以单晶银纳米方块为液相外延生长晶种的纳米晶形貌可控合成方法

本文简要综述了以单晶银纳米方块做为可控外延生长的品种来合成各种银纳米晶的相关工作．通过改变银前驱体和晶种颗粒的比例、表面包裹分子及其用量、还原剂浓度、添加欠电位金属阳离子等手段,我们成功地控制了银纳米晶的外延生长方向和裸露晶面,并合成出一系列尺寸、形貌可控的银纳米晶,包括立方体、立方八面体、八面体、八足体、二十四面体、凹面立方八面体和凹面八面体等．除了对合成方法和过程的介绍,本文还简要讨论了每种纳米结构的形成机制．     

Representing the sporadic Archimedean polyhedra as abstract polytopes

We present the results of an investigation into the representations of Archimedean polyhedra (those polyhedra containing only one type of vertex figure) as quotients of regular abstract polytopes. Two methods of generating these presentations are discussed, one of which may be applied in a general setting, and another which makes use of a regular polytope with the same automorphism group as the desired quotient. Representations of the 14 sporadic Archimedean polyhedra (including the pseudorhombicuboctahedron) as quotients of regular abstract polyhedra are obtained, and summarised in a table. The information is used to characterize which of these polyhedra have acoptic Petrie schemes (that is, have well-defined Petrie duals).     

On degenerate multi-row Gomory cuts

Borozan and Cornuéjols show that valid inequalities for an infinite relaxation for MIPs, relative to some vertex f of the linear relaxation, are determined by maximal lattice-free convex sets containing f. We show that cuts for the original MIP are given by such sets with f in the interior.     

Generalized mixed integer rounding inequalities: facets for infinite group polyhedra

We present a generalization of the mixed integer rounding (MIR) approach for generating valid inequalities for (mixed) integer programming (MIP) problems. For any positive integer n, we develop n facets for a certain (n + 1)-dimensional single-constraint polyhedron in a sequential manner. We then show that for any n, the last of these facets (which we call the n-step MIR facet) can be used to generate a family of valid inequalities for the feasible set of a general (mixed) IP constraint, which we refer to as the n-step MIR inequalities. The Gomory Mixed Integer Cut and the 2-step MIR inequality of Dash and günlük  (Math Program 105(1):29–53, 2006) are the first two families corresponding to n = 1,2, respectively. The n-step MIR inequalities are easily produced using periodic functions which we refer to as the n-step MIR functions. None of these functions dominates the other on its whole period. Finally, we prove that the n-step MIR inequalities generate two-slope facets for the infinite group polyhedra, and hence are potentially strong.      

Calculus of convex polyhedra and polyhedral convex functions by utilizing a multiple objective linear programming solver

ABSTRACT

The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for one convex polyhedron are, for example, the polar, the conical hull and the image under affine transformation. The concept of a P-representation of a convex polyhedron is introduced. It is shown that many polyhedral calculus operations can be expressed explicitly in terms of P-representations. We point out that all the relevant computational effort for polyhedral calculus consists in computing projections of convex polyhedra. In order to compute projections we use a recent result saying that multiple objective linear programming (MOLP) is equivalent to the polyhedral projection problem. Based on the MOLP solver bensolve a polyhedral calculus toolbox for Matlab and GNU Octave is developed. Some numerical experiments are discussed.     

极地船舶冰区操纵性能的六自由度离散元分析

极地船舶操纵破冰性能是破冰船设计建造过程中需重点考虑的问题。为分析极地船舶操纵性能,本文发展了冰区船舶六自由度操纵破冰运动模型,采用扩展多面体离散元模拟海冰,舵桨操纵模型提供破冰力。开展平整冰区定常直航模拟计算,并与Lindqvist船体冰阻力经验公式展开对比验证;开展雪龙号敞水35°舵角操纵性仿真,并与实船试航结果进行对比。在此基础上,开展冰厚及舵角影响下的船体结构冰载荷及破冰轨迹计算,模拟得到操纵破冰航行中船体垂荡、横摇及纵摇运动时程;最后分析操纵破冰船体线载荷分布与直航破冰下的差异。     

How tight is the corner relaxation?

Given a mixed-integer linear programming (MILP) model and an optimal basis of the associated linear programming relaxation, the Gomory’s corner relaxation is obtained by dropping nonnegativity constraints on the basic variables. Although this relaxation received a considerable attention in the literature in the last 40 years, the crucial issue of evaluating the practical quality of the corner-relaxation bound was not addressed so far. In the present paper we report, for the first time, the optimal value of the corner relaxation (in two possible variants) for a very large set of MILP instances from the literature, thus providing a missing yet very important piece of information about the practical relevance of this relaxation. The outcome of our experiments is that the corner relaxation often gives a tight approximation of the integer hull, the main so for MILPs with general-integer variables—the approximation tends to be less satisfactory when a consistent number of binary variables exists.     

Klein polyhedra and relative minima of lattices

We prove that in ?³, the relative minima of almost any lattice belong to the surface of the corresponding Klein polyhedron. We also prove, for almost any lattice in ?³, that the set of relative minima with nonnegative coordinates coincides with the union of the set of extremal points of the Klein polyhedron and a set of special points belonging to the triangular faces of the Klein polyhedron.     

Synthesis and Uncommon Structural Characterization of Novel Zinc and Cadmium Complexes with Imino Nitroxide Radical

Two novel complexes {[Zn(IM4py)2(tp)(H2O)]·2H2O}n 1 and {[Cd(IM4py)2(tp)- (H2O)]·1.25H2O}n 2 (IM4py = 2-(4'-pyridinyl)-4,4,5,5-tetramethylimidazoline-1-oxyl and tp = terephthalate dianion) have been synthesized and characterized by elemental analyses, IR spectrum and single-crystal X-ray diffraction. Crystal data for complex 1: monoclinic, space group C2/c, a = 20.648(7), b = 12.130(4), c = 14.036(4) , β = 106.351(5)o, C32H42N6O9Zn, Mr = 720.09, V = 3373.3(2) 3, Z = 4, Dc = 1.418 g/cm3, μ(MoKα) = 0.790 mm-1, F(000) = 1512, the final R = 0.0407 and wR = 0.0894 for 3480 independent reflections with Rint = 0.0432. Crystal data for complex 2: monoclinic, space group C2/c, a = 21.332(6), b = 12.063(3), c = 14.246(4) , β = 106.704(4)o, C32H40.50N6O8.25Cd, Mr = 753.60, V = 3511.2(2) 3, Z = 4, Dc = 1.426 g/cm3, μ(MoKα) = 0.679 mm-1, F(000) = 1554, the final R = 0.0419 and wR = 0.0961 for 3627 independent reflections with Rint = 0.0440. The framework structures of complexes 1 and 2 are 3-D networks via the hydrogen bonds among 1-D chains. The notable characteristics of the two complexes are that the coordination polyhedron of Zn(II) adopts a rare distorted five-coordinate square pyramidal geometry in 1, and the Cd(II) complex exhibits an unusual distorted seven-coordinate pentagonal bipyramid in 2.