Nonlinear Distortion Analyses in IM-DD SCM Lightwave Systems

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C80n (D2,Ih)的Jahn-Teller畸变和电子光谱

用INDO系列方法研究C80n(D2,Ih)的Jahn-Teller畸变,表明C80(D2)比C80(Ih)稳定,与实验一致;C80n(D2)未发生Jahn-Teller畸变,C80n(Ih)的部分离子发生明显的Jahn-Teller畸变,电荷对C80(Ih)稳定性有显著影响.首次计算其电子光谱,不仅得到C80(D2)与实验一致的吸收峰,还预测了C80n(D2,Ih)的电子光谱,对电子跃迁进行理论指认.C80n(D2)光谱与C80(D2)相比发生吸收峰红移,而C80n(Ih)光谱与C80(Ih)相比发生吸收峰兰移,其原因是C80n(D2)的LUMO-HOMO能隙比C80(D2)小,而C80n(Ih)的能隙则比C80(Ih)的能隙大.     

Calibrating camera radial distortion with cross-ratio invariability

The calibration of camera distortion plays an important role in the field of industrial machine vision application. In this paper, a novel approach for calibrating camera radial distortion is presented based on cross-ratio invariability for perspective projection. Assumed to be with one-order radial distortion, the image coordinates and the cross-ratio of only four collinear points in space are needed in this approach. The cross-ratio, easily known from a calibration target, is identical with that of the four corresponding image points. This is called the cross-ratio invariability for perspective projection. A monadic two-order equation is built based on the cross-ratio invariability, which gives an accurate solution to radial distortion coefficients. A digital simulation and a practical image correction prove this approach to be simple, accurate, efficient and time saving.     

Exact analytical expressions for diatomic rotational and centrifugal distortion constants for a Kratzer-Fues oscillator

The exact closed-form expression for the vibrational-rotational eigenvalues of the Kratzer-Fues oscillator served as the starting point for a derivation of exact analytical expressions for the rotational constant B_υ, and the set D_υ to S_υ of centrifugal distortion constants up to 11th-order. The derivations employed the MAPLE symbolic algebra coprocessor. The expressions for B_υ to S_υ were then employed in the calculation of a set of constants for a Kratzer-Fues potential with specified dissociation energy and equilibrium internuclear separation for a hypothetical diatomic molecule with a reduced mass of unity. The tabulated constants serve as a benchmark against which the reliability of various existing or future numerical methods for the determination of rotational and centrifugal distortion constants may be assessed. The near-dissociation behaviour of the calculated constants was also examined and is useful in predicting the behaviour of such constants for real electronic states having pure ionic long-range form.     

Centrifugal distortion analysis of the millimeter-wave spectrum of 2-fluorobenzonitrile and ab initio DFT calculations

The ground state (ν = 0) rotational spectrum of 2-fluorobenzonitrile has been reinvestigated in the frequency range 40.0-99.0 GHz. The millimeter-wave spectrometer used is a source-modulated system combined with a free space glass cell. Millimeter-wave radiation has been produced using a Gunn diode and frequency doubler combination. High J and K₋₁ (J ? 49 and K₋₁ ? 18) transitions have been measured and accurate rotational and centrifugal distortion constants have been determined. Finally, the experimental values were compared with the corresponding values calculated at the HF/DFT-B3PW91/6-31g(d,p) level of theory. A very good agreement has been found.     

再论高速运动物体视状

采用一种直观解析法，从研究高速运动细棒的视状出发来说明在相对论意义下运动物体（如正方体，球体等）的视状畸变，结果表明，高速运动物体的视状一般不仅仅是发生“表现旋转”而是依具体的条件而发生不同的形变，在特殊条件下，洛伦兹收缩也是可见的。     

计算机辅助的数字通信频谱分析

从Fourier级数出发 ,到任意闭区间上可积函数的Fourier分析 ,给出了数字信号Fourier分析的理论基础。以字符“b”为例 ,建立了严格的数学模型 ,严密推导了Fourier系数表达式。阐明了Fourier级数的“项”和“n阶Fourier级数”(前n项和 )的概念。详尽地分析了信道通频带B与Fourier阶数n(展开式“保留”项 )的关系。借助计算机计算了n≤ 10 0时各Fourier级数项和前n项和 ,并用Plot将计算结果绘成曲线 ,获得n≤10 0时各级Fourier展开曲线。与数字信号对照 ,Fourier级数的取项与波形的关系显而易见 ,特别是n取值较小时 ,Fourier级数取项少 ,波形失真严重 ;所以在B一定时传输速率不能过高 ,否则 ,由于波形失真而导致信号出错。     

Structure and magnetic properties of a new single-molecule magnet [Mn11Fe1O12 (CH3COO)16(H2O)4].2CH3COOH.4H2O

A new single-molecule magnet [Mn₁₁Fe₁O₁₂ (CH₃COO)₁₆(H₂O)₄]?2CH₃COOH?4H₂O (Mn₁₁Fe₁) has been synthesized.The structure has been studied by the single crystal x-ray diffraction. The difference of Jahn--Teller distortion between Fe³⁺ and Mn³⁺ ion reveals that Fe³⁺ ion substitutes for Mn³⁺ ion on the Mn(3) sites in the Mn₁₂ skeleton. The temperature dependence of the magnetization gives a blocking temperature T_B=1.9K for Mn₁₁Fe₁. Based on the magnetization process analysis of the crystal at T=2K, we suggest that Mn₁₁Fe₁ has the ground state with a total spin S= 11/2.     

关于某类解析函数的星象性和Ruscheweyh的一个问题

本文引入了一个涉及Ruscheweyh导数的解析函数子类，应用微分从属方法和Carlson-Shaffer算子讨论了它的从属关系和偏差定理；其次，应用单叶函数的性质和一个微分不等式研究了它的星象性条件和覆盖定理，最后，部分地解决了Ruscheweyh的一个问题。