Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.     

观赏南瓜色素的提取及性质研究

对观赏南瓜色素的提取及性质进行了初步的探索,研究了光、温度、pH、氧化剂、还原剂、常用的食品添加剂对色素的影响.结果表明:观赏南瓜色素对光和热都比较稳定;适宜在pH值4-12之间使用;耐氧化性和耐还原性均较好;Vc对色素有一定的消色作用;柠檬酸三钠对色素有增色作用;色素对常用的食品添加剂有较强稳定性.     

Liquid-liquid phase equilibria of aqueous two-phase systems containing salts and polyethylene glycol

Liquid-liquid phase equilibria of the ternary systems: (a) polyethylene glycol - ammonium sulfate- water and (b) polyethylene glycol - sodium carbonate -water have been determined experimentally at 15°, 25°, 35° and 45°C and for two different molecular weights of the polymer (Avg. M.W. 1000 and 2000). Details of the glass cell and of the equilibration and analytical procedures used are described. Equilibrium data along with phase diagrams are presented. Finally the effect of temperature and of the molecular weight of the polymer are also discussed.     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

氢氟烃/烷烃二元混合物的气液相平衡

整理了已公开发表的氢氟烃(HFC)/烷烃(HC)二元混合物气液相平衡实验数据,对实验数据进行了热力学一致性检验。采用PR方程加van der Waals混合规则描述该类混合物的气液相平衡性质,优化得到了11种混合物的二元交互作用系数,经比较表明采用优化结果能够高精度再现气液相平衡实验数据,比k_(ij)取0的计算结果有很大改善.     

On the origin of irreproducible behaviour of Na1−xLixNbO3 solid solutions

The irreproducibility of electrical properties of Na_0.88Li_0.12NbO₃ solid solution on thermal cycling reported by M.A.L. Nobre and S. Lanfredi is explained by gradual decomposition of the supersaturated solid solution below ca. 800 °C.     

红外光谱法分析淀粉接枝聚丙烯酸酯共聚物的各级结构

研究玉米淀粉接枝聚丙烯酸酯共聚物的各级结构，主要探讨去除均聚物和玉米淀粉侧链的方法。发现以环己烷为溶剂，用索氏萃取法除去均聚物比用苯萃取法时间短、效果好；用HCl酸解法除去淀粉侧链比用HClO4氧化法简单实用。用红外光谱进一步验证了各级结构的官能团，证实了所合成的共聚物是玉米淀粉接枝聚丙烯酸酯共聚物。     

萃取色谱法富集原子吸收法测定环境水中超痕量金属元素──两种萃取剂的比较

本文研究并比较了分别以８－羟基喹啉和巯基苯骈噻唑为萃取剂，以活性硅胶为载体的柱式萃取色谱法对环境水中Ｚｎ、Ｃｕ、Ｐｂ、Ｃｄ、Ｆｅ、Ｃｏ、Ｎｉ和Ｍｎ的最佳富集和洗脱条件。实验证明，后者明显优于前者。以巯基苯骈噻唑为萃取剂的色谱柱对金属元素的吸附具有快速、完全、寿命长和重现性好等特点。在ｐＨ＝７～８之间回收率可达９８％以上，富集倍数为２００倍。     

On Nash Equilibria for Noncooperative Games Governed by the Burgers Equation

Existence of a Nash equilibrium in a noncooperative game governed by the one-dimensional Burgers equation, proposed in the case of pointwise controls in Ref. 1, is proved under data qualifications that guarantee the diffusion term in the Burgers’ equation to be dominant enough with respect to the uniform convexity of the payoffs. This work was partly supported by Grants 201/03/0934 (GA čR) and MSM 0021620839 (MšMT čR). Inspiring discussions with Angel M. Ramos are acknowledged.