轴角编码器测量中偏心带来的误差分析

介绍了应运多面体和自准直光管组合测量高准确度编码器角度的原理和方法，具体分析了多面体中心和编码器轴中心偏心时对测量角度产生的测量误差，并对自准直光管光轴和多面体中心、编码器轴中心两者偏心连线不重合时产生的测量误差进行了分析，同时对两中心偏心的方向进行了判定．实验证明，多面体中心与编码器轴中心不重合时对测量将产生按正弦或余弦规律变化的系统误差，同时自准直光管光轴和两者中心连线不重合对测量结果将不会产生影响．     

On some coarse shape invariants

The author and N. Ugleši? have recently introduced a new classification of topological spaces, strictly coarser than the shape type classification. The corresponding coarse shape theory is founded on the coarse shape category. In this paper several topological and shape invariants are considered with respect to the coarse shape. It is shown that the coarse shape domination preserves connectedness, shape dimension, movability, n-movability and strong movability. Further, stability is a coarse shape invariant. Moreover, the coarse shape and shape coincide on the class of stable spaces.     

α‐Fe2O3 Polyhedral Nanoparticles Enclosed by Different Crystal Facets: Tunable Synthesis,Formation Mechanism Analysis,and Facets‐dependent n‐Butanol Sensing Properties

Three kinds of polyhedral α‐Fe₂O₃ nanoparticles enclosed by different facets including oblique parallel hexahedrons (op‐hexahedral NPs), cracked oblique parallel hexahedrons (cop‐hexahedral NPs), and octadecahedral nanoparticles (octadecahedral NPs), were successfully prepared by simply changing only one reaction parameter in the hydrothermal process. The structural and morphological of the products were systematically studied using various characterizations including X‐ray diffraction (XRD), scanning electron microscopy (SEM), and transmission electron microscopy (TEM), revealing that the three kinds of α‐Fe₂O₃ nanoparticles were enclosed by {104}, {110}/{104}, and {102}/{012}/{104} crystal planes, respectively. The exposed facets and shape of the nanocrystals were found to be affected by the adding amount of ethylene glycol in the solvent. The gas‐sensing properties and mechanism of the α‐Fe₂O₃ samples were studied and analyzed, which indicated that the sensitivity of the three samples followed the order of octadecahedral NPs > cop‐hexahedral NPs > op‐hexahedral NPs due to the combined effects of specific surface area and oxygen defects in the nanocrystals.     

Modeling method and preliminary model of Asteroid Toutatis from Chang’E-2 optical images

Shape modeling is fundamental to the analysis of dynamic environment and motion around asteroid. Chang＇E- 2 successfully made a flyby of Asteroid 4179 Toutatis and obtained plenty of high-resolution images during the mis- sion. In this paper, the modeling method and preliminary model of Asteroid Toutatis are discussed. First, the optical images obtained by Chang＇E-2 are analyzed. Terrain and silhouette features in images are described. Then, the modeling method based on previous radar model and preliminary information from optical images is proposed. A preliminary polyhedron model of Asteroid Toutatis is established. Finally, the spherical harmonic coefficients of Asteroid Toutatis based on the polyhedron model are obtained. Some parameters of model are analyzed and compared. Although the model proposed in this paper is only a preliminary model, this work offers a valuable reference for future high-resolution models.     

The complexity of recognizing linear systems with certain integrality properties

Let A be a 0 − 1 matrix with precisely two 1’s in each column and let 1 be the all-one vector. We show that the problems of deciding whether the linear system (1) defines an integral polyhedron, (2) is totally dual integral (TDI), and (3) box-totally dual integral (box-TDI) are all co-NP-complete, thereby confirming the conjecture on NP-hardness of recognizing TDI systems made by Edmonds and Giles in 1984. Supported in part by NSA grant H98230-05-1-0081 and NSF grants DMS-0556091 and ITR-0326387. Supported in part by the Research Grants Council of Hong Kong and Seed Funding for Basic Research of HKU.     

一维链状配位聚合物[Cu(en)_2]_2[Cu(en)_2·α-As_8~ⅢV_(14)~ⅣO_(42)(HPO_4)]·8H_2O的合成与晶体结构

钒氧化合物由于其有趣的阴离子结构和在催化反应、药物化学以及材料科学等领域中的应用而受到人们的关注[1,2].近年来,一些具有1D链、2D层和3D开放骨架结构的钒氧化合物陆续被报道[3~7].由于柔软的V—O—V键和其可调变的多面体,一些金属原子(如W,Mo,P,As等)可被引入钒氧团簇而形成异构的或新的氧簇结构.在笼状的[As8V14O42]4-阴离子中可包含一些小的无机分子(如SO23-、SO42-、H2O或HPO24-)[8~14].我们[10]曾报道了[As8V14O42]4-笼内包含HPO4基团的化合物[Co(en)3]2·2H3O·[As8V14O42(HPO4)]·2H2O.本文通过在As-V反应体系…     

A polyhedral study of triplet formulation for single row facility layout problem

The single row facility layout problem (SRFLP) is the problem of arranging n departments with given lengths on a straight line so as to minimize the total weighted distance between all department pairs. We present a polyhedral study of the triplet formulation of the SRFLP introduced by Amaral [A.R.S. Amaral, A new lower bound for the single row facility layout problem, Discrete Applied Mathematics 157 (1) (2009) 183-190]. For any number of departments n, we prove that the dimension of the triplet polytope is n(n−1)(n−2)/3 (this is also true for the projections of this polytope presented by Amaral). We then prove that several valid inequalities presented by Amaral for this polytope are facet-defining. These results provide theoretical support for the fact that the linear program solved over these valid inequalities gives the optimal solution for all instances studied by Amaral.     

溶剂效应计算中两种积分方法的比较研究

采用多面体表面模拟溶质空腔, 讨论了溶剂效应计算中近似积分方法和解析积分方法的平行性和收敛性. 我们发现: 对所研究的40个中性分子, 近似方法和解析方法之间的平行性较好; 但是, 对于20个正离子和27个负离子, 当溶质空腔分别为0.002和0.001 a.u.的等电荷密度面时, 近似方法和解析方法之间的平行性较差, 因此, 近似方法的可靠性不一定有保证. 我们还发现当多面体的表面无限趋近空腔的表面时, 不管采用何种多面体序列, 近似方法和解析方法的基态总能量都基本趋向同一极限值.