A variable-penalty alternating directions method for convex optimization

We study a generalized version of the method of alternating directions as applied to the minimization of the sum of two convex functions subject to linear constraints. The method consists of solving consecutively in each iteration two optimization problems which contain in the objective function both Lagrangian and proximal terms. The minimizers determine the new proximal terms and a simple update of the Lagrangian terms follows. We prove a convergence theorem which extends existing results by relaxing the assumption of uniqueness of minimizers. Another novelty is that we allow penalty matrices, and these may vary per iteration. This can be beneficial in applications, since it allows additional tuning of the method to the problem and can lead to faster convergence relative to fixed penalties. As an application, we derive a decomposition scheme for block angular optimization and present computational results on a class of dual block angular problems. This material is based on research supported by the Air Force Office of Scientific Research Grant AFOSR-89-0410 and by NSF Grants CCR-8907671, CDA-9024618 and CCR-9306807.     

Nontriviality of the first Hochschild cohomology of some block algebras of finite groups

We show that for some finite group block algebras, with nontrivial defect groups, the first Hochschild cohomology is nontrivial. Along the way we obtain methods to investigate the nontriviality of the first Hochschild cohomology of some twisted group algebras.     

节理岩体中地下洞室超挖计算

讨论了超挖的定义以及不稳定块体体积与超挖的关系 ,总结了计算块体位置和体积的方法可分为随机、确定性和半概率方法三类 ,为今后超挖方面的研究提出了指导方向。重点分析并给出了被三个节理面切割的岩块以及隐含危险岩块的位置计算的确定性方法 ,提出了岩块体积计算简易的近似算法。超挖计算对洞室安全、高效地现场施工具有重要指导意义.     

岩质边坡设计坡角和锚固方案的确定

本文运用赤平极射投影、块体理论和岩体力学的基本原理, 试探求一种可供边坡工程设计采用的确定人工岩质边坡最大安全设计坡角和锚固方案的简易方法。     

热/机械载荷下功能梯度材料矩形厚板的弯曲行为

采用Reddy高阶剪切板理论，考虑材料物性参数随坐标和温度变化的特性，研究在均匀变化的温度场内功能梯度材料矩形板在面内与横向载荷共同作用下的横向弯曲问题，基于一维DQ法和Galerkin技术，给出了一对边固支，另对边任意约束时板弯曲问题的半解析解，以Si3N4/SUS304板为例考察了材料组份，温度场，面内载荷及边界约束条件等对功能梯度材料板弯曲行为的影响。     

Advanced analytical methods for the structure elucidation of polystyrene-b-poly(n-butyl acrylate) block copolymers prepared by reverse iodine transfer polymerisation

Reverse iodine transfer polymerisation (RITP) is a living radical polymerisation technique that has shown to be feasible in synthesising segmented styrene-acrylate copolymers. Polymers synthesised via RITP are typically only described regarding their bulk properties using nuclear magnetic resonance spectroscopy and size exclusion chromatography. To fully understand the complex composition of the polymerisation products and the RITP reaction mechanism, however, it is necessary to use a combination of advanced analytical methods. In the present RITP procedure, polystyrene was synthesised first and then used as a macroinitiator to synthesise polystyrene-block-poly(n-butyl acrylate) (PS-b-PBA) block copolymers. For the first time, these PS-b-PBA block copolymers were analysed by a combination of SEC, in situ¹H NMR and HPLC. ¹H NMR was used to determine the copolymer composition and the end group functionality of the samples, while SEC and HPLC were used to confirm the formation of block copolymers. Detailed information on the living character of the RITP process was obtained.     

超分子水凝胶作为胰岛素缓释体系的研究

利用α-环糊精(α-CD)与含有聚乙二醇(PEG)链段的聚合物Pluronic F127的超分子作用制备水凝胶.该物理交联水凝胶的交联点包括α-CD与PEG链包合物堆积形成的微晶区和聚合物疏水链段聚集区.优化水凝胶组分,得到具有较低固含量和较短凝胶化时间的体系用于胰岛素的负载和释放研究.通过X射线衍射(XRD),扫描显微镜(SEM)对水凝胶结构进行表征.通过紫外分光光度计监测胰岛素的释放过程,结果表明,水凝胶释药时间约为65 h,且释放曲线较为平缓.细胞毒性实验结果表明该水凝胶材料对细胞生长无明显抑制作用.小鼠体内释药实验结果表明该水凝胶载体对延长胰岛素的释药时间有一定效果,可作为多肽类药物的缓释体系.     

基于聚乙烯的无规和嵌段接枝共聚物的制备

采用乙烯配位聚合和巯基-烯点击化学相结合的方法制备了羟基封端的线性聚乙烯,末端羟基含量接近100%;利用酰氯与羟基的高效反应,将羟基封端的聚乙烯转化为降冰片烯封端的聚乙烯大单体(PE-NB).使用Grubbs II代催化剂,将大分子单体与降冰片烯(NB)单体进行开环易位共聚,通过调整单体的投料比和加料方式制备了分子量和组成可控的聚降冰片烯-g-聚乙烯(PNB-g-PE)接枝共聚物.其中,无规共聚时,大单体的转化率接近100%,所得无规接枝共聚物的重均分子量为1.79×10~4~3.14×10~4,分子量分布指数为2.09~2.60,聚乙烯链段的质量分数为4.6%~16.8%;而嵌段共聚时,由于空间位阻原因,大单体的转化率约为80%.热分析研究发现,由于空间位阻,接枝共聚物的结晶度较聚乙烯前驱体略有下降,且接枝度越大,结晶能力下降得越多.     

股票市场的长记忆及其动态结构

本文提出了结合平均小波系数法和自回归原始自助法的稳健长记忆检验,蒙特卡罗模拟显示该方法对于短期记忆过程具有稳定性。基于该方法对2005年4月8日至2015年6月30日的中国、美国、香港和德国股市进行了实证分析。全局检验结果表明仅中国的股票市场存在显著的长记忆,并且风险因素无法对长记忆解释,而美国、德国和香港的股市不存在长记忆。基于递增窗口的动态Hurst指数分析显示,金融危机时期4个股市都存在显著的长记忆。2010年后,除中国股市外,其余三个股市几乎不存在长记忆现象。