Attractors of derivative complex Ginzburg-Landau equation in unbounded domains

The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg-Landau (DCGL) equation in an unbounded domain Ω ⊂ ℝ² is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov’s ɛ-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in ℝ² is detailed studied.      

光学多普勒层析三维矢量测速方法研究

光学多普勒层析术(ODT)是一种高分辨、非侵入的生物医学成像手段,能同时得到组织的结构信息和组织内血管的流速信息.提出了一种新型的基于相位分辨技术的ODT三维矢量测速方法.在ODT系统样品臂的准直镜和聚焦透镜之间加入窄带相位片,形成三个不同的相位延迟,通过计算多普勒频移和不同相位延迟下的多普勒展宽,可得到毛细管内的三维矢量流场分布.对已知浓度的聚苯乙烯溶液进行了一系列不同角度和不同流速的实验,结果证明这种新型的ODT矢量测速方法可以较精确的实现三维矢量流速的测量.     

How to make a triangulation of polytopal

We introduce a numerical isomorphism invariant for any triangulation of . Although its definition is purely topological (inspired by the bridge number of knots), reflects the geometric properties of . Specifically, if is polytopal or shellable, then is ``small' in the sense that we obtain a linear upper bound for in the number of tetrahedra of . Conversely, if is ``small', then is ``almost' polytopal, since we show how to transform into a polytopal triangulation by local subdivisions. The minimal number of local subdivisions needed to transform into a polytopal triangulation is at least . Using our previous results [The size of triangulations supporting a given link, Geometry & Topology 5 (2001), 369-398], we obtain a general upper bound for exponential in . We prove here by explicit constructions that there is no general subexponential upper bound for in . Thus, we obtain triangulations that are ``very far' from being polytopal. Our results yield a recognition algorithm for that is conceptually simpler, although somewhat slower, than the famous Rubinstein-Thompson algorithm.

     

Quantum information processing in optical images

Optical images can be used to transport, store and process information in a parallel way. We discuss different results obtained in the domain of ‘quantum imaging’, aiming at exploiting at the same time the quantum properties of optical images and their intrinsic parallelism. We define the notion of standard quantum limit (SQL) in optical resolution, set by the quantum noise of usual coherent light, and show that it can be much lower than the diffraction limit. We also prove that this limit can be circumvented by especially designed nonclassical and multimode light. We present an experiment showing that OPOs oscillating inside an exactly confocal cavity actually produce such transverse multimode nonclassical light. We finally describe another experiment which has surpassed the SQL in the case of beam positioning, both in the 1D and 2D cases.     

我国东西部高等教育布局结构研究

关于我国东西部高等教育布局均衡性问题,目前国内的研究观点和结论大相径庭,研究方法各不相同.一种观点认为,东西部高等教育无论从规模还是从质量上都有相当大的差距;另一种观点认为,在某种意义下,高等教育并不存在东西部分布的不均衡.本文针对我国高等学校地理(空间)布局的不平衡问题及目前研究方法的缺陷,采用国际上通用的衡量分布不平衡的G IN I模型,对基本衡量指标作相对化处理,分析了东西部高等教育的差异及变化趋势;提出西部高等教育发展的对策及建议.     

利用双光子吸收效应测量激光脉冲的相干时间

研究了利用反向泵浦－探测双光子吸收材料的方法来测量脉冲激光的相干时间，并测量量了２３ｐｓ，５３２ｎｍ Ｎｄ：ＹＡＧ激光脉冲的相干时间。实验和理论分析表明，光束相干作用增加了双光子吸收，利用此方法可测量其它脉宽激光的相干时间。     

微波场驱动下V型三能级原子的吸收和色散特性

当用微波场作用到V型三能级原子的两个激发态能级时,系统跃迁路径之间发生交叉耦合导致了量子相干效应.通过调节微波场的强度,可实现对原子吸收和色散性质的改变,并呈现零吸收高折射率现象.此外,微波场诱导的量子相干也可实现相对相位对探测光增益的控制.     

市场潜能、预期收入与跨省人口流动——基于空间计量模型的分析

综合新经济地理学模型与迁移效应函数,本文构建了包含市场潜能和预期收入的人口迁移理论模型,并采用空间计量模型及其稳健性检验进行了中国数据的实证分析。研究结果表明:市场潜能和预期收入及其空间溢出效应对人口迁入有显著的促进作用,但是两者对人口迁移的作用路径不同,市场潜能仅对本地区有直接正向作用,对相邻地区的空间溢出效应不明显,相邻地区则对本地区的人口迁移存在负向反馈效应;而预期收入对本身以及相邻地区的影响为正向,相邻地区的预期收入反馈效应也为正;地区的人口密度和消费水平则对人口迁移有显著的负向作用。     

自适应光学对大气扰动波前的补偿效果研究：I.理论推导

在采用冻结湍流假设和几何光学近似的条件下，得到了经自适应光学系统校正后的剩余波前相位扰动的结构函数，进而根据剩余相位结构函数与系统Ｓｔｒｅｈｌ比的关系，求出自适应光学系统的补偿效果受系统的时空传递函数，大气湍流，光波传播路径上的横向风，观察目标的旋转角速度以及系统时间延迟影响情况的解析表达式。     

Numerical propagation of partially coherent laser beams through optical systems

The propagation of partially coherent beams through optical systems is computed numerically in one transverse dimension. The optical system is divided into different elementary segments, through which the propagation of light can be calculated by appropriate operators, working on the coherence function or the Wigner distribution function respectively. For the necessary changes between these two functions describing the partially coherent beams, the use of the remarkable z-transform seems to be an advantage. With this algorithm the grid and the resolution in the spatial frequency domain can be arbitrarily chosen in contrast to the usual Fourier transform, the influence of phase aberrations on the focusability of Gauss-Schell model beams is discussed as an application example of the numerical model. With the help of this tool, practical beam guiding systems can be simulated for use with multimode laser radiation.