On Spin Models,Triply Regular Association Schemes,and Duality

Motivated by the construction of invariants of links in 3-space, we study spin models on graphs for which all edge weights (considered as matrices) belong to the Bose-Mesner algebra of some association scheme. We show that for series-parallel graphs the computation of the partition function can be performed by using series-parallel reductions of the graph appropriately coupled with operations in the Bose-Mesner algebra. Then we extend this approach to all plane graphs by introducing star-triangle transformations and restricting our attention to a special class of Bose-Mesner algebras which we call exactly triply regular. We also introduce the following two properties for Bose-Mesner algebras. The planar duality property (defined in the self-dual case) expresses the partition function for any plane graph in terms of the partition function for its dual graph, and the planar reversibility property asserts that the partition function for any plane graph is equal to the partition function for the oppositely oriented graph. Both properties hold for any Bose-Mesner algebra if one considers only series-parallel graphs instead of arbitrary plane graphs. We relate these notions to spin models for link invariants, and among other results we show that the Abelian group Bose-Mesner algebras have the planar duality property and that for self-dual Bose-Mesner algebras, planar duality implies planar reversibility. We also prove that for exactly triply regular Bose-Mesner algebras, to check one of the above properties it is sufficient to check it on the complete graph on four vertices. A number of applications, examples and open problems are discussed.     

环形聚乙炔分子桥的电导研究

我们选择了由40个CH基团组成的环形聚乙炔链作为分子桥,基于Landauer-Buttiker理论,利用求解散射波函数的方法,研究了这种环状聚乙炔分子桥与金属多端连接的电导随能量的变化关系.结果表明,在给定入射端的条件下,电导在正负能量上是对称的,当各个端口满足旋转对称性时,相对于入射端对称的两个出射端的电导相同.当分子桥耦合较弱时,电导对能量的变化相当敏感.     

关于K(A,B)与K(P1,P2,…,Pn)的多项式不变量的几点注记

T.Kanenobu研究了K(a,b)与K(p1,p2,…,pn)的多项式不变量的基本结构,此文讨论了更一般的K(A,B)与K(P1,P2,…,Pn)的多项式不变量的性质.所采用的工具是skein理论,主要结果为命题5～9.其中关于K(A,B)的结论可以推广到一族Km(A,B)(m∈Z).     

Knots and the Bracket Calculus

In this paper, we introduce a way of encoding links (long links). This ways leads to a combinatorial representation of links by words in a given finite alphabet. We prove that the link semigroup is isomorphic to some algebraically defined semigroup with a simple system of relations. Thus, knot theory is represented as a bracket calculus: the link recognition problem is reduced to a recognition problem in this semigroup.     

皮秒脉冲传输系统中三阶色散补偿的研究

模拟了皮秒高斯光脉冲在理想的二阶和三阶色散都作了补偿的光纤链中的传输。结果表明,与二阶色散补偿能消除脉冲展宽一样,三阶色散补偿不仅能防止脉冲展宽,而且也能有效地消除脉冲边沿部的振荡结构和脉知的时移。文中画出了100Gb/s码率的64位高斯光脉冲序列在色散补偿光纤链中传输2000km后的眼图,由眼图的清晰程度可看出这种补偿系统对改善短脉冲传输的有效性。     

Radio-frequency method for characterization of superconducting weak links

The advantages of a radio-frequency (r.f.) method in comparison with conventional transport measurements for characterization of superconducting weak links are discussed. In particular it is pointed out, that (i) the current–phase relationship (CPR) can be deduced from r.f. measurements of the phase-biased weak link without any fitting parameters and (ii) the supercurrent is measurable even if the Josephson coupling energy is considerably smaller than the thermal energy. Examples of the CPR for several configurations of Josephson junctions are shown.     

光纤制导双向传输系统

光纤制导战术导弹是一种精确制导武器,它主要用于远距离打击敌方的高价值目标,光纤制导战术导弹具有射程远,抗电磁干扰,隐蔽发射,图像制导等一系列优点,因而受到军方的高度重视并得到迅速的发展,光纤双向传输系统是光纤制导导弹系统中一个重要标志性的组成部分。本文详细地介绍弛光纤制导双向传输系统的特点,构成及工作原理。     

基于功能化溶胶-凝胶膜的乳腺癌抗原免疫传感器

结合溶胶-凝胶(sol-gel)和交联技术,将乳腺癌抗体固定在铂盘电极表面的氨基化sol-gel功能膜上,制备出用于检测乳腺癌抗原(CA15-3)的免疫传感器.用红外光谱验证了该传感器功能膜的形成过程和组成结构,采用循环伏安法对传感器逐层修饰过程进行了表征,并对传感器功能膜的作用机理进行了探讨.该法检测CA15-3的线性范围为8～240U/mL,线性回归方程为ΔE=75.75lgc-56.36,r=0.998.结果表明,该方法很好地保持了被固定抗体的活性,增强了传感器的稳定性,所制备的传感器于4℃干态保存30d,其响应信号基本不变.且该传感器响应迅速、灵敏度高、选择性好,血清中常见抗原不干扰测定.     

Knotted Picture of Degree of Entanglement of Quantum Pure State of Two Nodes |χ>=α|↑↓>+β|↓↑>

From the knotted pictures this article gives a possible quantitative measure of the degree of entanglement. We suggest to use the area ratio to measure the degree of entanglement, moreover, from the two parts of the non-overlapping area we can also know vividly and pictorially the phase difference between the two variable coefficients α and β.     

A Zoom-In Approach to Design SDH Mesh Restorable Networks

Mesh restorable networks based on SONET (Synchronous Optical Network, standard optical transmission technology widely accepted and implemented in North America) or SDH (Synchronous Digital Hierarchy, the European standard currently adopted by the major European telecom operators) are an economically attractive solution in areas where high demand and high connectivity are involved (Wu, 1995). In these networks, the reconfiguration capability of the digital cross connect systems (DCS) allows to reroute the demand affected by network failures. The degree of sharing of spare capacity in networks based on this architecture is high.This paper presents a heuristic algorithm for solving the near-optimal design of SDH mesh-type link restorable networks, i.e. determining the network topology and assigning the capacity to transport the demand in normal situations and to allow full link restorability in case of single link failures. The algorithm is based on a Zoom-In technique, a novel approach which forms a compromise between sequential and integrated techniques. The different building blocks of the algorithm are tested extensively and compared with other results mentioned in literature. Comparison of the simulation results for the overall design problem with other solution techniques indicates that the Zoom-In method is a quite promising approach, able to combine the accuracy of integrated approaches with the calculation speed of sequential approaches.