Fractional cyclic integrals and Routh equations of fractional Lagrange system with combined Caputo derivatives

In this paper, we develop a fractional cyclic integral and a Routh equation for fractional Lagrange system defined in terms of fractional Caputo derivatives. The fractional Hamilton principle and the fractional Lagrange equations of the system are obtained under a combined Caputo derivative. Furthermore, the fractional cyclic integrals based on the Lagrange equations are studied and the associated Routh equations of the system are presented. Finally, two examples are given to show the applications of the results.     

Data analysis method to achieve sub‐10 pm spatial resolution using extended X‐ray absorption fine‐structure spectroscopy

Obtaining sub‐10 pm spatial resolution by extended X‐ray absorption fine structure (EXAFS) spectroscopy is required in many important fields of research, such as lattice distortion studies in colossal magnetic resistance materials, high‐temperature superconductivity materials etc. However, based on the existing EXAFS data analysis methods, EXAFS has a spatial resolution limit of π/2Δk which is larger than 0.1 Å. In this paper a new data analysis method which can easily achieve sub‐10 pm resolution is introduced. Theoretically, the resolution limit of the method is three times better than that normally available. The method is examined by numerical simulation and experimental data. As a demonstration, the LaFe_1–xCr_xO₃ system (x = 0, 1/3, 2/3) is studied and the structural information of FeO₆ octahedral distortion as a function of Cr doping is resolved directly from EXAFS, where a resolution better than 0.074 Å is achieved.     

Study on the imaging characteristics of far-field superlens

The optical transfer function of the far-field superlens imaging system is established in this thesis to make it easy to describe the corresponding relation between the far-field angular spectrum and the near-field object superresolution information. We utilized the established optical transfer function to make detailed research on the imaging characteristics of the far-field superresolution, also reconstruct the near-field nano-information through the far-field angular spectrum, which proves that the resolution of the far-field superlens with structure coupled with metal grating can reach 50 nm, and provides a helpful reference for the study of the new optical microscope imaging of superresolution.     

Effects of time delay on the statistical fluctuations for a bistable system driven by cross-correlated noises

We study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T _c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T _c and C(s) are obtained. Based on numerical computations, it is found that the delay time τ slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (∈ > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (∈ < 0). The effects of the delay time τ on the T _c and C(s) are entirely opposite for ∈ 〉 0 and ∈ < 0.      

航空稳像光电平台设计

分析了随机振动对调制传递函数的影响,指出角位移是影响航空成像质量的主要因素.研究了特定条件下可容许的MTF下降,并转变为稳定系统的设计参量,用来指导稳像系统的设计.利用空间机构学及平行四边形平动原理,研制了一种新的无角位移减振稳像平台,满足既无角位移又达到减振要求.根据设计理论给出了设计实例,对频率高于100 HZ的振动,衰减达34dB,并利用动力学软件进行测试仿真,仿真曲线验证无角位移减振的正确性,同时对无角位移机构进行光学测试,结果耦合角度小于8″,可以满足航空成像要求.     

Measurement of optics for the SSRF storage ring in commissioning

The Shanghai Synchrotron Radiation Facility (SSRF) is a low emittance third-generation synchrotron radiation light source. Some optics parameters of the storage ring were measured when commissioning. This report presents the common methods for measuring some optics parameters of the storage ring, including the betatron tune, beta function, chromaticity, natural chromaticity and dispersion. The results and analysis of measurement for the optics parameters are given here, which are indispensable for the orbit correction of the accelerator and the nonlinear optimization.     

Software lens compensation applied to athermalization of infrared imaging systems

A different approach, aiming to achieve the constant blur status of point-spread function (PSF) at a certain defocused plane, is described. The correlation between the two PSF is used to control the PSF blur similarity, and simultaneously the Strehl ratio is also used to control the PSF blur minimization. By designing the PSF so that it is significantly insensitive to defocus or related defocus quantity, for example, due to temperature change, all the constantly blurred images can be accurately de-blurred by a simple inverse restoration filter for an adequate range of defocus. We refer to that as “software lens compensation” and apply a design method to solve the athermalization of middle wavelength infrared (MWIR) imaging systems. The resultant PSF is almost invariant in the temperature range from −10 to 50°C at the same focal plane. Consequently, the constant blur spot can be removed by a simple digital signal processing. Thus, clear and sharp de-blurred images at different temperatures are obtained.     

Exact Analytical Solution to Equations of Perihelion Advance in General Relativity

Previously the perihelion advance in binary system was computed approximately. We will present an exact analytical solution to nonlinear differential equation of perihelion advance by method of Jacobian elliptic function and the advanced angle between successive perihelions. Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars from Ministry of Education, China (Grant No. [2004]527) and the Natural Science Foundation of Hunan Province, China (Grant No. 06JJ2026)     

Breather Lattice Solutions to Negative mKdV Equation

In this paper, dependent and independent variable transformations are introduced to solve the negative mKdV equation systematically by using the knowledge of elliptic equation and Jacobian elliptic functions. It is shown that different kinds of solutions can be obtained to the negative mKdV equation, including breather lattice solution and periodic wave solution.     

一维无限深势阱中粒子运动的路径积分解法

用路径积分的分析方法求得了一维无限深势阱中粒子的传播函数,并由传播函数导出了粒子的波函数和能量,展示了路径积分与传统方法的等价性,同时还介绍了一种有用的数学函数——雅可比θ_3函数．