Mobility of water molecules in Li+, Na+ and Cs+ ionic forms of Nafion membrane studied by NMR

Correlation times and diffusion coefficients of water molecules were measured for the first time by ¹H spin relaxation and pulsed field gradient NMR in Li⁺, Na⁺ and Cs⁺ ionic forms of Nafion 117 membrane. Hydration numbers of Li⁺, Na⁺ and Cs⁺ cations were calculated. It was shown that at high humidity macroscopic transfer is controlled by the local translational motion of water molecules.     

视觉搜索中图标布局的影响机理

采用视觉搜索范式，研究图标视觉特征及数量变化对图标布局认知绩效的影响.实验表明，当图标数量N=6时，仅图标视觉特征主效应显著，布局方式对搜索速度无显著影响，图标视觉特征是认知绩效的主要影响因素;当图标数量N=15时，仅图标布局方式主效应显著，横向排列搜索速度最快.通过图标数量的连续性变化实验发现，图标数量超过10个，横向排列反应时显著低于纵向排列，两者错误率无显著差异;随着图形面板 L_○长度 / S_○宽度比值的降低，两者平均反应时差距逐渐缩小，趋于一致.研究表明，图标数量的变化对布局方式和视觉特征的认知绩效产生显著影响.     

Maximal Subrings and Covering Numbers of Finite Semisimple Rings

We classify the maximal subrings of the ring of n×n matrices over a finite field, and show that these subrings may be divided into three types. We also describe all of the maximal subrings of a finite semisimple ring, and categorize them into two classes. As an application of these results, we calculate the covering number of a finite semisimple ring.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.