求坐标表象中压缩算符显式的3种方法

分别用提取变量积分法、正规乘积内的积分技术及投影算符转换法,得到了坐标表象中压缩算符的显式.     

双模坐标-动量积分型投影算符及其在量子光学中的应用

引进了幺正的双模坐标-动量积分型投影算符,利用有序算符内的积分（IWOP）技术分析了其变换特性,并导出了其正规乘积展开式.然后利用该积分型投影算符对角化了双模耦合量子谐振子体系的哈密顿量,从而求出了体系的本征能级与本征波函数.最后讨论了特例情形. 关键词： 积分型投影算符 有序算符内的积分技术 坐标-动量耦合     

一种单目运动像机对点状运动物体的三维定位方法

针对单目运动像机无法确定点状运动物体三维位置的难题,提出了一种求解点状运动物体三维位置的方法,利用直线在其法平面上的投影为点这个特性,将各时刻像机光心与物体位置的连线(以下称观察视线)投影到以运动物体轨迹为法线的平面上,通过迭代使其投影线交于一点,交点对应的直线就是物体的运动轨迹,仅需要取大于等于5个时刻的数据就可以确...     

Forming an Edge Dislocation Image at Anomalous X-ray Transmission

Physics of the Solid State - The features of forming section and projection topography images of an edge dislocation normal to the crystal surface are considered for the case of X-ray anomalous...     

A systematic investigation of the Coriolis antipairing effect in the rare earth region including projection onto exact particle number and angular momentum

The Coriolis antipairing effect is investigated for the rare earth nuclei. A new two-parameter expression for the pairing strength is introduced which is adjusted to the even-odd mass differences. Good agreement with the experimental results concerning the linear part of the moment of inertia as a function of the square of the angular velocity can be reached if projection onto exact particle number is taken into account. The latter causes an essential stabilization of the pair correlations. The critical angular velocity for the transition from the suprafluid to the normal state is defined and calculated. It is substantially increased by projection onto exact particle number whereas it remains almost unchanged by projection onto exact angular momentum. The critical angular velocity at which the neutron pairing vanishes is systematically larger than the angular velocity at which back-bending is observed. From this it is concluded that backbending cannot be caused by a collapse of pairing.     

Comment on "Identification of low order manifolds: validating the algorithm of Maas and Pope" [Chaos 9, 108-123 (1999)

It is claimed by Rhodes, Morari, and Wiggins [Chaos 9, 108-123 (1999)] that the projection algorithm of Maas and Pope [Combust. Flame 88, 239-264 (1992)] identifies the slow invariant manifold of a system of ordinary differential equations with time-scale separation. A transformation to Fenichel normal form serves as a tool to prove this statement. Furthermore, Rhodes, Morari, and Wiggins [Chaos 9, 108-123 (1999)] conjectured that away from a slow manifold, the criterion of Maas and Pope will never be fulfilled. We present two examples that refute the assertions of Rhodes, Morari, and Wiggins. In the first example, the algorithm of Maas and Pope leads to a manifold that is not invariant but close to a slow invariant manifold. The claim of Rhodes, Morari, and Wiggins that the Maas and Pope projection algorithm is invariant under a coordinate transformation to Fenichel normal form is shown to be not correct in this case. In the second example, the projection algorithm of Maas and Pope leads to a manifold that lies in a region where no slow manifold exists at all. This rejects the conjecture of Rhodes, Morari, and Wiggins mentioned above.     

迭代目标转换因子分析光度法同时测定钐铕钆富集物中的铁和铝

基于铬天青S－CTMAB与Fe^3 、AI^3 离子的显色体系中两组分吸收光亦灵敏度高及选择性差的特点,采用迭代目标转换因子分析法处理数据。首先根据主因子分析对未知样品进行组分数统计,然后构造列空间正交投影矩阵,以体系中可能存在组分的光谱向量为待检验光谱,确定试样的真实组成从而完成定性分析。然后以构成的行空间正交投影矩阵对浓度矩阵进行迭代运算而完成定量分析。本方法对人工合成样及实际钐铕钆富集物样品的分析均取得了满意结果。     

Short-TE projection reconstruction NMR microscopy of trabecular bone.

The aim of this study was to assess the potential of projection reconstruction (PR) NMR microscopy in the quantitative evaluation of trabecular bone architecture. Short-TE PR spin-echo microimages were acquired at 7.05 T on normal bone explants. The main structural parameters such as bone volume fraction (BVF), trabecular thickness (Tb.Th.) and trabecular separation (Tb.Sp.) were obtained from the 3D microimages using the method of directed secants. Quantitative structural data were then compared with those derived from conventional spin-echo microimages. Our study indicates that projection reconstruction NMR microscopy promises to be more accurate than the conventional FTI method in the analysis of trabecular bone.     

Angular momentum projected Hartree-Fock-Theory

The Euler Lagrange equations corresponding to the Hartree-Fock variational problem after angular momentum projection (PHF) are derived. The exact equations are simplified employing the Gaussian overlap approximation. The solution of the PHF equations in this approximation is seen to be not much more complicated than the solution of the normal HF problem.     

Elastic friction drive of surface acoustic wave motor

Importance of elastic deformation control to obtain large output force with a surface acoustic wave (SAW) motor is discussed in this paper. By adding pre-load to slider, stator and slider surfaces are deformed in a few tens nanometer. Appropriate deformation in normal direction against normal vibration displacement amplitude of SAW existed. By moderate deformation, the output force of the SAW motor was enlarged up to about 10 N and no-load speed was 0.7 m/s. To produce this performance, the transducer weight and slider size were only 4.2 g and 4 x 4 mm(2).By traveling wave propagation, surface particles of the SAW device move in elliptical motion. Due to the amplitude of the elliptical motion is 10 or 20 nm order, the contact condition of the slider is very critical. To control the contact condition, namely, the elastic deformation of the slider and stator surface in nanometer order, a lot of projections were fabricated on the slider surface. The projection diameter was 20 micro m. In static condition, the elastic deformation and stress were evaluated with the FEM analysis. From this calculation and the simulation result, it is consider that the wave crest is distorted, hence the elasticity has influence on the friction drive condition.Elastic deformation of the stator surface beneath the projection from the initial position were evaluated. In 4 x 4 mm(2) square area, the sliders had from 1089 to 23,409 projections. Depression was independent to the contact pressure. However, the output force depended on the depression although the projection density were different. From the view point of the output power of the motor, the proper depression was independent to the projection density. Around 25 nm depression, the output force and output power were maximized. This depression value was almost same as the vibration displacement amplitude of the stator transducer.     

Analysis of Spectral Reflectance Using Normalization Method from Endoscopic Spectroscopy System

Objective assessment of gastrointestinal mucosal color is extremely important in the endoscopic diagnosis of digestive tract disease. In this paper, we propose a method to clarify the spectral characteristics of gastric and colon cancer. A large number of spectral reflectance data of mucous membrane are measured by the endoscopic spectroscopy system (ESS) in the National Cancer Center Hospital East, Kashiwa, Japan and the Department of Internal Medicine, Self-Defense Force Center Hospital, Tokyo, Japan. We assume that early cancer appears primarily in the spectral data of short wavelength, because it is usually present in a superficial cell where short wavelength light is scattered more strongly than long wavelength light. To identify the features in the short wavelength components, the spectral reflectance was divided by the reflectance of a long wavelength. We investigated the possibility of distinguishing early cancer from normal spectral data through statistical analysis, employing the projection axis as the mean difference between them. Early cancer and normal spectral data were projected on the projection axis, and the Student’s T-test was applied to evaluate the mean of the distribution between these data.     

An iterative virtual projection method to improve the reconstruction performance for ill-posed emission tomographic problems

In order to improve the reconstruction performance for ill-posed emission tomographic problems with limited projections, a generalized interpolation method is proposed in this paper, in which the virtual lines of projection are fabricated from, but not linearly dependent on, the measured projections. The method is called the virtual projection(VP) method.Also, an iterative correction method for the integral lengths is proposed to reduce the error brought about by the virtual lines of projection. The combination of the two methods is called the iterative virtual projection(IVP) method. Based on a scheme of equilateral triangle plane meshes and a six asymmetrically arranged detection system, numerical simulations and experimental verification are conducted. Simulation results obtained by using a non-negative linear least squares method,without any other constraints or regularization, demonstrate that the VP method can gradually reduce the reconstruction error and converges to the desired one by fabricating additional effective projections. When the mean square deviation of normal error superimposed on the simulated measured projections is smaller than 0.03, i.e., the signal-to-noise ratio(SNR)for the measured projections is higher than 30.4, the IVP method can further reduce the reconstruction error reached by the VP method apparently. In addition, as the regularization matrix in the Tikhonov regularization method is updated by an iterative correction process similar to the IVP method presented in this paper, or the Tikhonov regularization method is used in the IVP method, good improvement is achieved.     

Theory of Gaussian-beam optical bistability

We describe an analysis of transverse coupling effects in a plane parallel Fabry-Perot containing a medium exhibiting non-linear refraction. The method involves projection on to a set of ortho normal mode functions and numerical solution of the resulting coupled equations. We find evidence for hysteresis in the profile of the transmitted beam without accompanying power hysteresis, in first interference order.     

The forward and backward projection of acoustic fields from axisymmetric ultrasonic radiators using impulse response and Hankel transform techniques

A generalized impulse response formulation to evaluate the harmonic pressure field of ultrasonic planar vibrators having axisymmetric nonuniform surface velocity distributions is presented. The harmonic pressure is expressed as a Fourier transform of a generalized impulse response which is a function of the spatially nonuniform velocity of the vibrator. A backward projection method is then developed to reconstruct the normal surface velocity of axisymmetric vibrators from harmonic field pressures using an angular spectrum or Hankel transform formulation. The numerical accuracy of the backward projection technique is evaluated using the impulse response formulation to evaluate the pressure fields for several velocity distributions on disk vibrators. Experiments were performed to reconstruct the velocity distributions over the surface of a uniformly driven piezoelectric ceramic disk and ceramic ring using farfield measurements of the complex pressure. The experimental results were in good agreement with theoretical results based on the electrode patterns of the transducers.     

Theory of open systems I

A new method of treating open systems is presented. The normal treatment using the generalized master equation with the projection of Argyres and Kelley is meaningful only if the state of the reservoir never deviates appreciably from the reference state which appears in the projection. Otherwise, one must make at least a partial resummation of the perturbative expansion of the kernel of the generalized master equation. The present method avoids the introduction of a projection operator and allows us to overcome such resummation difficulties. It is based on an integrodifferential equation for the statistical operator of the composite system, which naturally provides a hierarchy of equations involving the statistical operator ?(t) of the open system and suitable quantities describing higher and higher order bath-system correlations. Treating the deviations of the bath from its initial equilibrium or stationary state as expansion parameters, one gets an approximation scheme, each step of which gives a closed system of equations for ?(t) and a suitable set of correlation quantities.Eliminating such quantities one obtains a closed linear integrodifferential equation for ?(t). The zeroth approximation in the deviations coincides with the Born approximation of the generalized master equation which uses the projection of Argyres and Kelley.On the other hand, even the first approximation is equivalent to the resummation of infinite contribution of the Born series of such a generalised master equation. When it is suitable, the concentration of the bath can also be used as an expansion parameter to handle the hierarchy.     

基于拉曼光谱的改进投影算法快速鉴别药品

投影算法常用于混合物分析中确定灰色体系是否存在未知干扰,而在用于药品鉴别时,由于其判定标准不充分,故不能同时准确鉴别不同药品和相似药品。提出将投影算法的判定标准(待测物质光谱的量测误差大小是否在限定水平)改进为待测物质光谱与标准物质光谱的量测误差大小水平是否相当、量测误差分布是否相近。将改进投影算法与未经改进投影算法用于六种(拜耳阿司匹林肠溶片、泰诺对乙酰氨基酚缓释片、拜耳复方对乙酰氨基酚片Ⅱ、华中复合维生素C片、华中维生素B片、吗丁啉多潘立酮片)不同药品的鉴别以及三种相似药品(拜耳阿司匹林肠溶片、上海信宜药阿司匹林肠溶片、巴米尔阿司匹林泡腾片)的区分,实验结果表明改进投影算法实现了不同药品的准确鉴别及相似药品的准确区分,准确率均高达100%,有望发展成为普适,可靠的自动化药品识别算法,并为基于拉曼光谱的物质识别算法研究提供参考依据。     

On the nature of pulsars

The paper contains a relatively non-technical summary of some recent work by the author and Jeremy Butterfield. The goal is to find a way of assigning meaningful truth values to propositions in quantum theory: something that is not possible in the normal, instrumentalist interpretation. The key mathematical tool is presheaf theory where multi-valued, contextual truth values arise naturally. We show how this can be applied to quantum theory, with the ‘contexts’ chosen to be Boolean subalgebras of the set of all projection operators.     

LED微阵列投影系统设计

为满足便携式投影仪的市场需求,设计了一种基于LED微型阵列的投影系统。该系统由显示单元和投影物镜构成。采用尺寸为12 mm×9 mm的自发光LED微型阵列作为系统的显示单元,利用光学设计软件设计了投影物镜。投影物镜采用反远距光学结构,全视场角为80°,焦距为8 mm,属于强光、广角镜头。在空间频率20 lp/mm处,该物镜的调制传递函数大于0. 85,畸变小于2%,符合投影系统的设计要求。该投影系统具有体积小,结构简单,投影效果好,易加工等诸多优势,可为第三代投影技术的发展提供参考。     

平行光干涉投影三维形貌恢复方法

传统傅立叶变换轮廓术多采用散光斜式投影,需要满足4个约束条件才能得到较为准确的相位与高度映射关系,并且散光投影带来的相位非线性二次项误差也会降低形貌恢复精度。为了能在欠约束条件下减少相位非线性误差的影响,建立了基于平行光干涉投影下的普适模型。平行光干涉投影下的参考平面相位沿着x轴呈线性变化,相位分布较散光或倾斜式投影更具准确性。对比分析了散光及平行光投影下被测物体的恢复情况,实验结果表明,新模型在欠约束条件下,具有较高的灵活性和可操作性,恢复精度良好,相对误差为1.1%。