一类摆动方程概周期解的存在性

讨论了一个工程问题所导出微分方程,利用微分方程系统的指数二分性理论和一类Banach空间的不动点定理,证明了所讨论的微分方程具有概周期解。     

Effects of the structural order of canthaxanthin on the Raman scattering cross section in various solvents: A study by Raman spectroscopy and ab initio calculation

In this work,we measure the Raman scattering cross sections(RSCSs) of the carbon-carbon(CC) stretching vibrational modes of canthaxanthin in benzene,acetone,n-heptane,cyclohexane,and m-xylene.It is found that the absolute RSCS of CC stretching mode of canthaxanthin reaches a value of 10 24 cm 2 ·molecule 1 ·sr 1 at 8×10 5 M,which is 6 orders of magnitude larger than general RSCS(10 30 cm 2 ·molecule 1 ·sr 1),and the RSCSs of canthaxanthin in various solvents are very different due to the hydrogen bond.A theoretical interpretation of the magnetic experimental results is given,which is introduced in a qualitative nonlinear model of coherent weakly damped electron-lattice vibration in the structural order of polyene chains.In addition,the optimal structure and the bond length alternation(BLA) parameter of canthaxanthin are calculated using quantum chemistry calculation(at the b3lyp/6-31g(d,p) level of theory).The theoretical calculations are in good agreement with the experimental results.Furthermore,the combination of Raman spectroscopy and the quantum chemistry calculation study would be a quite suitable method of studying the structures and the properties of the π-conjugated systems.     

反应扩散系统中波传播的锁频现象

在空间延展系统中,当增强外部光强时,作者观察到波传播的N∶N-1(N≥2)锁频现象.此现象是在光敏BZ反应实验中观察到的.通过构建一个映射函数,发现在波周期和外部光强的关系中存在魔鬼阶梯,并且此阶梯与实验数据相吻合.     

光在突变介质界面传输特性的FDTD方法研究

利用时域有限差分(FDTD)方法,结合Matlab编程,研究了光在突变介质界面的反射、透射与干涉.研究改变边界位置介电系数的变化率、连续性等,对反射光强的影响;调整薄膜厚度、电磁参数等,实现了对光干涉现象的动态建模.FDTD方法能够获得电磁场的时域数值解,可以直接进行动态演示;同时,运用FDTD方法可以通过改变介质结构,电磁参数等构筑计算机试验,真正实现让学生自己动手,去观察,去发现隐藏在物理表象下的物理本质.     

基于逐步回归分析的激光惯导温度补偿研究

针对激光陀螺惯导的温度补偿,将影响激光陀螺零偏的各种可能的变量作为零偏补偿的状态变量,利用逐步回归分析方法,挑选出对零偏贡献较大的显著变量,建立精准的数学物理模型,并对实测的激光陀螺进行温度补偿建模。结果表明,温度变化率以及与温度的交叉积对温度补偿模型的影响不显著,得到的温度补偿模型可以对陀螺的零偏进行实时补偿,提高了陀螺的精度。     

一维等离子体光子晶体的带隙研究

采用时域有限差分方法(FDTD),结合等离子体计算中的分段线性电流密度卷积技术(PLJERC)对一维等离子体光子晶体(1D-PPC)进行了数值模拟,给出了微分高斯脉冲在一维等离子体光子晶体中的传播过程。计算得到的带隙结构与K-P模型方法的结果一致。计算并分析了等离子体频率、介质介电常数、等离子体-介质层的厚度比以及周期厚度对一维等离子体光子晶体带隙结构的影响。     

A biosensor based on graphene nanoribbon with nanopores: a first-principles devices-design

A biosensor device,built from graphene nanoribbons(GNRs) with nanopores,was designed and studied by firstprinciples quantum transport simulation.We have demonstrated the intrinsic transport properties of the device and the effect of different nucleobases on device properties when they are located in the nanopores of GNRs.It was found that the device’s current changes remarkably with the species of nucleobases,which originates from their different chemical compositions and coupling strengths with GNRs.In addition,our first-principles results clearly reveal that the distinguished ability of a device’s current depends on the position of the pore to some extent.These results may present a new way to read off the nucleobases sequence of a single-stranded DNA(ssDNA) molecule by such GNRs-based device with designed nanopores     

Diffraction grating single-shot correlation system for measurement of picosecond laser pulses

We study and experimentally demonstrate a sensitive single-shot correlation system in which only a diffraction grating is used to produce a transverse time delay (TTD) in the reference pulse.The mechanism of the TTD introduced by the grating and the formation of the relative time delay (RTD) in the noncollinear correlation system are analyzed in detail.By using our system,we successfully measured the temporal duration of picosecond laser pulses,and a time resolution of ～0.047 ps is obtained at 1047 nm.The impact of the grating dispersion and the second harmonic beam walk-off effect on the measurement are considered.     

高等数学课程建设探索与实践

本探索了高等数学课程应适应当今教育要求，达到培养学生数学素质和能力的建设思路，总结了高等数学课程建设在师资队伍建设，教学方法、手段改革，高等数学双语教学及开展第二课堂等方面所取得的成果。     

Chebysher不等式的推广形式

在本文中，我们借用线性变换的方法证明了Ｃｈｅｂｙｓｈｅｖ不等式的一个推广形式。