Lie symmetries and invariants of constrained Hamiltonian systems

According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.     

基于无信息变量和偏最小二乘投影分析的高光谱散射图像最优波段选择

提出了一种无信息变量消除和偏最小二乘投影分析相结合的苹果高光谱散射图像最优波段选择方法.经该算法提取后的波段降为全谱的26%,将选择后的波段作为输入变量建立了苹果硬度的偏最小二乘预测模型.预测均方根误差由6.00N降为5.73N,相关系数也有所提高,并与遗传算法作了比较.结果表明,该算法能有效消除原光谱矩阵中冗余的信息...     

频率随时间变化的受迫谐振子的压缩态和压缩数态

研究了频率随时间变化的受迫谐振子系统的不变量和不变量的一般形式,并利用基本不变量构造了此含时系统的压缩态和压缩数态.     

Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems

Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.     

氟诺喹酮类药物分子抗肺炎克雷伯氏菌的结构活性关系研究

利用主成分分析和分层聚类分析方法研究了具有抗肺炎克雷伯氏菌的氟诺喹酮类药物分子的结构活性关系．主成分分析方法表明变量ELUMO、ΔEHL、μ、Q3、Q5、QA、lgP、MP、MR能够有效地对抗肺炎克雷伯氏菌的氟诺喹酮类药物进行分类．分层聚类方法和主成分分析方法的结果一致．这表明两种方法都能够对新的具有抗肺炎克雷伯氏菌的氟诺喹酮类药物的分类提供一个可信的规律．利用主成分分析法和分层聚类分析法对其他4个氟诺喹酮类药物分子进行分析，结果都表明有三个药物分子具有较强的抗肺炎克雷伯氏菌活性，此结果和临床结果相吻合．     

Exact Solution to the One-Dimensional Dirac Equation with Time Varying Mass

We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable for the case with time-independence mass.     

A Novel Class of Coherent Localized Structures for the Maccari System

By means of the Baecklund transformation, a quite general variable separation solution of the (2 1)-dimensional Maccari systems is derived. In addition to some types of the usual localized excitations such as dromion, lumps, ring soliton and oscillated dromion, breathers solution, fractal-dromion, fractal-lump and chaotic soliton structures can be easily constructed by selecting the arbitrary functions appropriately, a new novel class of coherent localized structures like peakon solution and compacton solution of this new system are found by selecting apfropriate functions.     

Controlling Halo-Chaos via Variable Structure Method

We propose a variable structure control method which is another innovative technique for suppressing beam halo-chaos in the periodic focusing channels of high-current proton beam accelerator, which belongs to a high-tech field.The analysis and numerical results show that the method is effective for controlling beam halo-chaos. Physical implementation of such a kind of control strategy remains an important and open issue for further applications.     

EchSGB远距离照明条件下的焦开关

推导了复变量双曲余弦平方-高斯光束(EchSGB)被无光阑透镜聚焦后的轴上光强分布公式,在此基础上通过数值计算和分析发现,EchSGB只有在远距离照明条件下才存在焦开关现象.焦点跃变位置随光束参数和对应高斯光束的菲涅尔数不同而变化,得到了EchSGB在平顶情形下产生焦开关的相对入射距离为11.13,表明在远距离照明和无光阑透镜精密调焦时,对于EchSGB要考虑焦开关现象的影响.     

激光干涉法测量弹性模量

从光的干涉原理出发，讨论了金属丝弹性模量的光电测量方法．设计了激光干涉法测量长度微变量的测量装置，并介绍了测量原理，给出了动镜移动方向判别电路．