Direct Images,Fields of Hilbert Spaces,and Geometric Quantization

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H _s of Hilbert spaces, and the question arises if the spaces H _s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787–902, 1991) and Hitchin (Commun. Math. Phys. 131:347–380, 1990) suggest viewing H _s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle ${E \to Y}$ along a non–proper map ${Y \to S}$ . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Sz?ke (Bull. Lond. Math. Soc. 44:367–374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.     

基于不可控微扫描的高分辨力图像重构方法

针对存在不可控微位移的序列低分辨力图像,提出了一种基于2×2不可控微扫描的高分辨力图像重构方法,采用投影法估算出低分辨力图像LR的微位移量,采用基于泰勒级数展开的重构算法由4帧图像重构高分辨力图像.模拟表明：该算法能精确地估计序列图像的帧间位移量并取得较好的重构效果,且算法简单有效可行,处理量小,有利于实现快速处理,在一定程度可满足同步轨道卫星、公安监视等领域对高分辨力成像处理的需求.       

激光触发多级多通道开关研究

 研究了200kV激光触发多级多通道开关的运行机理，该开关在直流电压下以四倍频Nd:YAG激光器为触发源进行的实验结果表明：开关触发延迟时间及其抖动随开关电压、激光能量和充气压力上升呈指数下降趋势，对混合气体则随气体密度上升而上升。随透镜焦距的增大延迟时间及其抖动呈上升趋势。该开关实现了多通道放电。     

Syntheses and modifications of bisdiazonium salts of 3,8-benzo[c]cinnoline and 3,8-benzo[c]cinnoline 5-oxide onto glassy carbon electrode and the characterization of the modified surfaces

The goal of this study was to prepare novel glassy carbon electrode surfaces using two similar bis-diazonium salts, 3,8-benzo[c]cinnoline (3,8-BCC-BDAS) and 3,8-benzo[c]cinnoline 5-oxide (3,8-BCCNO-BDAS) at the glassy carbon (GC) surface. These diazonium salts were reduced electrochemically and covalently electrografted onto the glassy carbon electrode surface to form modified electrodes. Electrochemical reduction of 3,8-BCC-BDAS and 3,8-BCCNO-BDAS salts on the electrode surface yielded a compact and stable film. The existence of BCC moieties on the GC surface was characterized by X-ray photoelectron spectroscopy, reflectance-adsorption infrared spectroscopy, cyclic voltammetry, ellipsometry, and electrochemical impedance spectroscopy. The stability and working potential range of the novel modified electrodes were also studied. The possibility of analytical application of these novel surfaces for inorganic cations and especially selectivity to copper ions was investigated. 3,8-diaminobenzo[c]cinnoline (3,8-DABCC) and its 5-oxide derivative (3,8-DABCCNO) were synthesized from the reductive cyclization of 2,2′-dinitrobenzidine and prepared their bisdiazonium salts via the tetrazotization reactions of the diamines with NaNO₂. The structures of 3,8-DABCC and 3,8-DABCCNO and their corresponding bisdiazonium salts are confirmed by spectral analysis.     

Simulation of Dynamic Light Scattering Signals of Ultrafine Particles

In order to conveniently obtain dynamic light scattering (DLS) signal, a simulation method of DLS signal is proposed in this paper. This method regards the light intensity fluctuation of DLS as a stationary random process. According to autocorrelation function (ACF) of DLS signal, the stationary random process of DLS can be generated by auto‐regressive (AR) model. Signal simulations of several kinds of distribution particles and comparison of simulations and experiment prove that AR model can be used for DLS signal simulation. Moreover, by analyzing effect of simulation parameters on simulation precision, we obtained the relationship between simulation parameters and simulation precision. Finally, application of simulation signal verifies the effectiveness and convenience of this simulation method.     

Multi-component fractional quantum Hall states in graphene: SU(4) versus SU(2)

Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two- or four-component fractional quantum Hall effects in different parameter regions. We address the stability of various states in the SU(2) and SU(4) limits. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7, etc; SU(4) skyrmions are not found to be relevant for the low-energy physics. These results are discussed in light of experiments.     

Revealing Bell’s nonlocality for unstable systems in high energy physics

Entanglement and its consequences—in particular the violation of Bell inequalities, which defies our concepts of realism and locality—have been proven to play key roles in Nature by many experiments for various quantum systems. Entanglement can also be found in systems not consisting of ordinary matter and light, i.e. in massive meson–antimeson systems. Bell inequalities have been discussed for these systems, but up to date no direct experimental test to conclusively exclude local realism was found. This mainly stems from the fact that one only has access to a restricted class of observables and that these systems are also decaying. In this Letter we put forward a Bell inequality for unstable systems which can be tested at accelerator facilities with current technology. Herewith, the long awaited proof that such systems at different energy scales can reveal the sophisticated “dynamical” nonlocal feature of Nature in a direct experiment gets feasible. Moreover, the role of entanglement and CP\mathcal{CP} violation, an asymmetry between matter and antimatter, is explored, a special feature offered only by these meson–antimeson systems.     

Application of hollow fiber liquid phase microextraction for pinic acid and pinonic acid analysis from organic aerosols

A method based on hollow fiber liquid phase microextraction (HF-LPME) for analysis of pinic acid and pinonic acid was developed and for the first time successfully applied to ambient aerosol samples. In this method, the aerosol samples were dissolved in 0.05 M H₂SO₄ and the solution was extracted using three-phase HF-LPME where donor phase was 0.1 M (NH₄)₂CO₃. Different parameters like type of organic solvent for membrane phase, extraction time and stirring speed etc. were optimized. Optimum extraction time was 4.5 h and optimum-stirring speed was found to be 900 rpm. We used 6-undecanone as organic phase along with tri-n-octylphosphine oxide (optimum TOPO contents was 15% w/v), which gave an enormous enrichment for both pinic and pinonic acid. Enrichment factors of 28,050 and 27,400 times were obtained for pinonic acid and pinic acid, respectively, that are the highest ever published. The extraction efficiency for pinic acid and pinonic acid were 68.5% and 70.1%, respectively. Very low limits of detection were obtained. Values of 1.0 ng L^?1 and 0.5 ng L^?1 in aqueous solutions, corresponding to 24 pg m^?3 and 12 pg m^?3 in aerosol samples were the limits of detections for pinonic acid and pinic acid, respectively. Both pinonic acid and pinic acid were found in all aerosol samples analyzed.     

Stability of the rectilinear motion of a railway Wheelset

A railway wheelset rolling on rails without slip is studied with consideration of the creep hypothesis. The wheelset is represented by two cones having a common base; the rails are represented by two circular cylinders with parallel axes. The kinematic characteristics of undisturbed rolling for the wheelset are determined when its center of mass moves along a straight line; these characteristics are also determined in the case of disturbed motion when the mass center of the wheelset moves along a sinusoidal trajectory. For these modes of motion, the constraint reactions are found with an accuracy up to the second order of smallness with respect to the values of disturbed variables. When the absolutely rigid point contact is replaced by the elastic contact, the creep hypothesis is used, the method of averaging with respect to the fast variables is applied, and a critical velocity above which the rectilinear rolling becomes unstable is determined on the basis of the averaged equations.     

在线分析己烷中痕量四氢呋喃的气相色谱柱系统研究

 根据 30万t乙烯工程“橡胶”装置中生产工艺控制的实际需要 ,研究了在线分析己烷中痕量四氢呋喃的气相色谱柱系统。使用自制的 7μm特厚膜甲基硅氧烷大孔径弹性石英毛细管柱 ,通过试验不同条件下色谱柱的分离特性及研究组分在柱内的运动轨迹 ,给出了总的柱切换时间程序。在上述基础上 ,完成了正己烷、环己烷中 10 -6(体积分数 )级的四氢呋喃分析。现场应用一年多的实践表明 ,所研制的柱系统从分析时间、运行稳定性、定量准确性 (相对标准偏差小于 5 % )等方面均满足工艺控制的要求。