Collocation Methods for a Class of Volterra Integral Functional Equations with Multiple Proportional Delays

In this paper, we apply the collocation methods to a class of Volterra integral functional equations with multiple proportional delays (VIFEMPDs). We shall present the existence, uniqueness and regularity properties of analytic solutions for this type of equations, and then analyze the convergence orders of the collocation solutions and give corresponding error estimates. The numerical results verify our theoretical analysis.     

针对多发性硬化症病人的综合步态分析

 设计了一个针对多发性硬化症患者的三维步态分析实验,利用三维光学捕捉系统对实验被试身体不同部位标记点的三维坐标进行追踪和记录,成功发现了多个步态参数发生的变化,这些变化不仅能反映实验被试细微的步态功能上的变化,而且还与接受治疗的时间密切相关。此套基于步态数据的量化评估体系能够弥补目前广泛应用的评估方法主观和不够准确的缺点,为临床医生改进治疗方案以及制定更加有效的治疗方法提供帮助。     

基于动态混沌映射的三维加密正交频分复用无源光网络

提出了一种基于混沌映射的三维加密正交频分复用无源光网络保密通信系统.该系统通过相关性检测锁定收发端混沌系统参数,实现收发双方混沌系统同步;并利用同步混沌系统生成密钥,实现符号扰动以及二重子载波加密.该加密方案的密钥空间超过10~(86),能够有效对抗穷举攻击.实验实现了13.3 Gb/s基于64进制正交幅度调制的加密正交频分复用信号在25 km标准单模光纤中的传输,并完成了信息的有效解密.     

纳米半导体中多重激子效应研究进展

多重激子效应是指纳米半导体吸收一个高能光子后产生两个甚至多个电子-空穴对的物理过程,不仅具有重要的基础研究意义,而且在新型太阳电池及高性能光电子器件领域具有潜在应用价值.综述了多重激子效应的发展历程;总结了纳米半导体的材料组分、体系结构甚至表面质量对多重激子效应的影响;介绍了多重激子效应的实验测试分析方法以及解释多重激子效应的理论方法;概括了目前多重激子效应在器件中的应用并对其应用前景进行展望.     

球极坐标系下角动量平方算符与拉普拉斯算符的推导——多元复合函数微商法则在量子力学中的应用

采用引入变量的多元复合函数微商法则,将直角坐标系下的1阶偏微分形式变换成球极坐标形式,进而推导出球极坐标系下角动量平方算符与拉普拉斯算符的表达式.这将使得在量子力学中求解Schr?dinger方程、各角动量算符对应的各角量子数变得更加简单.     

具有三个数字集的Cantor测度的谱特征值

设μ3k是由迭代函数系统fd(x)＝3k(1)(x＋d)：d∈{0,1,2}所生成的自相似测度,该文首先利用Compatible对的概念, 给出了μ3k的一组谱Λ,然后重点刻画了正整数p, 使得pΛ也为μ3k的谱.     

基于马尔科夫决策过程的多目标跟踪算法

目前,多目标跟踪算法仍面临诸多挑战,例如遮挡、快速运动等所造成的影响难以完全规避.为了解决上述问题,提出一种基于马尔科夫决策过程的多目标跟踪算法.该算法将每个目标建模成一个马尔科夫决策过程,通过最大化奖励函数来驱动状态间的转移,并将强化学习训练用于数据关联相似度函数,有效地解决了目标遮挡问题.同时,为了解决物体快速运动...     

Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression

In this paper, we propose a new explicit analytical formula of the critical buckling load of double-walled carbon nanotubes (DWCNT) under axial compression. This formula takes into account van der Waals interactions between adjacent tubes and the effect of terms involving tube radii differences generally neglected in the derived expressions of the critical buckling load published in the literature. The elastic multiple Donnell shells continuum approach is employed for modelling the multi-walled carbon nanotubes. The validation of the proposed formula is made by comparison with a numerical solution. The influence of the neglected terms is also studied.     

Effective dielectric constant model of electromagnetic backscattering from stratified air–sea surface film–sea water medium

Studies of surface film medium on the sea surface are carried out in this paper for developing the technology to automatically detect and classify sea surface films, and an effective dielectric constant model of electromagnetic backscattering from a stratified air–ocean interface. Numerical results of the new model show the characteristics of effective dielectric constants for the air–sea surface film–sea water medium as follows. The effective dielectric constants decrease with increasing relative dielectric constants of the sea surface films. The effective dielectric constants decrease in horizontal polarization(abbr. HH polarization) and increase in VV vertical polarization(abbr. VV polarization) with increasing radar incident angle. Effective dielectric constants vary with relative sea surface film thickness as a cosinusoidal function of sea surface film thickness. Effective dielectric constant of VV polarization is larger than that of HH polarization. Two potential applications are found with our model, i.e., the retrieval of dielectric constants from the sea surface film, and the film thickness retrieval with our model. Our model has a highly significant influence on improving the technology related to the remote sensing of sea surface films.     

Multiple exp-function method for soliton solutions of nonlinear evolution equations

We applied the multiple exp-function scheme to the(2+1)-dimensional Sawada-Kotera(SK) equation and(3+1)-dimensional nonlinear evolution equation and analytic particular solutions have been deduced. The analytic particular solutions contain one-soliton, two-soliton, and three-soliton type solutions. With the assistance of Maple, we demonstrated the efficiency and advantages of the procedure that generalizes Hirota's perturbation scheme. The obtained solutions can be used as a benchmark for numerical solutions and describe the physical phenomena behind the model.