Ultrafast carrier dynamics in ferromagnetic InGaMnAs

We have carried out an ultrafast time-resolved differential reflectivity study of a ferromagnetic semiconductor InGaMnAs and made a systematic comparison with low-temperature grown and high-temperature grown InGaAs reference films. Very short carrier lifetimes (2 ps) were observed in InGaMnAs and the low-temperature grown InGaAs film, but not in the high-temperature grown InGaAs film. We attribute the short lifetimes to carrier trapping by mid-gap states introduced during low-temperature MBE growth. Furthermore, at long times, we observed periodic oscillations in the differential reflectivity signal with period 20 ps, which we interpret as coherent acoustic phonons.     

一类非线性退化方程混合问题解的渐进性态

本文利用比较原理以及一种特殊变换研究了一类非线性退化方程的混合问题，得到了这类复杂问题解的渐进性质。     

Enhancement of the Kerr effect for a quantum dot in a cavity

Nonlinear susceptibility of a quantum dot (QD) embedded in a two-sided cavity, is studied theoretically from a weak-coupling to a strong-coupling regime. In the relevance of a quantum logic gate, the corresponding nonlinear phase shifts (Kerr effect) are estimated for coherent wavepackets including one photon on average. In the weak-coupling regime, the phase shift enhances strongly as a function of a coupling constant between the cavity photon and QD, and eventually saturates in the strong-coupling regime. We also show transmission spectra to evaluate the efficiency of the phase shift. Although the efficiency decreases monotonically in the weak-coupling regime, it rises in the strong-coupling regime.     

S3上阿诺德弦猜想中的变分方法

本文使用变分方法证明了三维标准切触球的标准勒让德扭结，至少存在一个弦连结适应于标准切触结构的任何选定切触形式，这部分证明了著名的阿诺德弦猜想。     

Optimal Path Planning Based on Visibility

Various problems associated with optimal path planning for mobile observers such as mobile robots equipped with cameras to obtain maximum visual coverage of a surface in the three-dimensional Euclidean space are considered. The existence of solutions to these problems is discussed first. Then, optimality conditions are derived by considering local path perturbations. Numerical algorithms for solving the corresponding approximate problems are proposed. Detailed solutions to the optimal path planning problems for a few examples are given.     

Pressure induced transitions in calcium: a tight-binding approach

A tight-binding (TB) hamiltonian for calcium is built with a high precision parametrization technique based on density functional calculations of the energy bands and the total energy at various lattice volumes. The new set of TB parameters is appropriate to study phenomena under pressures as high as 20 GPa. Specifically, both the metal to nonmetal transition at 4 GPa and the structural transition fcc to bcc at 19 GPa are well reproduced. These transitions and several static properties are in excellent agreement with experiments. Phonon frequencies, plasmon energy, melting temperature and the coefficient of thermal expansion were calculated with a molecular dynamics scheme of this TB hamiltonian.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

A new generalized algebra method and its application in the (2 + 1) dimensional Boiti–Leon–Pempinelli equation

In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics.     

Crystallographic report: Bis(norfloxacin)dilead(II) tetranitrate, [Pb2(H‐Norf)2(ONO2)4]

The centrosymmetric binuclear structure of [Pb₂(H‐Norf)₂(ONO₂)₄]shows the geometry around each lead(II) atom to be distorted trigonal bipyramidal with Pb–O distances ranging from 2.357(3) to 2.769(4) Å. Copyright © 2003 John Wiley & Sons, Ltd.     

Essentially normal Hilbert modules and Khomology Ⅲ: Homogenous quotient modules of Hardy modules on the bidisk

In this paper, we study the homogenous quotient modules of the Hardy module on the bidisk. The essential normality of the homogenous quotient modules is completely characterized. We also describe the essential spectrum for a general quotient module. The paper also considers K-homology invariant defined in the case of the homogenous quotient modules on the bidisk. This work is partially supported by the National Natural Science Foundation of China (Grant No. 10525106), the Young Teacher Fund, the National Key Basic Research Project of China (Grant No. 2006CB805905) and the Specialized Research for the Doctoral Program