影像数据集,并与基于传统的水体指数阈值分割法和基于低质量水体标签直接学习的深度语义分割网络进行比较,交并比（intersection-over-union,IoU）分别提升了5.5%和7.2%。结论 实验结果表明,本文方法具有收敛性,并且光学影像和合成孔径雷达（synthetic aperture radar,SAR）影像的融合有助于提高水体检测性能。在使用分辨率低、噪声多的水体标签进行训练的情况下,训练所得多视角模型的水体检测精度明显优于基于传统的水体指数阈值分割法和基于低质量水体标签直接学习的深度语义分割网络。     

锥度量空间中四个自映射的公共不动点定理

在完备的锥度量空间中讨论了4个自映射的公共不动点定理,其存在性和唯一性得到证明。所得主要结果将锥度量空间中的公共不动点定理进行了推广。     

CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel

In this paper, a computational method for numerical solution of a class of integro-differential equations with a weakly singular kernel of fractional order which is based on Cos and Sin (CAS) wavelets and block pulse functions is introduced. Approximation of the arbitrary order weakly singular integral is also obtained. The fractional integro-differential equations with weakly singular kernel are transformed into a system of algebraic equations by using the operational matrix of fractional integration of CAS wavelets. The error analysis of CAS wavelets is given. Finally, the results of some numerical examples support the validity and applicability of the approach.     

点云配准在大型曲面工件定位中的应用

针对工业生产中大尺寸薄壁工件的高精度加工需求,本文利用点云配准技术解决弱刚度及缺少定位信息等实际问题,对工件位姿进行迭代调整。最近点迭代(ICP)算法对于平坦曲面和有限点数据的精度不高,本文结合ICP算法和曲面点参数反求方法,减小了在边缘和角点的匹配误差,提高了整体匹配效果。仿真结果表明,该方法能够在保证整体性能的前提下得到较优的局部匹配精度,为解决大型曲面工件的主动寻位和自动调位问题提供了一个有效途径。     

基于裁剪的弱硬实时调度算法

针对当前弱硬实时调度算法无法保证超过窗口长度的执行序列的满足率达到一定比例的问题,基于(m~-,p)弱硬实时约束,提出了一种基于裁剪的调度算法(cut-down based scheduling,简称CDBS).由于判断(m~-,p)约束是否满足需要遍历任务的整个执行序列,因此判断复杂度很大.为此,提出一种高效的裁剪执行序列的算法,同时证明其正确性,并利用适当的数据结构,使得计算复杂度与序列长度无关,通过实验说明其降低计算复杂度的有效性.进一步与其他经典实时调度算法(EDF(earliest deadline first),DBP(distance-based priority),DWCS(dynamic window constraint schedule))进行比较,验证该算法与其他算法具有相当的性能.     

基于注意力机制及类别层次结构的弱监督目标定位

弱监督目标定位是指仅利用图像级的类别标注信息来训练目标定位器, 而不需要使用精确的目标位置标注信息来进行算法训练. 当前的一些方法往往只能定位出目标对象中最具鉴别性的部分而无法准确地标识出完整的目标对象, 或者易受背景无关信息干扰从而导致定位结果不精确. 为了解决上述问题, 提出一种基于注意力机制和类别层次结构的弱监督目标定位方法. 该方法通过对卷积神经网络的注意力图进行均值分割提取更完整的目标区域. 进一步, 通过类别层次结构网络实现对背景区域注意力的削弱, 从而提高对感兴趣目标的定位精度. 基于多个网络结构和公共数据集上的大量实验结果表明, 相比目前已有的弱监督定位方法, 所提方法在多个评价指标下均能够获得更好的定位效果.