关于一个猜想的探讨

作者在文献[1]中证明了一个结果:有限群G如果满足|P(G),p|=1,则G为P~-可解群。本文将指出,这个论断的逆命题不成立。并且还指出,满足条件(|P(G)|,p)=1的有限群也不一定是p~-超可解群。     

Local Hartree–Fock orbitals using a three‐level optimization strategy for the energy

Using the three‐level energy optimization procedure combined with a refined version of the least‐change strategy for the orbitals—where an explicit localization is performed at the valence basis level—it is shown how to more efficiently determine a set of local Hartree–Fock orbitals. Further, a core–valence separation of the least‐change occupied orbital space is introduced. Numerical results comparing valence basis localized orbitals and canonical molecular orbitals as starting guesses for the full basis localization are presented. The results show that the localization of the occupied orbitals may be performed at a small computational cost if valence basis localized orbitals are used as a starting guess. For the unoccupied space, about half the number of iterations are required if valence localized orbitals are used as a starting guess compared to a canonical set of unoccupied Hartree–Fock orbitals. Different local minima may be obtained when different starting guesses are used. However, the different minima all correspond to orbitals with approximately the same locality. © 2013 Wiley Periodicals, Inc.     

Initial guess by improved population-based intelligent algorithms for large inter-frame deformation measurement using digital image correlation

Digital image correlation (DIC) has received a widespread research and application in experimental mechanics. In DIC, the performance of subpixel registration algorithm (e.g., Newton-Raphson method, quasi-Newton method) relies heavily on the initial guess of deformation. In the case of small inter-frame deformation, the initial guess could be found by simple search scheme, the coarse-fine search for instance. While for large inter-frame deformation, it is difficult for simple search scheme to robustly estimate displacement parameters and deformation parameters simultaneously with low computational cost. In this paper, we proposed three improving strategies, i.e. Q-stage evolutionary strategy (T), parameter control strategy (C) and space expanding strategy (E), and then combined them into three population-based intelligent algorithms (PIAs), i.e. genetic algorithm (GA), differential evolution (DE) and particle swarm optimization (PSO), and finally derived eighteen different algorithms to calculate the initial guess for qN. The eighteen algorithms were compared in three sets of experiments including large rigid body translation, finite uniaxial strain and large rigid body rotation, and the results showed the effectiveness of proposed improving strategies. Among all compared algorithms, DE-TCE is the best which is robust, convenient and efficient for large inter-frame deformation measurement.     

(X+K)mod 2~n运算和XK运算异或差值的概率分析及其应用

对(X+K)mod 2~n运算和X⊕K运算异或差值函数的概率分布规律进行了研究,并基于穷举攻击中大概率优先选取原则,给出了一个解决(X+K)mod 2~n和X⊕K等价问题的计算复杂度为O(n)的算法,基于此对Hawkes等人针对SNOW1.0的猜测决定攻击进行了改进,使其数据量由O(2~(95))降为O(2~(90)),而计算复杂度由O(2~(224))略微提高到O(2~(224.482)).     

Iterative process acceleration of calculation of unsteady,viscous, compressible,and heat‐conductive gas flows

In this paper, extrapolation technique is introduced in the Semi‐Implicit Method for Pressure‐Linked Equations ‐ Time Step (SIMPLE‐TS) finite volume iterative algorithm for calculation of compressible Navier–Stokes–Fourier equations subject of slip and jump boundary conditions. The initial state, required by the iterative solver in simulation of unsteady flow problems, is approximated in time by Lagrange polynomial extrapolation in each node. The approach is applicable to a parallel code in a straightforward way due to algorithmic independence of the neighboring nodes in the computational grid. A criterion is proposed to determine the order of extrapolation polynomial and stop the extrapolation execution, when the local steady state is reached. The approach is tested on different microflow problems: Couette flow, flow past a square in a microchannel at subsonic and supersonic speeds, and convective Rayleigh–Bénard flow of a rarefied gas. The acceleration varies from 1.14‐fold to 2.8‐fold. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of Electromagnetic Information Leakage Based on Cryptographic Integrated Circuits

Cryptographic algorithm is the most commonly used method of information security protection for many devices. The secret key of cryptographic algorithm is usually stored in these devices’ registers. In this paper, we propose an electromagnetic information leakage model to investigate the relationship between the electromagnetic leakage signal and the secret key. The registers are considered as electric dipole models to illustrate the source of the electromagnetic leakage. The equivalent circuit of the magnetic field probe is developed to bridge the output voltage and the electromagnetic leakage signal. Combining them, the electromagnetic information leakage model’s function relationship can be established. Besides, an electromagnetic leakage model based on multiple linear regression is proposed to recover the secret key and the model’s effectiveness is evaluated by guess entropy. Near field tests are conducted in an unshielded ordinary indoor environment to investigate the electromagnetic side-channel information leakage. The experiment result shows the correctness of the proposed electromagnetic leakage model and it can be used to recover the secret key of the cryptographic algorithm.     

四色猜想的解析论证及其在地图绘制中的应用

依据欧拉定理,研究了边数差和着色数计算公式,对四色猜想进行了研究．借助四面体顶点数与面积数相等的原则、多面体边数不变的原则和多余理论,用边数差数学计算方法论证了四色猜想．用简单的数学公式和几何作图方法说明了四色猜想的合理性,为其提供了可靠的理论依据．用“三色包点”和“以面切体”的几何作图法,证明多面体和平面地图的着色数恒为4;非三色包点的图形,可以通过“以面切体”的方法转换成三色包点的图形;使用多余国家、多余边数的数学技巧代替计算机使用的不可避免性、可约性是合适的．理论分析及实例论证表明该方法简单可行．     

牛顿二项式史话及其启示

介绍了牛顿二项式的发现过程及其思想方法,从中可以看出其真实的过程和现在教师讲授这个公式的方法有多大的不同.由此,作者谈了三点启示,值得人们回味.     

大学物理实验教学中的推测应用

作者将推测引入到大学物理实验教学中,从实验题目分析推测实验内容、从实验仪器面板推测仪器设计思路和使用方法、从实验描述推测实验细节等几方面的应用,教学效果和学生综合能力都有明显的提高和进步。总结了近几年的教学实践经验,具体介绍了教师在教学如何应用推测,注意将推测和介绍、分析、讲解、讨论结合,控制教学节奏,逐步培养学生综合能力,最后能够成为独立的设计者。