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.     

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。     

Color accurate monitors: Basic features and comparison of four monitors

Color accurate monitors are high resolution, luminance‐controlled displays with very large color gamut. They have internal controls to match specific color standards (e.g., sRGB, Adobe‐RGB, REC‐709) and well‐defined gamma functions (mostly γ = 2.2, but others such as Equal Probability of Detection, Digital Imaging and Communications in Medicine). Usually, they come with external tools for automatic calibration (like Chroma 5 or Spider) and for communicating with the host computer through USB port, and with software to control the calibration process. Most of them allow a calibration to a specific customer selected color gamut, besides the precalibrated standards, but limit the gray levels calibration to a gamma type function (typically γ = 2.2). Their unique properties, challenges, and applications will be discussed. A comparison between the properties of four monitors and optical test results of their parameters is presented.     

同形映射下的曲面场景的匹配算法的性能分析

针对移动机器人在曲面场景的匹配问题中,同形约束用于解决极约束产生的匹配模糊性问题和发现新的匹配点.实际上是平面块对曲面进行近似逼近的过程.逼近程度和逼近性能需要有指标进行定性和定量的衡量.故提出了两种性能评价指标:平均映射误差和平均映射匹配对.仿真实验结果的分析证明,场景深度变化或者场景距离摄像机的距离变化,对立体匹配算法性能本身不受影响,但映射和建立匹配关系时所需要的同形矩阵的数量不同.而且,随着特征点的稠密度提高,曲面场景的稳定性降低.可随着迭代过程的进行,算法本身结果还趋于稳定.     

Weakly supervised temporal action localization with proxy metric modeling

Temporal localization is crucial for action video recognition. Since the manual annotations are expensive and time-consuming in videos, temporal localization with weak video-level labels is challenging but indispensable. In this paper, we propose a weakly-supervised temporal action localization approach in untrimmed videos. To settle this issue, we train the model based on the proxies of each action class. The proxies are used to measure the distances between action segments and different original action features. We use a proxy-based metric to cluster the same actions together and separate actions from backgrounds. Compared with state-of-the-art methods, our method achieved competitive results on the THUMOS14 and ActivityNet1.2 datasets.