Ergodic Properties of the Quantum Geodesic Flow on Tori

We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on . We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10.     

Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes

The folk questions in Lorentzian Geometry which concerns the smoothness of time functions and slicings by Cauchy hypersurfaces, are solved by giving simple proofs of: (a) any globally hyperbolic spacetime (M, g) admits a smooth time function whose levels are spacelike Cauchy hyperfurfaces and, thus, also a smooth global splitting if a spacetime M admits a (continuous) time function t then it admits a smooth (time) function with timelike gradient on all M.The second-named author has been partially supported by a MCyT-FEDER Grant, MTM2004-04934-C04-01.To Professor P.E. Ehrlich, wishing him a continued recovery and good health     

On the Well-Posedness Problem and the Scattering Problem for the Dullin-Gottwald-Holm Equation

In this paper, we study the well-posedness of the Cauchy problem and the scattering problem for a new nonlinear dispersive shallow water wave equation (the so-called DGH equation) which was derived by Dullin, Gottwald and Holm. The issue of passing to the limit as the dispersive parameter tends to zero for the solution of the DGH equation is investigated, and the convergence of solutions to the DGH equation as ²0 is studied, and the scattering data of the scattering problem for the equation can be explicitly expressed; the new exact peaked solitary wave solutions are obtained in the DGH equation. After giving the condition of existing peakon in the DGH equation, it turns out to be nonlinearly stable for the peakon in the DGH equation.     

光在一维周期结构中的分布和局域化

运用传播矩阵对不同种类的一维周期结构(periodic structure, PS)中的光场分布和局域化进行了理论分析．结果表明: 当光以禁带频率入射到PS上时,绝大部分光被反射,在PS中是以衰减的驻波形式存在的．需要强调的是,当光以禁带带边频率入射时,光场在PS中有显著的局域化,在介质中引入适当的缺陷可以极大地增加这种局域化程度．另外,当光从掺杂有特定缺陷层的PS的左右两个不同界面入射时,可引起光场在PS中不同的分布,这对通过光的非线性调制实现的光学二极管非常有用.在线性吸收的PS中光强随光进入介质的厚度及消光系数的增加迅速衰减．     

Influence of the KTP crystal boundary temperature on conversion efficiency in high power green laser

The influence of the KTiOPO4 (KTP) crystal boundary temperature on conversion efficiency in high power green laser has been studied theoretically and experimentally. Temperature distribution inside the KTP crystal has been analyzed by solving the thermal conductivity equation. From the temperature distribution inside the KTP crystal, we have calculated the optimal phase-matching angles of the type-Ⅱ KTP crystal as a function of temperature. The second-harmonic conversion efficiency as a function of temperature has also been calculated. In the experiment, two KTP crystals with different phase-matching angles were used in the intrcavity-frequency-doubled resonator. When the boundary temperature of KTP-A (φ = 23.6°,θ = 90° under the condition of 27 ℃ temperature) was setting at 4 ℃, a maximum green light power of 104 W was generated at repetition rate of 20.7 kHz and pulse width of 132 nm with pumping current of laser diode of 18.3 A, leading to 10.2% optical-to-optical conversion efficiency. When KTP-B crystal (φ = 24.68°, θ = 90° under the condition of 80 ℃ temperature) was employed, an average output power of 110 W at 532 nm has been achieved with values of 11.5% and 2% for the optical-to-optical efficiency and the instability, respectively. The optimal boundary temperature of this KTP crystal has been found to be 48.8 ℃.     

Trapping of Neutral^87Rb Atoms on an Atomchip

We report an experiment of trapping of neutral ^87Rb atoms on a self-made atomchip. The H-shaped atomchip is made by magnetron sputtering technology, which is different from the atomchip technology of other teams. We collect 3×10^6 ^87Rb atoms in the mirror magneto-optical trap （MOT） using the external MOT coils, and 1×10^5 ^87 Rb atoms are transferred to U-MOT using U-shaped wire in chip and a pair of bias coils.     

Spectra Analysis of a Novel Ti-Doped LiAlO2 Single Crystal

LiAlO2 single crvstals doped with Ti at concentration 0.2at.% are grown by the Czochralskl technique with dimensions φ42×55mm. Ti ions in the crystal are quadrivalence proven by comparing the absorption and fluorescence spectra of pure LiAlO2 and Ti： LiAlO2. After air and Li-rich atmosphere annealing, the absorption peaks in the range of 600-800nm disappear. We conclude that 682 and 756nm absorption peaks are attributed to the VLi and Vo absorptions, respectively： The peaks at 716nm and 798nm may stem from the VLi^＋ and absorptions. The colour-centre model can be applied to explain the experimental phenomena. Ti^4＋-doping produces more lithium vacancies in the LiAlO2 crystal. The intensities of [LiO4] and the associated bonds remain unchanged, which improves the anti-hydrolyzation and thermal stability of LiAlO2 crystals.     

Neuronal expression of muskelin in the rodent central nervous system

Background  

The kelch repeat protein muskelin mediates cytoskeletal responses to the extracellular matrix protein thrombospondin 1, (TSP1), that is known to promote synaptogenesis in the central nervous system (CNS). Muskelin displays intracellular localization and affects cytoskeletal organization in adherent cells. Muskelin is expressed in adult brain and has been reported to bind the Cdk5 activator p39, which also facilitates the formation of functional synapses. Since little is known about muskelin in neuronal tissues, we here analysed the tissue distribution of muskelin in rodent brain and analysed its subcellular localization using cultured neurons from multiple life stages.