Vaidya-Bonner时空中荷电Dirac粒子的Hawking辐射

在Vaidya-Bonner时空中对荷电Dirac旋量粒子的动力学行为进行了研究,得到荷电Dirac方程的径向部分在黑洞视界附近的渐近解,并且准确地定出了带电蒸发黑洞的事件视界、Hawking温度以及Dirac粒子的Hawking辐射谱。从而为处理动态黑洞辐射反作用问题提供了一种新的方法。     

多道HCN激光干涉仪在HL－1装置上的电子密度分布测量

本文描述了为测量ＨＬ－１装置电子密度分布而研制的多道远红外（ＦＩＲ）激光干涉仪系统及其特点。首次对装置在弹丸加料以及拉瓦尔（Ｌａｖａｌ）超声分子束注入实验条件下的等离子体电子密度时－空分布进行了观测和初步分析。同时，介绍一种处理密度相移信号的新方法。     

多项式的最大公因式的一种新求法

本文介绍了一种利用数域上矩阵的初等行变换求一组一元ｎ次多项式的最大公因式的方法．     

Broer-Kaup系统的达布变换及其孤子解

根据Broer-Kaup系统的Lax对, 借助Broer-Kaup系统的谱问题的规范变换, 一个包含多参数的达布变换被构造出. 以一个平凡解作为种子解, 利用达布变换, 可以求得Broer-Kaup系统的非平凡解的一般表达式. 并且讨论了N=1和N=2两种孤子解的情形. 这是一种与2X2谱问题有关的孤子碰撞图像的新类型.     

紧致齐性空间上的调和分析（IV）：Riesz变换与Bessel变换

本文研究了紧致齐性空间上的Ｒｉｅｓｚ位势算子与Ｂｅｓｓｅｌ位势算子，Ｒｉｅｓｚ变换与Ｂｅｓｓｅｌ变换，给出了上述算子对应的核函数的具体构造并证明了Ｒｉｅｓｚ变换与Ｂｅｓｓｅｌ变换作为奇异积分算子的Ｈ＾ｐ有界性，Ｐ＞０。     

一类广义KdV—Burgers型方程的拟谱方法

本文研究一类带三阶粘性项的广义Kdv-Burgers型方程的初值问题。运用拟谱方法，研究了拟谱格式的收敛性、稳定性．给出了数值例子．     

沿抛物线(t,t2)的Hilbert变换的交换子的Lp(R2)有界性

本文考虑由抛物型BMO函数和沿抛物线γ(t)=(t,t2)的Hilbert变换生成的交换子.通过局部化方法,Fourier变换估计和bootstrap讨论,得到了所考虑的交换子的Lp(1＜p＜∞)有界性.     

小波系数压缩用于柴油十六烷值近红外光谱分析建模

近红外光谱分析建模中存在多变量高维数据处理问题,导致计算量大,不利于过程控制中应用.为此提出利用小波变换压缩近红外光谱数据的算法与准则,并结合柴油十六烷值定量分析研究压缩数据的建模效果.研究表明,经小波方法处理后,变量维数压缩30倍左右,光谱主要信息基本保留,而模型的预测精度和常规预处理方法分析相比有明显提高.光谱数据压缩的同时包含了噪声滤除和基线校正,简化数据处理步骤,有利于NIRS实际应用时提高建模效率.     

光学空间滤波过程的计算机仿真

提出了一种利用MATLAB软件并通过计算机仿真光学空间滤波实验过程的新方法.其特点是:既可以随意改变所设计滤波器的参量,又可以对输入图象进行振幅、相位或复合滤波,并且可实现傅里叶变换频谱中相位信息的提取、存储和利用,因而能够完成一般光学实验中往往难以实现的某些操作.并分别给出了网格滤波、低通、高通及相位滤波等仿真实验结果.这种仿真实验给光学滤波器的设计和图象处理带来很大方便,同时也为相关器件的设计提供了一条新的途径.     

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.