Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

A new molecular rectifier device and some research in its processing

Organic materials of D-π-A type MR-X (MR-1: p-dimethylaminophenylethenetrica-rbonitrile and MR-2: p-diphenylaminophenylethene tricarbonitrile) were designed and synthesized. The device with a sandwich structure shows good rectificative phenomena. The highest rectification ratio 10000 was achieved in device Cu/MR-1/Ag, and about 100 in other device M/MR-X/M (M: Cu, Ag). It has been found that rectificative phenomena exist only in the atmosphere-liquid interface region by means of liquid adsorption, and electric field could help form the oriented molecular film. __________ Translated from Journal of Fudan University (Natural Science), 2005, 44(4) (in Chinese)     

钙钛矿型Sr_（1－x）Bi_xFeO_（3－y）系列物的结构、电性及铁氧化态研究

在１１００℃制备了钙钛矿型非计量系列物Ｓｒ_（１－ｘ）Ｂｉ_ｘＦｅＯ_（３－ｙ），与文献相比，明显具有温度低、时间短、能耗少的特点。用化学分析方法测得其化学式及Ｆｅ离子的平均价态，用ＸＲＤ、交流阻抗、ＩＲ、Ｍｏｓｓｂａｕｅｒ谱等方法研究了其结构与性质，该类化合物具有Ｐｍ３ｍ对称性和半导体性质，铁离子会产生电荷歧化现象。     

Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.     

Algebra matrix and similarity classification of operators

In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem.     

Duality for Finite Hopf Algebras Explained by Corings

We give a coring version for the duality theorem for actions and coactions of a finitely generated projective Hopf algebra. We also provide a coring analogue for a theorem of H.-J. Schneider, which generalizes and unifies the duality theorem for finite Hopf algebras and its refinements. This paper was written while the first author visited the Mathematics Departments of Syracuse University and California State University Dominguez Hills. He would like to thank both departments for their hospitality.