STUDY ON ISOMORPHISM OF PLANAR KINEMATIC CHAINS

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Synthesis of a complete set of contracted graphs for planar non-fractionated simple-jointed kinematic chains with all possible DOFs

The contracted graph shows the primary topological structure of kinematic chains and is the foundation for constructing kinematic structures of mechanisms. In this paper, a fully-automatic method is proposed to synthesize a complete set of contracted graphs for planar non-fractionated simple-jointed kinematic chains with all possible degrees of freedom. First, based on the 4-parameter index and link assortment array, the relationships of link assortment arrays and non-fractionated contracted graphs for different types of kinematic chains are revealed. Then, the general steps to generate the adjacency matrices of contracted graphs from the synthesis equation set are given. Efficient methods to detect fractionated structures and isomorphism are also addressed. Finally, a human-machine interactive synthesis program is developed, and the complete list of both contracted graphs and valid contracted graphs for planar non-fractionated simple-jointed kinematic chains with up to 19 links and all possible degrees of freedom is presented for the first time.     

湖北塆铅锌矿石中镉的赋存状态

湖北塆铅锌矿床是一个中型矿床,含银、镉有益组分,本文根据对矿石的矿物成分、化学成分、单矿物测试,查明了镉与闪锌矿、纤锌矿有关,为类质同象赋存。     

Graph isomorphism problem and 2-closed permutation groups

We demonstrate a number of hard permutation group algorithmic problems, such as Group Intersection and Setwise Stabilizer, which become polynomially equivalent to the Graph Isomorphism Problem after restricting them to 2-closed permutation groups. It is shown that these problems are closely related to problems concerning coherent configurations. We also present a polynomial-time procedure for determining the 2-closure of a nilpotent group. This procedure provides a polynomial-time reduction of the 2-closure problem for odd order groups to the same problem for primitive odd order groups.     

量子计算的表象无关性探讨

大因数分解和数据检索量子算法的提出带来了量子计算与量子信息的研究高潮。由于量子计算具有并行性、不可克隆性及量子态的不可测性,使得量子信息及量子计算在某些方面具有传统计算所无法比拟的优势。量子的态空间作为一个完备的Hilbert空间,在定义了内积和范数并赋予相应的物理意义后,就构成了理论意义上的量子计算系统。该文抽象了量子系统的本质,描述了量子计算及遵循的计算规则以及如何实现量子信息表示和进行信息的处理与测量,从理论上阐述了量子态系统迁移的线性同构和等距同构,说明了量子计算与量子信息的研究与具体的量子表象空间无关。     

ER isomorphisms and uniqueness conditions

Given a collection of entity types (database tables) there is usually more than one way to model their associations. Consequently, two data models may appear different while essentially they are the same. To simplify the task of comparing data models, necessary and sufficient conditions are defined for a collection of entity types to have a unique Entity Relationship Diagram (ERD). The sufficient conditions for uniqueness are translated into modeling constraints that can be easily used to build an Entity-Relationship model. It is shown that the constraints do not prevent the representation of information requirements except for rare types of involuted relationships that seldom appear in the real world. Additionally, sufficient conditions are established for two ERDs to be isomorphic. All of this is done under the assumption that relationships are degree 2 or less. The results are extended to models containing relationships of higher degree.     

A crystallographic re-investigation of Cu2Sb-related binary,ternary, and quaternary structures: how many structure types can exist upon the same topology of a unit cell?

Crystal chemical analysis of several large sets of topologically related structures confirms earlier suggestions that within the same cell content, space group, and Wyckoff site occupancies, there may exist several structure types of sometimes quite different coordination chemistry and bonding arrangement. The original Flahaut's suggestion of demarcating anti-Cu₂Sb and PbFCl structure types has been extended to an analysis of structures of over 350 compounds in terms of various structural characteristics as free parameters. For the Cu₂Sb family, structural field maps indicate formation of at least three distinct structure types: Cu₂Sb, PbFCl, CeFeSi (anti-type of PbFCl) and UAs₂ (which is not an anti-type of Cu₂Sb). The formerly suggested ternary ZrSiS structure type is in fact an ordered version of UAs₂. Extension of this approach to “filled” versions of these structure types permits clear demarcation of two other topologically related structure types, LaOAgS and HfCuSi₂, the latter being a derivative of UAs₂ but not Cu₂Sb. Very similar relationships have been observed for several smaller structural families. Perspectives of using different structural parameters as free coordinates are discussed.     

利用邻接矩阵的幂序列进行运动链和机构的同构判定

从同构的图论意义出发,提出了一个新的运动链结构不变量,进而提出了利用邻接矩阵的幂序列进行运动链同构判定的方法。它与现有的其他方法相比,具有直观、简便和显明图论依据的特点,且该方法不仅可以实现运动链的同构判定,而且可以成功地判定一般图的同构。在此基础上,本文最后给出了从同一运动链中识别出不同机构的两个方法。     

红河州屏边县钒矿钒的赋存状态研究

经化学分析、磨制光薄片(显微镜下观察)、人工重砂分析和扫描电镜电子探针分析等研究发现:红河屏边的钒矿为沉积型钒矿,主要的岩石类型为粉砂质泥岩、细砂屑灰岩、泥晶灰岩和硅质板岩等。钒有两种赋存状态:第一种主要以类质同象的形式(部分不排除是由于矿物包裹吸附钒的碳质),普遍赋存在石英、铝硅钡石、磷灰石、方解石、褐铁矿和含钒金红石等矿物中,在矿石中占97%以上;第二种以吸附状态存在,被碳质吸附。由于该矿石中的钒以类质同象的形式分散在多种矿物中,未发现以独立矿物形式存在的钒,所以该钒矿无法通过物理选矿方法分离和富集,该矿石今后的选矿研究方向应采用化学选矿。      

某铷矿石选矿试验

我国某大型铷矿床为国内首个独立铷矿床,Rb₂O品位为0.12%,总金属量近10万t,矿石中的铷以类质同象形式存在于黑云母中。为高效回收该铷矿资源,采用富集黑云母的方式进行了铷回收试验研究。结果表明,在磨矿细度为-0.074 mm占60%的情况下,采用2粗3精、中矿顺序返回流程处理该矿石,可取得Rb2O品位为0.28%、回收率为65.93%的铷精矿。试验指标较好,可实现铷的高效回收。