Recursive fault-tolerance of Fibonacci cube in hypercubes

Fibonacci cube is a subgraph of hypercube induced on vertices without two consecutive 1's. If we remove from Fibonacci cube the vertices with 1 both in the first and the last position, we obtain Lucas cube. We consider the problem of determining the minimum number of vertices in n-dimensional hypercube whose removal leaves no subgraph isomorphic to m-dimensional Fibonacci cube. The exact values for small m are given and several recursive bounds are established using the symmetry property of Lucas cubes and the technique of labeling. The relation to the problem of subcube fault-tolerance in hypercube is also shown.     

直流高压加速管轴向绝缘的优化设计

 为了降低500 mA直流高压加速管高梯度区的电位梯度，对加速管轴向绝缘结构进行优化设计。首先分析了沿面闪络的机理和该加速管轴向绝缘体结构。根据SEEA理论并通过数值模拟，发现阴极、真空和绝缘体三结合点处电场畸变是产生高场强的原因，并分别对4种绝缘体结构进行模拟分析，最终确定出比较理想的结构：绝缘体沿面与阴极电极夹角为+45°，绝缘体两端开槽并均匀嵌入金属电极环，绝缘体均匀嵌入阳极电极片内。     

YBCO涂层导体用Ni5W基带的制备和立方织构的发展

为了制作能满足YBCO涂层导体（coated conductor）所需要的高强度、低磁性的立方织构基带，本工作用粉末冶金方法制作了Ni-5at％W合金基带．为评估基带中立方织构的发展，用March-Dollase函数对各种热处理样品的择优取向度进行了研究，结果与用X射线极图法和电子背散射衍射法得到的结果基本一致．研究结果表明，在实验中所用的工艺参数范围内，随总加工率和热处理温度的提高，基带中立方织构百分数明显增高．提高总加工率实际增加了冷加工样品中立方织构晶粒或立方核心的数量．实验中得到了较好的和实用的工艺制度，用这种工艺可以制作出具有99％～100％立方织构百分数，并具有很好一致取向度的Ni5W基带．     

A controlled boundary theorem for Hilbert cube manifolds

In this paper a boundary theorem for Hilbert cube manifolds is established,where it is required that the boundary be put on the manifold with arbitrarily small control in a given compact metric parameter space.     

Internal fundamental sequences and approximative retracts

We introduce the notion of internal fundamental sequence and prove that any shape morphism from an arbitrary compactum X to an internally movable compactum Y is induced by an internal fundamental sequence. We use this special kind of fundamental sequences to give characterizations and some properties of AANR_C-sets and AANR_N-sets. The paper ends with a section devoted to internal FANR's.     

球面角锥棱镜非稳腔钕玻璃激光器

为了将虚共焦非稳腔输出光束质量高和角锥棱镜谐振腔具有免调试的优点结合到一起,提出了用球面角锥棱镜构成虚共焦非稳腔的方案。利用已有虚共焦非稳腔钕玻璃激光器,设计加工了一球面角锥棱镜非稳腔钕玻璃激光器。模拟计算了两谐振腔输出光束的模式分布,然后对两钕玻璃激光器进行了实验对比研究。结果表明:实验得到的模式分布与模拟计算结果相吻合,球面角锥棱镜非稳腔钕玻璃激光器与虚共焦非稳腔钕玻璃激光器分别获得了最大2176.9J和2340.6J的能量输出,二者的电光效率与束散基本相同,分别为4.3%,0.30mrad和4.6%,0.26mrad。     

On the stability of a compressible Rivlin's cube made of transversely isotropic material

^** Email: kostas.soldatos{at}nottingham.ac.uk This paper considers a unit cube made of a compressible, transverselyisotropic elastic material, with the direction of transverseisotropy being aligned normal to one pair of the cube's faces,and investigates the stability of a dilatation equilibrium stateof that cube, with respect to superposed pure homogeneous deformationswith principal directions parallel to the cube edges. This dilatation,intermediate equilibrium state (state I) of the cube is assumedattainable in two different ways. Accordingly, in what is termedas the ‘principal stability problem’ under investigation,state I is considered to be that of uniform dilatation, whichis attained upon loading normally and uniformly the oppositefaces of the unit cube with certain pairs of equal and oppositelydirected forces having appropriately selected magnitudes. Inwhat is termed as the ‘modified stability problem’under investigation, the same compressible, transversely isotropicunit cube is loaded uniformly by three identical pairs of equaland oppositely directed forces acting normally to its faces,and, hence, it attains in state I the shape of a certain rectangularparallelepiped. The necessary and sufficient conditions forstability of state I of the cube deformation are obtained inthe form of three inequalities, which are found to hold regardlessof whether the intermediate equilibrium state I is that of uniformdilatation or that of the aforementioned rectangular parallelepiped(non-uniform dilatation). These, however, lead to quite differentspecific results and conclusions when applied in connectionwith, first, the principal and, then, the modified stabilityproblem of a unit cube made of a particular type of a transverselyisotropic extension of the Blatz–Ko (isotropic) material.     

Shape‐directed platinum nanoparticle synthesis: nanoscale design of novel catalysts

Platinum‐based catalytic materials have received significant attention, particularly in the shape and size control of faceted materials for catalysis. More recently, there has been a rapid increase in the number of reports of successful preparations in this field; however, a fundamental understanding of controlled growth towards catalytic material design is essential for future implementation and broad application. In this review, we provide an overview of the recent findings reported since 2009, focusing on methods for shape control as well as the effects of exposed surface facets on select catalytic reactions. Copyright © 2013 John Wiley & Sons, Ltd.     

On the faces of an <Emphasis Type="Italic">n</Emphasis>-dimensional cube

The structure of the faces of an n-dimensional cube is studied. Some combinatorial results describing the mutual arrangement and the metric characteristics of this structure are obtained.