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。     

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。     

锚链钢弯环内侧开裂分析原因

对锚链钢弯环的原材料和车削后热处理材料及开裂的弯环进行低倍、组织、断口检验，结果表明弯环开裂是由车削后的热处理工艺和焊接工艺控制不当造成的。