Static Theory for Planar Ferromagnets and Antiferromagnets

Here we generalize the “BBH”-asymptotic analysis to a simplified mathematical model for the planar ferromagnets and antiferromagnets. To develop such a static theory is a necessary step for a rigorous mathematical justification of dynamical laws for the magnetic vortices formally derived in [1] and [2]. Received March 15, 2001, Accepted May 16, 2001     

中医方药量化研究中“相对药量”的数学模型体系

建立中医方药量华研究的"相对药量"概念模型体系;方法:运用微分方程理论;提出五种情况下,中药常用量范围内相对药量概念的数学模型,分别为直线模型、指数函数模型、对数函数模型、二次函数模型(开口向上和向下两种),并说明该模型体系的和理性与适应性;结论:相对药量概念核心体系的建立,增加了中医方药"相对药量"可比性的全面性,这对进一步研究单位药乃至方剂中各药在性、味、归经等方面的影响程度及其规律性,将起到至关重要的作用.     

关于线性算子的概率范数与算子空间

由于满足(PN-5)条件的PN空间(E,F)就是MangerPN空间(E,F,min),因此,肖建中等给出的关于PN空间上线性算子概率范数的结果有较大的局限性.本文中,在较一般的MengerPN空间上研究有关线性算子的概率范数和算子空间的问题,改进和推广了肖建中等的结果.     

从Bα到Qk的复合算子

用K—Carleson测度刻画了B^α（B0^α）到QK的复合算子的有界性，以及B^α到QK,0的复合算子的有界性和紧性．     

TWO-SCALE FINITE ELEMENT DISCRETIZATIONS FOR PARTIAL DIFFERENTIAL EQUATIONS

Some two-scale finite element discretizations are introduced for a class of linear partialdifferential equations. Both boundary value and eigenvalue problems are studied. Basedon the two-scale error resolution techniques, several two-scale finite element algorithmsare proposed and analyzed. It is shown that this type of two-scale algorithms not onlysignificantly reduces the number of degrees of freedom but also produces very accurateapproximations.     

Periodicities in Cluster Algebras and Cluster Automorphism Groups

We study the relations between two groups related to cluster automorphism groups which are defined by Assem,Schiffler and Shamchenko.We establish the relation-ships among (strict) direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices,respectively,in the language of short exact sequences.As an application,we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type.Finally,we study the relation between the group Aut(A) for a cluster algebra A and the group AutMn(S) for a mutation group Mn and a labeled mutation class S,and we give a negative answer via counter-examples to King and Pressland's problem.     

阿基米德螺旋微纳结构中的表面等离激元聚焦

研究光在微纳结构中的分布与传播, 实现在纳米范围内操纵光子, 对于微型光学芯片的设计有着重要意义. 本文利用聚焦离子束刻蚀方法, 在基底为石英玻璃的150 nm厚金膜上刻制了不同参数的阿基米德螺旋微纳狭缝结构, 通过改变入射光波长、手性、及螺旋结构手性和螺距等方式, 在理论和实验上系统地研究了阿基米德螺旋微纳结构中的表面等离激元聚焦性质. 我们发现, 除了入射激光偏振态、螺旋结构手性之外, 结构螺距与表面等离激元波长的比值也可以用来控制结构表面电场分布, 进而在结构中心形成0阶、1阶乃至更高阶符合隐失贝塞尔函数的涡旋电场. 通过相位分析, 我们对涡旋电场的成因进行了解释. 并利用有限时域差分的模拟方法计算了不同螺距时, 结构中形成的电场及相应空间相位分布. 最后利用扫描近场光学显微镜, 观测结构中不同的光场分布, 在结构中心得到了亚波长的聚焦光斑及符合不同阶贝塞尔函数的涡旋形表面等离激元聚焦环.     

磁控溅射制备W掺杂VO2/FTO复合薄膜及其性能分析

为了获得相变温度低且热致变色性能优越的光学材料, 室温下在F:SnO₂ (FTO)导电玻璃基板表面沉积钨钒金属膜, 再经空气气氛下的热氧化处理, 制备了W掺杂VO₂/FTO复合薄膜, 利用X射线光电子能谱、X射线衍射和扫描电镜对薄膜的结构和表面形貌进行了分析. 结果表明: 高温热氧化处理过程中没有生成W, F, V混合氧化物, W以替换V原子的方式掺杂. 与采用相同工艺和条件制备的纯VO₂/FTO复合薄膜相比, W掺杂VO₂薄膜没有改变晶面取向, 仍具有(110)晶面择优取向, 相变温度下降到35 ℃左右, 热滞回线收窄到4 ℃, 高低温下的近红外光透过率变化量提高到28%. 薄膜的结晶程度明显提高, 表面变得平滑致密, 具有很好的一致性, 对光电薄膜器件的设计开发和工业化生产具有重要意义. 关键词： W掺杂 2')" href="#">VO₂ FTO导电玻璃 磁控溅射     

Properties of train traffic flow in a moving block system

The development direction of railways is toward the improvement of capacity and service quality, where the service quality includes safety, schedule, high speed, and comfort. In light of the existing cellular automaton models, in this paper, we develop a model to analyze the mixed running processes of trains with maximal speeds of 500 km/h and 350 km/h respectively in the moving block system. In the proposed model, we establish some sound rules to control the running processes of a train, where the rules include the departure rules in the intermediate stations, the overtaking rules, and the conditions of speed limitation for a train stopping at a station or passing through a station. With the consideration of the mixed ratio and the distance between two adjacent stations, the properties of the train traffic flow (including capacity and average speed) are simulated. The numerical results show that the interactions among different trains will affect the capacity, and a proper increase of the spatial distance between two adjacent stations can enhance the capacity and the average speed under the moving block.     

The population and decay evolution of a qubit under the time-convolutionless master equation

We consider the population and decay of a qubit under the electromagnetic environment. Employing the time-convolutionless master equation, we investigate the Markovian and non-Markovian behaviour of the corresponding perturbation expansion. The Jaynes-Cummings model on resonance is investigated. Some figures clearly show the different evolution behaviours. The reasons are interpreted in the paper.