FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

Solubility of Si3N4 in Liquid SiO2

The nitrogen solubility in the SiO₂-rich liquid in the metastable binary SiO₂-Si₃N₄ system has been determined by analytical TEM to be 1%–4% of N/(O + N) at 1973–2223 K. Analysis of the near edge structure of the electron energy loss peak indicates that nitrogen is incorporated into the silicate network rather than being present as molecular N₂. A regular solution model with a positive enthalpy of mixing for the liquid was used to match the data for the metastable solubility of N in the presence of crystalline Si₃N₄ and to adjust the computed phase diagram. The solubility of Si₃N₄ in fused SiO₂ is far less than reported in liquid silicates also containing Al, Mg, and/or Y. Apparently, these cations act as modifiers that break anion bridges in the silicate network and, thereby, allow further incorporation of Si₃N₄ without prohibitive amounts of network cross-linking. Finally, indications emerged regarding the diffuse nature of the Si₃N₄-SiO₂ interface that leads to amorphous regions of higher N content.     

A unified model for the structure of polymers in semidilute solution

A model is developed to analyse the concentration dependence of the range ξ_? of the monomer pair correlation function. In semidilute solution, three concentration regimes are found for semiflexible molecules and the crossover points between the various regimes are predicted in terms of the characteristic ratio of the chains in dilute solution and in terms of the Flory interaction parameter χ. A simple physical interpretation is given which explains the concentration dependence of ξ_? based on binary contacts initially and then ternary contacts at higher concentration. Temperature-concentration diagrams are developed for several common polymer-solvent systems.     

Advanced underfill for high thermal reliability

The key to the success of flip‐chip technology lies in the availability of sucessful underfill materials. However, the reliability of flip‐chip technology using current underfill materials is generally found to be lower than that of conventional wire‐bond connection packaging materials such as epoxy molding compound (EMC) because of the high coefficients of thermal expansion (CTE) and moisture absorption of cured underfill material. In this study desbimide (DBMI), which has a low melting point (about 80°C), was used in the underfill materials as a cohardener. As a result, DBMI‐added underfill can show excellent thermal reliability, which is due to the superior properties of the CTE, the elastic modulus, and water resistance. When the properties of a 2 wt % DBMI‐added underfill were compared with those of a typical underfill (epoxy/anhydride), the CTE value was reduced to less than one‐half at the solder reflow temperature (about 200°C), the elastic modulus was reduced to less than one‐half in the temperature region below the glass‐transition temperature, and the water resistance was improved twofold. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 83: 2617–2624, 2002     

晋中民俗文化对当地食品包装设计的影响

承载着千年文化的山西晋中,有着独特的地域民俗文化,在当今如何把当地传统民俗文化内涵运用在食品包装设计当中成为一种趋势,越来越多的设计师和消费者深刻的认识到本土民俗文化元素对食品包装设计内涵的重要性,因此在现代食品包装设计中合理的融入民俗文化元素,从而使食品包装设计显示出独特、深厚并富有魅力的乡土风情和地域性文化内涵。     

交互式教学实践在设计教学中的应用研究

交互式实践教学模式是指在设计教学过程中,不仅考虑教学媒介与学习者之间的双向信息流动,也考虑设计教学中内容与实践的结合以及学生在课堂上的有效思考和设计实践能力。文章以包装设计课程为例,探讨交互式教学实践模式设计艺术课程教学改革的可能性。     

Chemical beneficiation of coal with aqueous hydrogen peroxide/sulphuric acid solutions

The removal of sulphur and ash from coal treated with aqueous hydrogen peroxide/sulphuric acid solutions has been studied at ambient temperature, under a variety of experimental conditions. Almost complete elimination of the sulphate and the pyritic sulphur was observed in most cases, as well as substantial reduction in the ash content. The other components of the organic coal matrix were not affected to a significant extent, indicating high selectivity of the $\text{H}{}_2\text{O}{}_2\text{H}{}_2\text{SO4}$ system towards sulphur oxidation. An optimal H₂SO₄ concentration was established, above which the acid was found to have an adverse effect on the oxidation of pyrite by hydrogen peroxide.     

社交网站安全问题分析与对策研究

文章全面分析了社交网站中存在的安全问题,提出对应的建议及解决策略,同时全面深入地分析社交网站的关键技术。在社交网站潜在隐患的分析过程中,重点探讨了社交网站在网络安全、信息安全、品牌危机、社会生活等方面存在的安全问题,并分别提出了相应的对策和建议,从而保障社交网站在中国的顺利应用,维护国家安全和社会稳定。     

一种基于Hough变换和图像融合的快速破损检测

针对工业破损检测的现状进行研究,提出运用数字图像处理系统代替传统的硬件检测。首先对薄膜进行图像预处理,运用Hough(霍夫)变换分割出连续2帧的感兴趣区域,运用小波变换增强图像对比度;其次计算各个像素点的EOI(拉普拉斯能量)和VI(对比度),将归一化处理后的值作为图像融合的系数;最后把融合后图像转化到HSI(色度、饱和度、亮度)空间,进行阈值分割,进行破损判别。实验表明,这种检测方法具有抗干扰性强、成本低、准确性高、计算量小、识别速度快的优点,基本能实现包装的实时检测。