Shape-controlled crystallisation pathways in dense fluids of ccp-forming hard polyhedra

Emergent directional entropic forces that favour facet-to-facet alignment of neighbouring colloidal particles – arising from multi-body interactions upon crowding – should cause the process by which colloidal crystals form from fluids of hard polyhedra to be different than that from fluids of hard spheres. We compute nucleation-free energy barriers for a family of shapes that all self-assemble the same cubic close-packed (ccp) crystal structure formed by hard spheres and find that changing rhombicuboctahedra into rhombic dodecahedra by successively removing facets that compete with the ccp structure cause a systematic decrease in barrier heights. We show that this decrease arises from the increased prominence of facets aligned with neighbouring shapes in the target crystal, which produce local environments in the fluid that facilitate crystallisation.     

Mixed-Integer Cuts from Cyclic Groups

We analyze a separation procedure for Mixed-Integer Programs related to the work of Gomory and Johnson on interpolated subadditive functions. This approach has its roots in the Gomory-Johnson characterization on the master cyclic group polyhedron. To our knowledge, the practical benefit that can be obtained by embedding interpolated subadditive cuts in a cutting plane algorithm was not investigated computationally by previous authors. In this paper we compute, for the first time, the lower bound value obtained when adding (implicitly) all the interpolated subadditive cuts that can be derived from the individual rows of an optimal LP tableau, thus approximating the optimization over the intersection of the Gomory corner polyhedron with the LP relaxation of the original problem formulation. The computed bound is compared with that obtained when only Gomory mixed-integer cuts are used, on a very large test-bed of MIP instances.     

Injectivity of real polynomial maps and Łojasiewicz exponents at infinity

In this paper we give a lower bound for the Łojasiewicz exponent at infinity of a special class of polynomial maps , s ≥ 1. As a consequence, we detect a class of polynomial maps that are global diffeomorphisms if their Jacobian determinant never vanishes. Work supported by DGICYT Grant BFM2003–02037/MATE.     

计算两个凸多面体间距离的一个新算法

文章讨论了计算两个凸多面体间的距离的问题。首先分析了不相交凸多面体间的距离的特点，证明了该距离恰是其公垂线段的长度，再利用正交投影把确定此距离转化为一个优化问题。给出了此优化问题的两种解法——5变量的线性观划算法和2变量的区域搜索算法，并对计算复杂性进行了分析。该方法的优点是存储量小，只需存储凸多面体的顶点信息，并可推广来确定移动凸多面体间的距离及一个凸多面体的最大(小)跨度。     

多面体有限基定理的一个证明

多面体有限基定理在最优化方法的理论研究与算法设计中起一着重要作用。本文利用 线性代数的知识和把Ｒｎ中的凸集变换成Ｒｎ＋１中凸锥的所谓齐次化方法，提供了这个 定理的一个构造性证明．同时还给出了多面体的极点、极方向和多面体的系数矩阵的关 系式。     

Lower Bound for Energies of Harmonic Tangent Unit-Vector Fields on Convex Polyhedra

We derive a lower bound for energies of harmonic maps of convex polyhedra in to the unit sphere S² with tangent boundary conditions on the faces. We also establish that C maps satisfying tangent boundary conditions are dense with respect to the Sobolev norm in the space of continuous tangent maps of finite energy.This revised version was published online in March 2005 with corrections to the cover date.     

Kristallstrukturen und spektroskopische Eigenschaften von 2λ3‐Phospha‐1, 3‐dionaten und 1, 3‐Dionaten des Calciums ‐ ein Vergleich am Beispiel der 1, 3‐Diphenyl‐ und 1, 3‐Di(tert‐butyl)‐Derivate

Crystal Structures and Spectroscopic Properties of 2λ³‐Phospha‐1, 3‐dionates and 1, 3‐Dionates of Calcium ‐ Comparative Studies on the 1, 3‐Diphenyl and 1, 3‐Di(tert‐butyl) Derivatives A hydrogen‐metal exchange between dibenzoylphosphane and calcium carbide in tetrahydrofuran (THF) followed by addition of the ligand 1, 3, 5‐trimethyl‐1, 3, 5‐triazinane (TMTA) furnishes the binuclear complex bis[(tmta‐N, N′, N″)calcium bis(dibenzoylphosphanide)] ( 1a ) co‐crystallizing with benzene. Similarly, reaction of bis(2, 2‐dimethylpropionyl)phosphane with bis(thf‐O)calcium bis[bis(trimethylsilyl)amide] in 1, 2‐dimethoxyethane (DME) gives bis(dme‐O, O′)calcium bis[bis(2, 2‐dimethylpropionyl)phosphanide] ( 1b ) in high yield. The carbon analogues 1, 3‐diphenylpropane‐1, 3‐dione (dibenzoylmethane) or 2, 2, 6, 6‐tetramethylheptane‐3, 5‐dione (dipivaloylmethane) and bis(thf‐O)calcium bis[tris(trimethylsilylmethyl)zincate] in DME afford bis(dme‐O, O′)calcium bis(dibenzoylmethanide) ( 2a ) and the binuclear complex (μ‐dme‐O, O′)bis[(dme‐O, O′)calcium bis(dipivaloylmethanide)] ( 2b ), respectively. Dialkylzinc formed during the metalation reaction shows no reactivity towards the 1, 3‐dionates 2a and 2b . Finally, from the reaction of the unsymmetrically substituted ligand 2‐(methoxycarbonyl)cyclopentanone and bis(thf‐O)calcium bis[bis(trimethylsilyl)amide] in toluene, the trinuclear complex 3 is obtained, co‐crystallizing with THF. The β‐ketoester anion bridges solely via the cyclopentanone unit.     

Two Zeolite-Type Frameworks in One Metal-Organic Framework with Zn(24) @Zn(104) Cube-in-Sodalite Architecture

Two in one: A metal-organic framework obtained from three different inorganic building blocks (tetrameric Zn(4) O, trimeric Zn(3) OH, and monomeric Zn) posseses a nested cage-in-cage and framework-in-framework architecture. 24 Zn(4) O tetramers and eight Zn monomers form a sodalite cage into which a cubic cage made from eight Zn(3) (OH) trimers is nestled. Eight monomeric Zn(2+) centers interconnect these two cages.