Polymer 4D printing: Advanced shape-change and beyond

4D printing is an exciting branch of additive manufacturing. It relies on established 3D printing techniques to fabricate objects in much the same way. However, structures which fall into the 4D printed category have the ability to change with time, hence the “extra dimension.” The common perception of 4D printed objects is that of macroscopic single-material structures limited to point-to-point shape change only, in response to either heat or water. However, in the area of polymer 4D printing, recent advancements challenge this understanding. A host of new polymeric materials have been designed which display a variety of wonderful effects brought about by unconventional stimuli, and advanced additive manufacturing techniques have been developed to accommodate them. As a result, the horizons of polymer 4D printing have been broadened beyond what was initially thought possible. In this review, we showcase the many studies which evolve the very definition of polymer 4D printing, and reveal emerging areas of research integral to its advancement.     

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.     

Springer basic sets and modular Springer correspondence for classical types

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (defined over a base field of odd characteristic $p$, and with coefficients in a field of odd characteristic $?\ne p$): the modular case is obtained as a restriction of the ordinary case to a basic set. In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence. We provide a quick proof, by sorting characters according to the dimension of the corresponding Springer fibre, an invariant which is directly computable from symbols.     

冷轧带钢局部高点卷取过程起筋控制的建模与仿真

为了研究带钢局部高点卷取起筋的控制方法，利用三维弹塑性变形基本理论，并引入带钢塑性流动因子，建立了弹塑性卷取应力和起筋量模型.基于应力函数假设、S. Timoshenko最小功原理和伽辽金虚位移法建立了起筋带钢的应力场分布和可用于在线计算的起筋临界卷取张力设定模型.仿真结果表明：局部高点在径向累积叠加所引起的带钢张力不均匀分布和轴向压应力是导致带钢起筋的主要原因；起筋量随局部高点高度、卷径和卷取张力增加而增大，薄带钢比厚带钢起筋量增幅明显；临界卷取张力随卷径、带钢厚度和局部高点高度增大而减小.     

On Potentially Abelian Geometric Representations

The finiteness is proved of the set of isomorphism classes of potentially abelian geometric Galois representations with a given set of data. This is a special case of the finiteness conjecture of Fontaine and Mazur.     

矩形型钢弯曲回弹曲率半径r值的确定

文章在分析矩形型钢弯曲变形过程及应力与应变等方面的关系的基础上，推导出工件曲率半径与工件回弹后曲率半径之间的关系，从而确定了凸模半径。     

因素空间理论与知识表示的数学框架（Ⅷ）─—变权综合原理

本文是文［１－７］的继续，研究变权综合问题，从确定变权的经验公式入手引出了变权原理，给出了变权的公理化定义，讨论了与之有关的均衡函数及其梯度向量。