张量广义特征值的S-型包含区域

设{A,B}为m阶n维正则张量对,通过将指标集N={1,2,…,n}划分为非空真子集S及其补集S珚=N/S,利用分类讨论的思想以及张量对{A,B}某些元素选取的任意性和不等式缩放技巧,解决了张量对{A,B}的特征值定位问题,并给出张量对{A,B}特征值的S-型包含区域.数值结果表明,所得包含区域比已有包含区域更精确.     

Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

非同分布φ混合序列加权和的强极限收敛性

利用φ混合序列矩不等式和截尾的处理方法,研究非同分布φ混合序列加权和强极限收敛性质的问题,得到了若干新结果,推广并改进了独立同分布情形下的相应结果.     

Synthesis of self‐healing polyurethane urea‐based supramolecular materials

Supramolecular polyurethane ureas are expected to have superior mechanical properties primarily due to the reversible, noncovalent interactions such as hydrogen bonding interactions. We synthesized polyurethane prepolymers from small molecular weight of poly(tetramethylene ether)glycol and isophorone diisocyanates, which were end capped with propylamine to synthesize polyurethane ureas with high contents of urea and urethane groups for hydrogen‐bonding formations to facilitate self‐healing. The effects of polyurethane urea molecular weight (3000 ≤ M_n ≤ 9000), crosslinking, and cutting direction were studied in terms of thermal, mechanical, and morphological properties with an emphasis on the self‐healing efficiency. It was found that the thermal self‐healability was more pronounced as the molecular weight of polyurethane urea decreased, showing a maximum of more than 96% with 3000 M_n when the sample was cut along the stretch direction. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 468–474     

连续刚构铁路桥收缩徐变效应监测与分析

对连续刚构铁路桥箱梁温度场及桥梁线形进行长期、连续监测,通过主梁跨中下挠的理论与实测对比揭示了连续刚构铁路桥收缩徐变效应。对比了国内外常用收缩徐变估算模型,选择CEB-FIP徐变模型对黄河特大连续刚构桥进行了有限元分析。采用实测温度数据,以箱梁内测温度、外侧温度、顶底板温度梯度、左右侧温度梯度作为箱梁温度场的评判指标,对箱梁1年内的四季温度场分布进行分析。在基于相同温度场的条件下,通过理论值与实测值对比,发现分析成果与实测结果较吻合,说明混凝土的收缩徐变是引起连续刚构铁路桥跨中下挠的主要原因,对比结果还说明通过改善箱梁顶底板应力差能够改善收缩徐变长期效应。     

桂林傩舞现状及问题研究--以秀峰区张家村为例

受神秘的巫文化影响，桂林傩舞有着悠久的历史，曾经盛极一时，但近年来逐渐趋于衰退。通过实地考察张家村傩舞，可以发现桂林傩舞艺术面临着缺乏继承人、观赏性不足、舞蹈造型和手势表达失传、道具不精、基层教育不重视、表演人员经济困难等生存困境。当地政府应该加强宣传力度，加大资金投入，培养傩舞表演的继承人和道具制作的传承人，强化对傩舞的理论与实践研究，不断提炼傩舞的特色内涵，促进桂林傩舞的保护和传承。     

一类Minimax分式规划问题的迭代算法

对一类Minimax分式规划问题(MFP)提出一个迭代算法.首先通过引进变量和指数变换,将问题(MFP)等价转化为问题(Q),然后利用代数-几何平均不等式以及合适的转化过程,将等价问题(Q)压缩为凸规划问题(Q).从而根据选择不同的点所对应的压缩问题(Q),将原问题的求解过程转化为求解一系列的凸规划问题.数值实验表明算法是可行有效的.     

Post李超代数结构的性质

通过post李超代数的定义, 讨论post李超代数结构的基本性质, 给出post李超代数的一些存在性结果, 并利用post李超代数可构造LR超代数和左对称超代数, 给出交换post李超代数结构的相关结果.     

专利风险评价指标体系构建及关键指标国际比较

 从经济安全的角度，基于专利价值链理论，构建了一套专利风险评估指标体系，用于衡量一个国家或地区在专利活动中遭遇风险的程度。利用专利基本活动中的4个关键指标，即专利质量水平、专利转化能力、专利纠纷风险程度和专利贸易国际地位，对美国、日本、韩国、德国和中国进行比较分析，得出2006-2015年，中国的专利发展“快而不高”“大而不强”，但与其他专利强国相比，在专利价值链关键环节的竞争中，中国不占优势，甚至存在较为严重的风险，尤其专利使用费逆差越来越大，对国家经济安全存在一定程度的威胁。