完全椭圆积分和Hersch-Pfluger偏差函数

该文建立了Hersch-Pfluger偏差函数ψK(r)和第二类完全椭圆积分ε(r)之间的关系. 通过对完全椭圆积分及某些初等函数的组合的单调性和凹凸性的研究获得了完全椭圆积分的一些不等式, 并且藉此得到Hersch-Pfluger偏差函数ψK(r)的几个渐进精确的上界估计.     

Application of hybrid oxidative processes based on cavitation for the treatment of commercial dye industry effluents

The present work demonstrates the significant role of ultrasound (US) in intensifying the efficacy of the combination with Fenton reagent and/or ozone for the treatment of real dye industry industrial effluent procured from the local industry. Initial part of the work focused on analysing the literature based on combination approaches of US with different oxidants applied for the treatment of real and simulated effluents focusing on the dyes. The work also provides guidelines for the selection of optimal operating parameters for maximizing the intensification of the degradation. The second part of the work presents an experimental study into combined approaches of ultrasound with ozone (O₃) and Fenton’s reagent for treatment of real effluent. Under optimized conditions (100 W, 20 kHz and duty cycle of 70%), maximum COD reductions of 94.79% and 51% were observed using a combined approach of US + Fenton oxidation followed by lime treatment for the treatment of effluent-I and effluent-II respectively at H₂O₂ loading of 17.5 g/L, H₂O₂/Fe²⁺ ratio of 3, pH of 4, CaO dose of 1 g/L and an overall treatment time of 70 min. US + Fenton + O₃ followed by lime was also applied for treatment under ozone loading of 1 g/h for the treatment of effluent-I and it was found that maximum COD reduction of 95.12% was obtained within 30 min of treatment time, indicating use of ozone did not result in significant value addition in terms of COD reduction but resulted in faster treatment. HC (inlet pressure: 4 bar) + Fenton + Lime scheme was successfully replicated on a pilot-scale resulting in maximum COD reduction of 57.65% within 70 min of treatment time. Overall, it has been concluded that the hybrid oxidative processes as US + Fenton followed by lime treatment is established as the best approach ensuring effective COD reduction at the same time obtaining final colourless/reusable effluent.     

Solubility prediction of deferiprone in N-methyl-2-pyrrolidone + ethanol mixtures at various temperatures using a minimum number of experimental data

Experimental solubility of deferiprone (DFP) in N-methyl-2-pyrrolidone (NMP) + ethanol (EtOH) mixtures at 293.2, 298.2, 303.2 and 308.2 K was determined and mathematically represented using various models. The trained versions of the van’t Hoff equation, its combined version with log-linear model, Jouyban–Acree model and a combination of van’t Hoff + Jouyban–Acree model were reported to simulate DFP solubility in the binary mixture compositions at various temperatures. The mean percentage deviation (MPD) was used as an accuracy criterion. The obtained overall MPDs for back-calculated and predicted solubility of DFP in NMP + EtOH mixtures varied from 1.1% to 3.2% and 2.6% to 6.6%, respectively. Some of apparent thermodynamic quantities for the dissolution processes of DFP are also reported.     

Solvent-free synthesis of dibenzo[b,j][1,10]phenanthroline derivatives using Eaton’s reagent as catalyst

A new class of dibenzo[b,j][1,10]phenanthrolines has been prepared. The synthon acridones were achieved in very good yield by a one-pot reaction of 2-amino-5-chloro or 2′-chloro/flouro-substituted benzophenones with 1,2-cyclohexanedione in the presence of freshly prepared Eaton’s reagent (phosphorus pentoxide–methanesulfonic acid) without solvent, through Friedländer synthesis. Then these intermediates were reacted with 2-amino-3,5-dibromobenzaldehyde to afford 1,3-dibromo-10-chloro-8-aryl-6,7-dihydrodibenzo[b,j][1,10]phenanthroline. Also an one-pot reaction between 2?mol of 2-amino-5-chloro aryl benzophenones with 1?mol of 1,2-cyclohexanedione to get 3,10-dichloro-5,8-diaryl-6,7-dihydrodibenzo[b,j][1,10]phenanthroline has also been reported. The newly synthesized structures of the compounds were deduced by spectroscopic techniques.     

水平层状介质中电磁场并矢Green函数的一种快速新算法

本文利用提取直射波并结合自适应数字滤波等技术提出一种计算水平层状介质中电磁场并矢Green函数的快速算法. 首先将谱域Green函数中表征均匀介质作用的直射波提取出来并对其积分进行解析计算,这种处理降低了谱域Green函数的奇异性,可在很大程度上缩短其积分收敛区间. 然后在将谱域Green函数剩余部分对应积分转化为三个快速下降积分的基础上,引入一种自适应数字滤波算法对其进行快速求解. 最后通过具体算例验证了本文所述算法的有效性. 关键词： 并矢Green函数 快速算法 水平层状介质     

Borch’s Theorem from the perspective of comonotonicity

This short note revisits the classical Theorem of Borch on the characterization of Pareto optimal risk exchange treaties under the expected utility paradigm. Our objective is to approach the optimal risk exchange problem by a new method, which is based on a Breeden–Litzenberger type integral representation formula for increasing convex functions and the theory of comonotonicity. Our method allows us to derive Borch’s characterization without using Kuhn–Tucker theory, and also without the need of assuming that all utility functions are continuously differentiable everywhere. We demonstrate that our approach can be used effectively to solve the Pareto optimal risk-sharing problem with a positivity constraint being imposed on the admissible allocations when the aggregate risk is positive.     

Further results on adaptive full-order and reduced-order observers for Lur’e differential inclusions

This paper is concerned with the adaptive observer design of Lur’e differential inclusions with unknown parameters. Under a relaxed assumption on nonlinear perturbation functions, a sufficient condition for the existence of an adaptive full-order observer is established. Comparing with results in the literature, the present conditions are complemented with a numerically reliable computational approach, which can be checked by means of linear matrix inequalities. Furthermore, it is shown that, under the sufficient condition, the existence of a reduced-order observer is guaranteed. Also, the reduced-order observer is designed. The effectiveness of the proposed design is illustrated via a simulation example.