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.     

Phosphoric-Acid Retention in High-Temperature Proton-Exchange Membranes

Great efforts have been conducted to develop high temperature proton exchange membrane fuel cell (HT-PEMFC) due to its features of enhanced electrocatalyst reactivity, simplified hydrothermal management system and high CO tolerance of catalysts, and remarkable progress has been achieved. However, the easy leaching of phosphoric acid (PA) from the membranes during operation limits its commercial scale-up in complicated environments. This concept here mainly focuses on the recent developments for mitigation of PA loss in PEMs. The probable mechanisms of PA loss are proposed. The approaches to improve PA retention for example via introduction of phosphonic acid by covalent bond, using ion-pairs interaction and siphoning effect, and blending with inorganic nanoparticles are described in detail. Among these strategies, the siphoning effect from the intrinsic microporous PEMs is the most efficient and enables the cell to operate flexibly within a broad temperature range. Therefore, this concept may provide new ideas for the scientists to retain PA, to improve the cell performance and expand the potential applications of PA doped PEMs at elevated humidity and wide temperature range.