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.     

激光干涉环圆心位置测定技术及应用

本文利用在平面内绕定轴旋转的线阵ＣＣＤ及微机系统自动测定激光干涉环圆心位置及应用于激光外径千分尺平行度检查仪平行度检查结果的自动数字化输出。     

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     

Optimal and Suboptimal Quadriphase Sequences Derived from Maximal Length Sequences over Z _{{\bf 4}}

The paper presents families of quadriphase sequences derived from maximal length sequences over having good correlation properties. These are: (i) families of quadriphase sequences of period from maximal length sequences over ; each family consisting of sequences, (ii) families of quadriphase sequences of period from interleaved maximal length sequences over ; each family consisting of sequences. Such sequences are of interest in quadriphase modulated code division multiple access communication systems, where it is desirable to have large sets of sequences that possess low value of , the maximum magnitude of the periodic crosscorrelation and out of phase auto-correlation values. The sequences over are viewed as trace functions of appropriately chosen unit elements of Galois extension rings of . Quadriphase sequences are then obtained from sequences, by a quadriphase mapping, , from to roots of unity, given by, ; where and . Periodic correlation properties (correlation values and their distribution) of the quadriphase sequences are obtained by using an Abelian association scheme on the elements of the corresponding Galois extension ring of . The majority of the families of sequences derived are optimal with respect to the Welch lower bound on ; the rest being suboptimal with bounded by , where is the period\newpage of the sequences. However nearly half of the sequences in these families are balanced. Received July 18, 1995; revised version November 29, 1996     

Effect of oil degradation during frying on the color of fried, battered squid rings

Oil degradation caused by the number of fryings performed and the effect of oil degradation on the color of fried battered squid rings were studied. Spectrophotometric techniques with absorbance in the UV and visible ranges, and iodine, peroxide, and acid values were used to determine oil degradation. Determination of various CIELAB parameters in order to study the external color of the fried battered squid rings revealed no differences in color due to the number of fryings. A study of the color of the battered squid rings at various frying times and temperatures showed significant differences for both variables. Although there was some degradation in the oil after 20 fryings, appearing as a slight darkening, it did not affect the final color of the fried, battered squid rings.     

QH-2型扁环填料的流体力学和传质性能研究

在内径60 0填料塔中 ,用空气 富氧水系统对3 8和5 0QH 2型扁环填料的流体力学和传质性能进行了研究 ,得出计算其压降、液泛气速和传质单元高度的关联式。并与3 8鲍尔环、5 0鲍尔环和3 8环矩鞍填料进行了比较 ,结果表明 ,QH 2型扁环具有优良的流体力学和传质特性。     

Crystalline complex between poly(γ-methyl l-glutamate) and dimethyl phthalate

The crystalline complex between poly(γ-methyl l-glutamate) (PMLG) and dimethyl phthalate (DMP) has been formed in films cast from a solution in dichloroethane. It has the stoichiometry of 1 mol of DMP to three or four residues of PMLG and shows two definite characteristics in X-ray diffraction patterns; one is the large hexagonal unit cell with the edge of around 28 Å and another the ‘extra’ 5.07 Å meridional reflection which can not be interpreted by a PMLG α-helical conformation. The structural examination for the films with various DMP contents is carried out by X-ray, viscoelastic, and d.s.c. measurements and the following structure is proposed for the crystalline complex. Four PMLG are associated to form a group which is hexagonally packed and DMP molecules, located in the gaps between groups, form a specific favourable helical structure along PMLG chains in which the van der Waals stacking of benzene rings of DMP is significant.     

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。