Valid constraints for the Point Packing in a Square problem

We consider the problem of placing n$n$ points in the unit square in such a way as to maximize their minimum pairwise distance m$m$. Starting from two properties of the optimal solution presented by Locatelli and Raber in [Discrete Applied Mathematics 122 (1–3) (2002) 139–166], and using the known theoretical lower and upper bounds, we derive some constraints for tightening the original formulation of the problem.     

Constraints in container loading – A state-of-the-art review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.     

An infinite family of subcubic graphs with unbounded packing chromatic number

Recently, Balogh et al. (2018) answered in negative the question that was posed in several earlier papers whether the packing chromatic number is bounded in the class of graphs with maximum degree 3. In this note, we present an explicit infinite family of subcubic graphs with unbounded packing chromatic number.     

Optimal packings of two to four equal circles on any flat torus

We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent vectors. We prove the optimality of the arrangements using techniques from rigidity theory and topological graph theory.     

Synthesis of Poly（p-phenyleneethynylene）s with Crosslinkable End or Side Groups and Its Solid State Structure and Optical Properties Before and after Crosslinking

Two crosslinkable poly(p-phenyleneethynylene)s(PPEs): poly[2,5-di(2'-ethyl-hexyloxy)-1,4-phenylenee-thynylene] with end-capped vinyl(PPE1) and poly[2,5-di(allyloxy)-1,4-phenyleneethynylene-2,5-di(2'-ethyl-hexyloxy)-1,4-phenyleneethynylene](PPE2) were synthesized. Via the thermal addition reactions of vinyl end groups of PPE1 and allyloxy side groups of PPE2, crosslinked polymers C-PPE1 and C-PPE2 were obtained, respectively. The two polymers were characterized by wide-angle X-ray diffraction(WXRD), ultravio...     

Separation of Cinchona alkaloids on a novel strong cation-exchange-type chiral stationary phase—comparison with commercially available strong cation exchanger and reversed-phase packing materials

A recently reported chiral strong cation exchanger (cSCX) type stationary phase was investigated for the LC separation of a series of Cinchona alkaloids and synthetic derivatives thereof to test its usefulness as alternative methodology for the separation of those important pharmaceuticals. The cSCX column-packing material was qualitatively compared on the one hand against a commercially available non-enantioselective SCX-material, PolySulfoethyl-A, and, on the other hand, against a modern C18 reversed-phase stationary phase which is commonly employed for Cinchona alkaloid analysis. Both SCX columns showed no pronounced peak-tailing phenomena which typically hamper Cinchona alkaloid RP analysis and require specific optimization. Thus, the cSCX-based assay provided new feasibilities for the separation of the Cinchona alkaloids in polar organic mode as opposed to conventional reversed-phase methodologies. In particular, a method for the simultaneous determination of eight Cinchona alkaloids (quinine, quinidine, cinchonine, cinchonidine, and their corresponding dihydro analogs) using the cSCX column in HPLC has been developed and exemplarily applied to impurity profiling of a commercial alkaloid sample. Furthermore, both SCX materials allowed successful separation of C9-epi and 10,11-didehydro derivatives from their respective educts in an application in synthetic Cinchona alkaloid chemistry. Figure An alternative separation principle - HPLC separation of strongly basic natural Cinchona alkaloids and synthetic derivatives thereof by means of a strong cation-exchanger type chiral stationary phase     

矩形区域不等圆形随机堆放的数值模拟

将若干待堆放的圆形堆放到一个给定矩形区域,是一类特殊的Packing问题。针对这一具有NP难度的困难问题,提出一种快速的数值模拟方法以及模拟力学检验的方法。该方法将圆形堆放的力学平衡规律化为几何形体相互接触的几何条件,把大量的圆形按级配及分布律等约束条件,随机堆放形成空间区域。按此方法得到的圆形堆体,在不加外力的情形下即可保持自身的稳定。使用该方法,在边长为15cm的正方形区域内,取圆形的直径范围为0.5cm~4cm,模拟了孔隙率小于25%(面积比)的圆形堆体。最后,将所模拟的圆形堆体试件进行了有限元网格划分及力学加载试算,结果表明该堆体是稳定的。为进一步在细观层次研究圆形堆体提供了一个快速的数值模拟方法。