Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

偏缠绕模的Frobenius性质

主要给出了偏缠绕模的Frobenius性质，推广了缠绕模相应的性质。     

Wall shear stress modified by bubbles in a horizontal channel flow of silicone oil in the transition region

We performed laboratory experiments on bubbly channel flows using silicone oil, which has a low surface tension and clean interface to bubbles, as a test fluid to evaluate the wall shear stress modification for different regimes of bubble migration status. The channel Reynolds numbers of the flow ranged from 1000 to 5000, covering laminar, transition and turbulent flow regimes. The bubble deformation and swarms were classified as packing, film, foam, dispersed, and stretched states based on visualization of bubbles as a bulk void fraction changed. In the dispersed and film states, the wall shear stress reduced by 9% from that in the single-phase condition; by contrast, the wall shear stress increased in the stretched, packing, and foam states. We carried out statistical analysis of the time-series of the wall shear stress in the transition and turbulent-flow regimes. Variations of the PDF of the shear stress and the higher order moments in the statistic indicated that the injection of bubbles generated pseudo-turbulence in the transition regime and suppressed drag-inducing events in the turbulent regime. Bubble images and measurements of shear stress revealed a correlated wave with a time lag, for which we discuss associated to the bubble dynamics and effective viscosity of the bubble mixture in wall proximity.     

Facile non‐lithographic route to highly aligned silica nanopatterns using unidirectionally aligned polystyrene‐block‐polydimethylsiloxane films

Thin films (monolayer and bilayer) of cylinder forming polystyrene‐block‐polydimethylsiloxane (PS‐b‐PDMS) were shear aligned by the swelling and deswelling of a crosslinked PDMS pad that was physically adhered to the film during solvent vapor annealing. The nanostructures formed by self‐assembly were exposed to ultraviolet‐ozone to partially oxidize the PDMS, followed by calcination in air at 500 °C. In this process, the PS segments were fully decomposed, while the PDMS yielded silica nanostructures. The highly aligned PDMS cylinders were thus deposited as silica nanolines on the silicon substrate. Using a bilayer film, the center‐to‐center distance of these features were effectively halved from 38 to 19 nm. Similarly, by sequential shear‐alignment of two distinct layers, a rhombic array of silica nanolines was fabricated. This methodology provides a facile route to fabricating complex topographically patterned nanostructures. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1058–1064     

简支及悬臂箱梁在角隅轴向荷载作用下的翼板纵向应力

基于能量变分原理，拟定轴向荷载作用下箱梁的纵向位移函数，得到关于翼板剪切变形引起的位移差函数的基本微分方程，继而推导出箱梁翼板纵向应力表达式，并首次得出角隅轴向荷载作用下翼板出现应力不均匀分布的荷载及边界条件。通过对一模型箱梁进行计算，并与通用有限元软件ANSYS壳单元计算结果进行比较，验证了该方法和所推导公式的正确性。研究结果表明，当作用于简支箱梁截面角隅处的轴向荷载（合力无偏心）为集中或分布荷载时，翼板不产生纵向应力不均匀现象；当作用于悬臂箱梁截面角隅处的轴向荷载（合力无偏心）为集中荷载时，翼板不产生纵向应力不均匀现象，而当荷载轴向分布时，翼板将产生纵向应力不均匀现象。实际工程中，横力弯曲使悬臂箱梁产生剪力滞效应，这种效应会与轴向分布荷载产生的效应叠加，设计时对此应予以充分考虑。     

Corrigendum to: on the inheritance of the strongly π-extending property

In this corrigendum, we provide correct versions of Theorem 2.8 and Corollary 3.2, retract two consequences of the previous form of the Theorem 2.8. To this end, the main results of the article remain after the aforementioned changes.