基于有限非阿贝尔群的密钥交换

从一般线性群GL（n,F）和对称群Sn上的困难问题出发,构造了几个密钥交换算法,新算法具有更高的效率.同时,指出基于一般线性群的密钥交换算法的安全性直接依赖于广义矩阵覆盖问题,基于对称群的密钥交换协议的安全性直接依赖于置换群上的共轭问题.     

A fast parallel clustering algorithm for molecular simulation trajectories

We implemented a GPU‐powered parallel k‐centers algorithm to perform clustering on the conformations of molecular dynamics (MD) simulations. The algorithm is up to two orders of magnitude faster than the CPU implementation. We tested our algorithm on four protein MD simulation datasets ranging from the small Alanine Dipeptide to a 370‐residue Maltose Binding Protein (MBP). It is capable of grouping 250,000 conformations of the MBP into 4000 clusters within 40 seconds. To achieve this, we effectively parallelized the code on the GPU and utilize the triangle inequality of metric spaces. Furthermore, the algorithm's running time is linear with respect to the number of cluster centers. In addition, we found the triangle inequality to be less effective in higher dimensions and provide a mathematical rationale. Finally, using Alanine Dipeptide as an example, we show a strong correlation between cluster populations resulting from the k‐centers algorithm and the underlying density. © 2012 Wiley Periodicals, Inc.     

Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

This article investigates the chaos control problem for the fractional‐order chaotic systems containing unknown structure and input nonlinearities. Two types of nonlinearity in the control input are considered. In the first case, a general continuous nonlinearity input is supposed in the controller, and in the second case, the unknown dead‐zone input is included. In each case, a proper switching adaptive controller is introduced to stabilize the fractional‐order chaotic system in the presence of unknown parameters and uncertainties. The control methods are designed based on the boundedness property of the chaotic system's states, where, in the proposed methods the nonlinear/linear dynamic terms of the fractional‐order chaotic systems are assumed to be fully unknown. The analytical results of the mentioned techniques are proved by the stability analysis theorem of fractional‐order systems and the adaptive control method. In addition, as an application of the proposed methods, single input adaptive controllers are adopted for control of a class of three‐dimensional nonlinear fractional‐order chaotic systems. And finally, some numerical examples illustrate the correctness of the analytical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 211–223, 2015     

大学基础化学教学中的知其所以然*

针对大学本科一年级基础化学如“化学概论”等课程教学中,学生对于不断出现的专业名词及物理化学含义的理解问题,以“焓”“熵”等外来词汇以及角动量l、能级分裂单位“Dq”等缩写为例,从专业名词来源开始讲解,使学生在学习过程中既知其然又知其所以然,更好地理解化学专业词汇,尤其是外来词汇的内涵与物理化学意义。     

基于电磁拓扑的多腔体屏蔽效能快速算法

提出基于电磁拓扑理论计算开孔多腔体屏蔽效能的快速方法.首先给出双腔体等效电路和电磁拓扑信号流图,并推导孔缝节点处的散射矩阵,给出拓扑网络的散射矩阵方程和传输矩阵方程,获得双腔体的广义Baum-Liu-Tesche(BLT)方程.在此基础上研究了开孔三腔体,包括串型级联三腔体和串并型混合级联三腔体的广义BLT方程.对于串型级联三腔体,其电磁拓扑网络和广义BLT方程在双腔体基础上直接扩展即可获得.而对于串并型混合级联三腔体,通过将位于三腔体公共面上的孔缝等效为三端口网络节点,并根据三端口网络散射参数定义推导获得该节点的散射矩阵,最终得到串并型混合级联三腔体的广义BLT方程.本文方法对双腔体的计算结果与文献结果和实验结果相符合,对3组不同类型和尺寸开孔腔的屏蔽效能的计算结果与时域有限差分法计算结果符合较好.该算法不仅效率高,通过对所有计算结果和实验结果的误差统计分析,表明该算法具有较高的计算准确度.     

一般矩阵函数的变差

设Sn是n次对称群,G为Sn的子群,χ是G的次数为1的特征标.如果A是一个n阶复变矩阵,定义一般矩阵函数dχG为dχG(A)=∑σ∈Gχ(σ)∏ni=1aiσ(i).本文用lp-算子范数(1≤p≤∞)的性质证明了一般矩阵函数变差的两个不等式.     

Immunity in the ABM-DSGE Framework for Preventing and Controlling Epidemics—Validation of Results

The COVID-19 pandemic has raised many questions on how to manage an epidemiological and economic crisis around the world. Since the beginning of the COVID-19 pandemic, scientists and policy makers have been asking how effective lockdowns are in preventing and controlling the spread of the virus. In the absence of vaccines, the regulators lacked any plausible alternatives. Nevertheless, after the introduction of vaccinations, to what extent the conclusions of these analyses are still valid should be considered. In this paper, we present a study on the effect of vaccinations within the dynamic stochastic general equilibrium model with an agent-based epidemic component. Thus, we validated the results regarding the need to use lockdowns as an efficient tool for preventing and controlling epidemics that were obtained in November 2020.     

常微分方程通解、特解、所有解的区别与联系

通过具体实例分析、讨论了高等数学中常微分方程的通解、特解和微分方程的所有解之间的区别与联系,并对高等数学教材中二阶线性微分方程的降阶法与二阶常系数非齐次线性微分方程特解求解过程中的作法进行了说明.     

一个改进的SQP型算法

本文建立非线性等式和不等式约束规划问题的一个序列二次规划(SQP)型算法.算法的每次迭代只需解一个确实可解的二次规划，然后对其解进行简单的显式校正，便可产生关于罚函数是下降的搜索方向，克服Maratos效应.在适当的假设条件下，还论证了算法的全局收敛性和超级收敛性.