GeX2(X=F,Cl)与甲醛环加成反应机理的理论研究

在从头算方法HF/6311+G水平上研究了单重态GeX2(X=F,Cl)与甲醛的环加成反应,找到了反应的中间配合物和过渡态,并在MP4(SDTQ)/6311+G计算水平上进一步进行单点算,对得到的复合物以振动频率确认其驻点性质(过渡态和稳定态),讨论了其反应机理.结果表明,二氟锗烯与甲醛的环加成反应分两步进行,第一步生成中间配合物,是一个无势垒的放热反应;第二步是中间配合物异构化为产物%D二氟锗杂环氧甲烷,计算的反应势垒为196.4kJ/mol,是整个反应发生的控速步骤.而在二氯锗烯与甲醛环加成反应中,对应的控速步骤的能垒仅为125.7kJ/mol.与二氟硅烯与甲醛环加成反应相比,二氟锗烯与甲醛的环加成反应速率要慢一些,而二氯锗烯与甲醛环加成反应速率则与其相当.     

An approach to achieve lateral superresolution for small probe confocal measurement system and its element

A shaped annular beam superresolution approach is proposed to improve a lateral resolution of a small probe laser confocal measurement system (LCMS). The approach proposed enables lateral superresolution measurement of LCMS to be achieved by using a binary optical diffractive element to shape a He–Ne Gaussian laser beam into an annular beam with an inner diameter of 0.87 mm and an outer diameter of 1.8 mm required for superresolution measurement, and shift the beam spatial frequency from low to high. And a binary optical element (BOE) with 16 phase levels is designed and fabricated to shape a Gaussian laser beam into an annular beam. Preliminary experimental results indicate that an intensity distribution of a shaped annular beam is in agreement with simulation results, the diffractive efficiency is 87.2%; LCMS lateral and axial resolutions of 0.2 μm and 3 nm are achieved, respectively, and its measurement range is expanded nearly to double, when BOE is used in LCMS and , NA=0.85.     

Necessary and Sufficient Conditions for Mcshane’s Identity and Variations

Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two generators Γ to SL(2,C), this was further generalized by the authors to obtain sufficient conditions for a generalized McShane’s identity to hold for arbitrary (not necessarily type-preserving) non-reducible representations in Tan et al. (Submitted). Here we extend the above by giving necessary and sufficient conditions for the generalized McShane identity to hold (Akiyoshi, Miyachi and Sakuma had proved it for type-preserving representations). We also give a version of Bowditch’s variation of McShane’s identity to once-punctured torus bundles, in the case where the monodromy is generated by a reducible element, and provide necessary and sufficient conditions for the variations to hold.     

3D reconstruction based on spatial vanishing information

An approach for the three-dimensional (3D) reconstruction of architectural scenes from two un-calibrated images is described in this paper. From two views of one architectural structure, three pairs of corresponding vanishing points of three major mutual orthogonal directions can be extracted. The simple but powerful constraints of parallelism and orthogonal lines in architectural scenes can be used to calibrate the cameras and to recover the 3D information of the structure. This approach is applied to the real images of architectural scenes, and a 3D model of a building in virtual reality modelling language (VRML) format is presented which illustrates the method with successful performance.     

Laser drilling of thick material using femtosecond pulse with a focus of dual-frequency beam

Laser drilling is one of the basic, most frequently performed, material removal processes. The drilling aspect ratio is theoretically limited by the size and the focal depth of the machining laser spot. The aspect ratio can be improved by using dual focus. In this paper we describe a focus of two different frequencies based on the longitudinal chromatic aberration arisen when polychromatic collimated light is incident on a positive lens element. In the experiments, a Ti:Sapphire laser of 800 nm wavelength and 150 fs pulse duration was used as a source. Two tightly focused laser spots few hundred micrometers apart from each other were formed by focusing a combined collimated laser beam which contains the fundamental optic frequency and the second harmonic optic frequency. The focus of dual-frequency beam was used to drill a 3 mm thick PMMA plate. The drilling aspect ratio of a dual-frequency beam was compared to that of a focus of single frequency beam. Experimental results reveal that dual-frequency beam increases the aspect ratio and improves the drilling quality in terms of profile of the produced features.     

Intra-cavity second harmonic generation with Nd:YVO4/BIBO laser at 542 nm

We report, for the first time, an efficient intra-cavity second-harmonic generation (SHG) at 1084 nm in a nonlinear optical crystal, BiB₃O₆(BIBO) at the direction of (θ, ?) = (170.1°, 90°), performed with a LD end-pumped cw Nd:YVO₄ laser. With 590 mW diode pump power, a continuous-wave (cw) SHG output power of 19 mW at 542 nm yellow-green color has been obtained using a 1.5 mm-thick BIBO crystal. The optical conversion efficiency was 3.22%. It was found that the output wavelength could be 532 nm, 537 nm or 542 nm according to regulating the angle of BIBO.     

一类具有两个抛物线解的中心对称三次系统存在极限环的条件

本文给出了具有两个抛线解的中心对称三次系统存在在极限环的条件，它可能也是充要条件。     

Wave Fronts for Hamilton-Jacobi Equations:¶The General Theory for Riemann Solutions in

The Hamilton-Jacobi equation describes the dynamics of a hypersurface in . This equation is a nonlinear conservation law and thus has discontinuous solutions. The dependent variable is a surface gradient and the discontinuity is a surface cusp. Here we investigate the intersection of cusp hypersurfaces. These intersections define (n-1)-dimensional Riemann problems for the Hamilton-Jacobi equation. We propose the class of Hamilton-Jacobi equations as a natural higher-dimensional generalization of scalar equations which allow a satisfactory theory of higher-dimensional Riemann problems. The fist main result of this paper is a general framwork for the study of higher-dimensional Riemann problems for Hamilton-Jacobi equations. The purpose of the framwork ist to unterstand the structure of Hamilton-Jacobi wave interactions in an explicit and constructive manner. Specialized to two-dimensional Riemann problems (i.e., the intersection of cusp curves on surfaces embedded in ), this framework provides explicit solutions to a number of cases of interest. We are specifically interested in models of deposition and etching, important processes for the manufacture of semiconductor chips. We also define elementary waves as Riemann solutions which possess a common group velocity. Our second main result, for elementary waves, is a complete characterization in terms of algebraic constraints on the data. When satisfied, these constraints allow a consistently defined closed form expression for the solution. We also give a computable characterization for the admissibility of an elementary wave which is inductive in the codimension of the wave, and which generalizes the classical Oleinik condition for scalar conservation laws in one dimension. Received: 9 September 1996 / Accepted: 22 April 1997     

D. CCD视频技术、等离子体诊断和脉冲辐射摄影

本文对CCD摄象技术、等离子体诊断和脉冲辐射摄影的国内外最新发展作了评述,并涉及到在高技术领域的应用。