A modern approach to the solution and analysis of the Simha-Somcynsky model for the description of pressure-volume-temperature properties of polymer fluids

We revisit the Simha-Somcynsky model of polymer fluids with the purpose of developing novel theoretical and computational approaches to simplify and speed up its solution as well as the fitting of experimental data, and decrease its level of mathematical complexity. We report a novel method that allows us to solve one of the two equations of the model exactly, thus putting the level of mathematical difficulty on a par with the one of other models for polymer fluids. Moreover, we describe a computational algorithm capable of fitting all five parameters of the model in an unbiased way. The results obtained reproduce literature results and fit experimental pressure-volume-temperature and solubility parameter data for three polymers very accurately. Moreover, the new techniques allow for the investigation of the model at very low temperatures. Unexpectedly, the model predicts behaviors that could be interpreted as a glass transition, as routinely observed in dilatometry and differential scanning calorimetry, and a glass phase. We compared the predicted and experimental T g’s for cis poly(1,4-butadiene) and found an excellent quantitative agreement.     

Autour de la conjecture de L. Markus sur les variétés affines

Summary For any subgroupG of (n), we introduce some integer discGn called thediscompacity ofG. This number measures to what extent the closure ofG is not compact. The Markus' conjecture says that a compact affinely flat unimodular manifold is complete. Our main result (called the discompact theorem) is that this conjecture is true under the assumption that the linear holonomy i.e. the parallel transport has discompacity 1. Because discSO(n–1, 1)=1, this ensures that a compact flat Lorentz manifoldM is geodesically complete. Hence, by a previous result of W. Goldman and Y. Kamishima [GK], such aM is, up to finite covering, a solvmanifold. This achieves the proof of a Bieberbach's theorem for compact Lorentz flat manifolds.     

种植沙生植物--沙棘改善内蒙古地区生态环境

结合内蒙古地区现状，对沙棘的生物学和生态学特性、沙棘属植物化学成分和微量元素及种植沙生植物——沙棘的重要性和必要性进行了详细的研究和探讨。研究表明，沙棘属植物具有极强的生态适应性并富含多种营养成分和生物活性物质，并以耐干旱、耐瘠薄、萌蘖及固氮能力强等特点被称为治理非宜林地水土流失、改善生态环境的先锋树种。种植沙棘是治理内蒙古脆弱生态环境最经济、最有效的措施，是贫瘠的不毛之地发展经济、增加收入的经济树种。另外．种植沙棘的技术简便，容易掌握，投资少，见效快。     

内蒙古地区天然植物沙棘果中黄色素的提取工艺及性质研究

以内蒙古地区沙棘果实为原料，研究了提取黄色素的工艺条件，同时对该色素的性质进行了初步探讨。结果表明，以95％的乙醇溶液作浸提剂，提取的黄色素浓度最高，工艺流程简单易行，且无毒，无污染。对提取的黄色素进行的性质试验表明，沙棘黄色素对光、热具有较好的稳定性，适用于酸性或弱碱性的食品中，葡萄糖、氧化剂(H2O2)、还原剂(Na2SO3)等食品添加剂均无明显影响以上结果为这种优良天然色素的开发与应用提供了参考。