面向21世纪高等数学教学内容与教学手段的改革研究与实践

本介绍了我们教研室近年来在教学内容、教学手段改革中做一些赏试和体会,指出教学内容应适应21世纪社会发展的需要,并在实践中利用现代教学手段进行教学,获得了一些初步的成效。     

Conservation laws of the generalized nonlocal nonlinear Schrodinger equation

The derivations of several conservation laws of the generalized nonlocal nonlinear Schr?dinger equation are presented. These invariants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.     

Potential Energy of the Di-nuclear System

We perform the calculation of the nucleus-nucleus interaction potential of the dinuclear system with deformed nuclei. Based on the calculated results by properly treating the double-folding method, some results from the analytical expressions for calculating both the nuclear and the Coulomb interactions are investigated. It is concluded that the analytical formula to calculate the Coulomb interaction by Wong [Phys. Rev. Lett. 31 (1973) 766] can reproduce good double folding results. However the results by the parametrized Morse formula, which are used to calculate the nuclear interaction, greatly deviate from the double folding results, unless the distance of nuclei is adjusted to be shifted to a smaller relative distance determined by the same distance between the nuclear surfaces as one of them pertains to the deformed nuclei. Using the double folding method to calculate the nuclear interaction and employing Wong‘s analytical formula to calculate the Coulomb interaction can keep good precision and can cost much less computation time.     

Controlling chaos in power system based on finite-time stability theory

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.     

原子吸收限附近完整晶体内的能流方向

研究了原子吸收限附近对称劳厄和布拉格情况下完整晶体内的能流方向．发现在对称劳厄情况下，只有当原子散射因子的虚部对衍射的贡献可以与实部的贡献相比较时，晶体内与色散面上某一结点相对应的能流会偏离色散面的实部的法向；而在对称布拉格情况下，即使在原子散射因子的虚部对衍射的贡献可以忽略时，在所谓的“全反射”区内也会偏离．当衍射仅由原子的虚部引起时，这种偏离在对称劳厄情况下最大，而在对称布拉格情况下最小． 关键词：     

Harmonic Enhancement Mechanism of a Superposition State Atom Irradiated by Short Pulses

We investigate the high-order harmonic generation （HHG） of a model atom whose initial state is prepared in a superposition of its ground state and an excited state irradiated by different duration laser pulses. Compared to the HHG generated from an atom whose initial state is in its ground state, its conversion efficiency obtains some enhancement. The enhancement originates from the higher ionization rate （rather than the ionization yield） of the atom with superposition initial state.     

基于双向稀疏表示的鲁棒目标跟踪算法

目前,基于稀疏表示的目标跟踪通常为在目标模板集上重构候选样本的正向模型或者在候选样本集上描述目标模板的反向模型.两个模型的共同点是均需计算候选样本与模板集合之间的稀疏相关系数矩阵.基于此,建立了一个双向联合稀疏表示的跟踪模型,该模型通过L2范数约束正反向稀疏相关系数矩阵达到一致收敛.与之前的单向稀疏表示模型相比,双向稀疏表示跟踪模型在正反向联合求解框架下可以更加充分地挖掘所有候选样本与模板集之间的稀疏映射关系,并将稀疏映射表上对正负模板区分度最好的候选样本作为目标.基于加速逼近梯度(accelerated proximal gradient)快速算法,以矩阵形式推导了双向稀疏表示模型的求解框架,使得候选样本集和目标模板集均以矩阵方式并行求解,在一定程度上提高了计算效率.实验数据表明所提出的算法优于传统的单向稀疏表示目标跟踪算法.     

X射线衍射动力学在原子吸收限近区的应用

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Neural adaptive chaotic control with constrained input using state and output feedback

This paper presents neural adaptive control methods for a class of chaotic nonlinear systems in the presence of constrained input and unknown dynamics.To attenuate the influence of constrained input caused by actuator saturation,an effective auxiliary system is constructed to prevent the stability of closed loop system from being destroyed.Radial basis function neural networks(RBF-NNs)are used in the online learning of the unknown dynamics,which do not require an off-line training phase.Both state and output feedback control laws are developed.In the output feedback case,high-order sliding mode(HOSM)observer is utilized to estimate the unmeasurable system states.Simulation results are presented to verify the effectiveness of proposed schemes.     

利用字频统计及机器学习的自动文摘方法

本文论述了用计算机对专业语料库进行单字及其后继字的统计,自动生成字频及各字后继同段信自、的方法.并应用于文献自动文摘.本方法能在系统的生成和使用过程中进行自学习.以不断地完善系统.