Quantum Hall Quantized Cyclotron Entrance Channels

Quantum Hall plateaus are entered via quantized cyclotron (QC) cloud-chamber orbits that have Landau-level (LL) energies and uniquely-defined angular momenta. The conservation of angular momentum in the quantum Hall system requires both canonical and magnetic angular momentum components, which add together to form the invariant kinematic angular momentum. The only LL radial eigenfunctions that satisfy the conservation-law requirements of the QC to LL transition are the u _n,l eigenstates u _n,2n+1, where n = 0, 1, 2, .... These same eigenstates uniquely have the correct scaled sizes to tile the observed families of = 1/(2n + 1) Hall plateaus. Quantum Hall plateau formation is a direct consequence of this tiling.     

Equivalence Classes and Symmetries of the Variable Coefficient Kadomtsev—Petviashvili Equation

We classify the variable coefficient Kadomtsev—Petviashvili (VCKP) equation into equivalence classes under the group of local point transformations, leaving the equation form invariant but changing the coefficient functions. We list the representatives of all equivalence classes with the corresponding transformations. Then, we obtain the symmetry group of the VCKP equation and in particular discuss how to use these transformations to classify low-dimensional symmetry algebras in the generic case. We conclude with a discussion of the implications of the present article.     

Electric-dipole allowed （El） and forbidden （E2, M1 and M2） transition probabilities of 4f for N＋

By applying systematically enlarged multi-configuration Dirac-Fock wavefunction, the transitions for electricdipole allowed （E1） and forbidden （E2, M1 and M2） lines are studied among 4f pair coupling and low-lying configurations for singly ionized nitrogen. Most important effects of relativity, electron correlation, the rearrangement of electron density, Breit interaction, and quantum electrodynamic effects are included in the computation. Then, allowed （E1） and forbidden （E2, M1 and M2） transition probabilities of 4f for N＋ are obtained and compared with experimental results. Good agreement with available experimental results is found and most of the data of 4f are presented for the first time.     

“禁戒光”近场光学显微镜原理与系统

扫描近场光学显微术是８０年代后期发展起来的一种分辨率超过衍射极限的新型光学显微镜技术。本文介绍了国外最近出现的“禁戒光”近场光学显微镜系统的工作原理及结构。透射式ＳＮＯＭ中部分光沿着光轴向前传播；部分光沿着大于全内反射临界角的方向传播。前者称为允许光；后者称为禁戒光。应用“禁戒光”近场光学显微镜可同时获得三幅图像，即允许光像、禁戒光像和反映样品表面形貌的剪切力图像。禁戒光图像能够提供很好的对比度和分辨率。     

Polymers and random graphs: Asymptotic equivalence to branching processes

In 1974, Falk and Thomas did a computer simulation of Flory's Equireactive RA _f Polymer model, rings forbidden and rings allowed. Asymptotically, the Rings Forbidden model tended to Stockmayer's RA _f distribution (in which the sol distribution sticks after gelation), while the Rings Allowed model tended to the Flory version of the RA _f distribution. In 1965, Whittle introduced the Tree and Pseudomultigraph models. We show that these random graphs generalize the Falk and Thomas models by incorporating first-shell substitution effects. Moreover, asymptotically the Tree model displays postgelation sticking. Hence this phenomenon results from the absence of rings and occurs independently of equireactivity. We also show that the Pseudomultigraph model is asymptotically identical to the Branching Process model introduced by Gordon in 1962. This provides a possible basis for the Branching Process model in standard statistical mechanics.     

本刊英文版Vol.38(2022),No.2论文摘要北大核心CSCD

Global Fujita-Kato’s Type Solutions and Long-time Behavior for the Multidimensional Chemotaxis Model Qiong Lei CHEN Xiao Nan HAO Jing Yue LI Abstract We establish the global well-posedness for the multidimensional chemotaxis model with some classes of large initial data,especially the case when the rate of variation of ln v_(0)(v_(0) is the chemical concentration)contains high oscillation and the initial density near the equilibrium is allowed to have large oscillation in 3D.     

极限切削宽度的模糊随机可靠性分析

使用系统工程理论术语,给出了切削过程稳定运行的传统意义上的安全准则、统计意义上的安全准则和模糊随机意义上的安全准则定义,依据实验建立了极限切削宽度模糊允许域的实验值曲线,并通过本文理论分析指出使用模糊随机意义上的安全准则和模糊随机可靠度评价切削过程的稳定性是科学的,也更符合人们认识问题的实际。     

考虑随机模糊缺陷率且允许缺货的EOQ模型

针对实际库存管理中的产品缺陷问题,研究了含随机模糊缺陷率且允许缺货的经济订购批量(EOQ)模型,并运用随机模糊理论将其转化为确定模型,设计了随机模糊模拟仿真算法进而确定了其最优订购策略.数值算例分析了缺陷率对最优订货量和最优利润的影响.     

变系数KdV-Burgers-Kuramoto方程的群论分析——容许变换及对称群

提出变系数KdV-Burgers-Kuramoto(VCKdVBK)方程$u_t+f(x,t)uu_x+g(x,t)u_{xx}+h(x,t)u_{xxx}+k(x,t)u_{xxxx}=0$的容许变换, 它不改变方程的形式但可能改变方程的系数$f, g, h$及$k$.然后, 基于这个容许变换, 给出了VCKdVBK方程的7种不同类型的等价类. 最后, 也给出了VCKdVBK方程的Lie点对称群.     

Electric-dipole allowed (E1) and forbidden (E2, M1 and M2)transition probabilities of 4f for N+

By applying systematically enlarged multi-configuration Dirac-Fock wavefunction,the transitions for electricdipole allowed(E1) and forbidden(E2,M1 and M2) lines are studied among 4f pair coupling and low-lying configurations for singly ionized nitrogen.Most important effects of relativity,electron correlation,the rearrangement of electron density,Breit interaction,and quantum electrodynamic effects are included in the computation.Then,allowed(E1) and forbidden(E2,M1 and M2) transition probabilities of 4f for N+ are obtained and compared with experimental results.Good agreement with available experimental results is found and most of the data of 4f are presented for the first time.