First fall degree and Weil descent

Polynomial systems arising from a Weil descent have many applications in cryptography, including the HFE cryptosystem and the elliptic curve discrete logarithm problem over small characteristic fields. Understanding the exact complexity of solving these systems is essential for the applications. A first step in that direction is to study the first fall degree of the systems. In this paper, we establish a rigorous general bound on the first fall degree of polynomial systems arising from a Weil descent. We also provide experimental data to study the tightness of our bound in general and its plausible consequences on the complexity of polynomial systems arising from a Weil descent.     

三维结构和氧化度对C6位氧化再生纤维素止血材料性能影响

C6位氧化再生纤维素作为可吸收止血材料,其止血性能受材料理化性质的影响。通过比较氧化再生纤维素的吸水率、凝胶化速率、溶解速率、降解速率、抗老化性能和止血效果,研究三维结构和氧化度对氧化再生纤维素性能影响。结果发现,氧化度增高,氧化再生纤维素吸水率增强,凝胶化速率加快,溶解速率和降解速率变快,抗老化性能变差,产品有效期变短。纤丝松散网状多孔结构比纱布致密结构更有利于提高吸水率,加快凝胶化速率和溶解速率;同时降低氧化剂用量,提高抗老化性能。同一氧化度条件下,纤丝止血速率优于纱布,止血效果更好。     

TiO2烧结助剂对纳米η-Al2 O3制备Al2 O3-Cr2 O3固溶体的影响研究

以纳米η-Al₂O₃粉和工业铬绿为原料,以摩尔比1:1配比制备Al₂O₃-Cr₂O₃固溶体,以TiO₂为烧结助剂,在还原气氛下经1400 ℃、1500 ℃和1600 ℃固相烧结.研究了TiO₂的加入对纳米η-Al₂O₃制备Al₂O₃-Cr₂O₃固溶体的致密度、线收缩率、相组成、晶胞参数、互扩散程度和微观结构的影响.结果表明:TiO₂的加入能促进Al₂O₃-Cr₂O₃固溶体的致密化;当温度为1600 ℃,TiO₂的添加量为2wt;时,试样的体积密度最大为4.57 g·cm^-3,线收缩率为19.8;;TiO₂的加入能使Al₂O₃-Cr₂O₃固溶体中Al³⁺和Cr³⁺的互扩散程度增加;微观结构表明,TiO₂的加入能使Al₂O₃-Cr₂O₃固溶体晶粒之间结合更紧密,实验温度范围内,随着TiO₂添加量的增加晶粒从沿晶断裂向穿晶断裂转变,只在晶间和晶内存在极少量气孔,当温度为1600 ℃,TiO₂的添加量为2wt;时,晶粒大小较均匀,平均晶粒尺寸约10μm.     

Structural optimization of highly branched thermally responsive polymers as a means of controlling transition temperature

Highly branched “smart” polymers have emerged as a unique class of polymers with wide‐ranging applications. Poly(N‐isopropylacrylamide) (pNIPAAm) is at the forefront of stimuli‐responsive polymers; however, few transition temperature‐modification methods of linear pNIPAAm have been explored in highly branched systems. In this study, the three primary techniques of transition temperature modification of linear pNIPAAm are investigated for their efficacy on highly branched polymers. Of these techniques, cosolvent‐mediated tacticity control demonstrates an effect opposite of that which is expected. Temperature transition control via end‐group modification shows a marked decrease in efficacy in highly branched systems, despite highly branched systems having more end groups per polymer. Copolymerization with hydrophilic comonomers exhibits varying changes in efficacy compared to linear analogs, lending insights into the specific effects on the structured water surrounding the copolymer. While copolymerization proved to be most versatile in changing the transition temperature, all of the techniques showed interesting secondary effects. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Graph‐theoretic method on the periodicity of multipatch dispersal predator‐prey system with Holling type‐II functional response

We study the periodicity of multipatch dispersal predator‐prey system with Holling type‐II functional response in this paper. By providing a new method, we overcome the difficulty to get the priori bounds estimation of unknown solutions of operator equation Lu=λNu. Graph theory with coincidence degree theory is used, and a sufficient criterion for the periodicity of the system is obtained. The criterion presented in this paper is closely related with topological structure of dispersal network and can be verified easily. Finally, a numerical example is also provided to verify the effectiveness of theoretical results.     

Synthesis of dendronized polymers through bergman cyclization of enediyne‐containing Frechet‐type dendrimers

In this article, dendronized polymers with rigid backbones were synthesized from enediyne‐containing Frechet‐type dendrimers. Two generations of dendrimers were conically incorporated with 3‐(2‐(2‐(trimethylsilyl)ethynyl)phenyl)prop‐2‐yn‐1‐ol. The trimethylsilyl protection groups of enediyne units were subsequently removed, and two types of brush polymers with rigid conjugated backbone were prepared through Bergman cyclization polymerization at elevated temperature under vacuum. The dendronized polymers were characterized with GPC, IR, UV–vis, and NMR spectroscopy. Furthermore, the morphology of the dendronized polymer was revealed by atomic force microscopy. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

有旋转自由度的高精度四边形单元

从具有三次位移模式的平面等参元出发 ,通过对单元自由度进行线性变换并引入连续介质力学中关于旋转度的定义 ,构造出角结点有旋转自由度的高精度四边形单元。该单元与平面等参元有相同的单元特征及精度     

FIXED POINT THEOREMS FOR FUZZY MAPPINGS IN PROBABILISTIC METRIC SPACES

ＦＩＸＥＤ　ＰＯＩＮＴ　ＴＨＥＯＲＥＭＳ　ＦＯＲ　ＦＵＺＺＹ　ＭＡＰＰＩＮＧＳ　ＩＮ　ＰＲＯＢＡＢＩＬＩＳＴＩＣ　ＭＥＴＲＩＣ　ＳＰＡＣＥＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）；ＺｈａｎｇＹｉｎｇ（张颖）；ＹｕａｎＪｉａｗｅｉ（袁家玮）（Ｒｅｃｅｉｖ...     

用相似接近度法从多目标优化非劣解中求最优解

本文讨论了从多目标优化非劣解中求最优解的各种方法及其不足,提出了用灰色关联度解决非劣解各序列间的形状差异问题,用模糊数学中海明距离和贴近度解决非劣解各序列间位置差异问题,然后加以合并,综合衡量两差异得到相似接近度概念,并用以确定最优解。