学生培养中交叉课程设置的一些思考和建议

就"教育部高等学校光电信息科学与工程专业教学指导分委员会及协作委员会2007年全体会议"内容,阐明了学科交叉对该学科教学模式和课程设置提出的诉求。从培养方案的知识体系结构入手,分析了现有教学模式存在缺乏纵向衔接和横向贯通的问题,并通过设置"交叉课程",成立关联课程"学科组"、开设"系统设计"课程和加强创新性实验四个方面入手,提出了改善培养模式,提高教学质量的建议。     

The Renormalization Group and Optimization of Entropy

We illustrate the possible connection that exists between the extremal properties of entropy expressions and the renormalization group (RG) approach when applied to systems with scaling symmetry. We consider three examples: (1) Gaussian fixed-point criticality in a fluid or in the capillary-wave model of an interface; (2) Lévy-like random walks with self-similar cluster formation; and (3) long-ranged bond percolation. In all cases we find a decreasing entropy function that becomes minimum under an appropriate constraint at the fixed point. We use an equivalence between random-walk distributions and order-parameter pair correlations in a simple fluid or magnet to study how the dimensional anomaly at criticality relates to walks with long-tailed distributions.     

Nizhnik-Novikov-Veselov方程的非李点对称及其精确解(英文)

对于非线性物理系统的有限对称群,一个新的方法被提出.将该方法作用于Nizhnik-Novikov-Veselov(NNV)方程,李点和非李点对称能同时得到,而使用经典李群法只能得到李点对称.最后,通过对称变化群能得到许多新的孤子解.     

计算对称群S10的所有子群

利用计算机,在GAP的环境下进行编程,计算出对称群S10共有1 593个共轭子群类,29594446个子群.其中循环群有42个共轭子群类,可解群有1 418个共轭子群类,幂零群有531个共轭子群类,超可解群有923个共轭子群类,并且通过本文中的表信息可计算出S10中各阶子群的个数及各共轭子群类中所含子群的个数.     

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.     

体上GP矩阵的刻划

在文[2]～[6]的基础上,本文证明了体上 GP 矩阵的15种刻划,并给出了强 P 除环上GP 矩阵的一个充要条件及其群逆的一个显式。     

Integral quantizations with two basic examples

The paper concerns integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also insist on the inherent probabilistic aspects of this classical–quantum map. The approach includes and generalizes coherent state quantization. Two applications based on group representation are carried out. The first one concerns the Weyl–Heisenberg group and the euclidean plane viewed as the corresponding phase space. We show that a world of quantizations exist, which yield the canonical commutation rule and the usual quantum spectrum of the harmonic oscillator. The second one concerns the affine group of the real line and gives rise to an interesting regularization of the dilation origin in the half-plane viewed as the corresponding phase space.     

Nonlinear spectral-like schemes for hybrid schemes

In spectral-like resolution-WENO hybrid schemes,if the switch function takes more grid points as discontinuity points,the WENO scheme is often turned on,and the numerical solutions may be too dissipative.Conversely,if the switch function takes less grid points as discontinuity points,the hybrid schemes usually are found to produce oscillatory solutions or just to be unstable.Even if the switch function takes less grid points as discontinuity points,the final hybrid scheme is inclined to be more stable,provided the spectral-like resolution scheme in the hybrid scheme has moderate shock-capturing capability.Following this idea,we propose nonlinear spectral-like schemes named weighted group velocity control(WGVC)schemes.These schemes show not only high-resolution for short waves but also moderate shock capturing capability.Then a new class of hybrid schemes is designed in which the WGVC scheme is used in smooth regions and the WENO scheme is used to capture discontinuities.These hybrid schemes show good resolution for small-scales structures and fine shock-capturing capabilities while the switch function takes less grid points as discontinuity points.The seven-order WGVC-WENO scheme has also been applied successfully to the direct numerical simulation of oblique shock wave-turbulent boundary layer interaction.     

Threshold effects on renormalization group running of neutrino parameters in the low-scale seesaw model

We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC).     

20Gb/s系统中偏振模色散的偏振度反馈控制分析

基于主偏振态理论和一阶偏振模色散近似,推导出光信号偏振度的一个简洁解析表达式。并利用该解析表达式和快速傅里叶变换,对20Gb／s系统的偏振模色散补偿中,偏振度监测法的灵敏度和跟踪范围受多种因素(如脉冲啁啾、占空比、消光比、放大自发辐射噪声、自相位调制等)的影响程度进行了数值模拟分析。发现利用偏振度监测法反馈控制偏振模色散补偿时,监测灵敏度和跟踪范围是折中的,较小的占空比有利于提高偏振度监测法的灵敏度,而且总可以对高达1．5个位周期(75ps)的差分群延时进行跟踪,但当占空比低于0．5时,跟踪范围迅速缩小,消光比和放大自发辐射噪声不会明显改变偏振度监测法的跟踪范围,自相位调制效应显著地影响偏振度监测法的性能。