一个R2上含双曲函数核的Hilbert型不等式

通过引入参数，构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开，建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用，通过赋予参数不同的值，建立了一些有意义的特殊结果。     

多元统计分析中一类矩阵迹函数最小化问题的有效算法

研究来源于多元统计分析中的一类矩阵迹函数最小化问题$\min c+ tr(AX)+\sum\limits_{j=1}^{m}tr(B_j X C_jX^{T}),\ \ {\rm s. t.} \ X^TX=I_p,$其中$c$为常数, $A\in R^{p\times n}\ (n\geq p)$, $B_j\in R^{n\times n}, C_j\in R^{p\times p}$为给定系数矩阵. 数值实验表明已有的Majorization算法虽可行, 但收敛速度缓慢且精度不高. 本文从黎曼流形的角度重新研究该问题, 基于Stiefel流形的几何性质, 构造一类黎曼非单调共轭梯度迭代求解算法, 并给出算法收敛性分析.数值实验和数值比较验证所提出的算法对于问题模型是高效可行的.     

密度泛函理论方法研究填料表面对聚合物摩擦化学的影响

采用超声分散法制备出氧化铝、高岭土、氧化硅/聚四氟乙烯复合材料, 使用线性往复摩擦磨损试验机对比三种复合材料的摩擦学性能. 结果表明 质量分数10%的氧化铝、高岭土能将聚四氟乙烯的磨损率降低约4个数量级, 而氧化硅仅能降低约3个数量级. 对金属对偶表面形成的转移膜的形貌和化学成分进行分析发现 氧化铝、高岭土/聚四氟乙烯在金属对偶面上形成了高度羧酸盐化的转移膜. 用密度泛函理论对三种填料表面上碳氟分子吸附过程进行模拟, 结果显示氧化铝、高岭土表面的路易斯酸性位点促进了碳氟分子的脱氟过程, 产生了更多的羧酸螯合物的中间产物; 氧化硅缺少路易斯酸性位点, 因此不能促进高度羧酸盐化的转移膜形成.     

High-efficient surface tailoring via reverse atom transfer radical polymerization and reversible addition-fragmentation chain-transfer polymerization in an aqueous system initiated by a monocenter redox pair

The commonly used multi-center initiation methods always lead to the formation of quantities of homopolymer in the surface tailoring based on reverse atom transfer radical polymerization (ATRP) and reversible addition-fragmentation chain-transfer (RAFT) polymerization. In this study, a monocenter redox pair constructed of silica bearing tert-butyl hydroperoxide groups and ascorbic acid (SiO₂-TBHP/AsAc) was applied to substitute the commonly used initiation method of R-supported RAFT grafting polymerization. All the propagating radicals were restricted on the surface of solid particles during the whole procedure theoretically, resulting in a higher grafting efficiency of 95.1% combined with the “controllable” feature at 10 h. This redox pair was also used to initiate the reverse ATRP in miniemulsion successfully with a grafting efficiency of 86.3% at 10 h. The grafting efficiency obtained under this monocenter initiation method was significantly higher than that of the frequently reported surface modification by reverse ATRP and RAFT polymerization. In addition, the high-efficient surface tailoring was traced and confirmed by nuclear magnetic resonance, Fourier transform infrared, X-ray photoelectron spectroscopy, thermogravimetric analysis, transmission electron microscopy, and other analysis tests. The advantage of this monocenter redox pair will open a new avenue for the potential “high-efficient” surface tailoring of various materials.