Conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems

Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated. Firstly, fractional generalized Birkhoff equations are obtained by studying fractional generalized Pfaff-Birkhoff principle. Secondly, the definition of fractional generalized quasi-symmetry is given, the criteria of fractional generalized quasi-symmetry and the corresponding conserved quantity are achieved for fractional generalized Birkhoffian systems. Thirdly, perturbation to symmetry and adiabatic invariants for disturbed fractional generalized Birkhoffian systems are presented. Finally, an example is given to illustrate the results.     

Normal coordinate in harmonic crystal obtained by virtue of the classical correspondence of the invariant eigen-operator

Noticing that the equation frac d²O_ndt²={H_c,{H_c,O_n}} =λO_n with double-Poisson bracket, where O_n is normal coordinate, H_c is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation (2004 Phys. Lett. A. 321 75), we can find normal coordinates in harmonic crystal by virtue of the invariant eigen-operator method.     

具有非线性两模场和原子与场非线性耦合的Jaynes-Cummings模型的解

利用Lewis和Riesenfeld不变量方法求解了具有任意非线性场和依赖任意强度耦合的多光子双模场与二能级原子相互作用的JC模型,得到原子一光场的态矢、时间演化算符、原子布居和双模场的光子数算符的演化式.     

Evolution and Generation of Dynamics of Two-Mode Squeezed States of Time-Dependent Coupled Boson System

The system of the Hamiltonian involving a driving part, a single mode part, and a two-mode squeezed one and a two-mode coupled one is discussed using the Lewis-Riesenfeld invariant theory. The time evolution operator is obtained. When the initial state is a coherent state, the quantum fluctuation of the system is calculated, and it is dependent on the squeezed part and the two-mode coupled part, but not dependent on the driving one.     

First determination of isotopically invariant parameters of the negative ion—Hydrogen sulfide anion (SH)

The first isotopically invariant Dunham analysis of a negative ion (the hydrogen sulfide anion SH⁻) that uses all available infrared and sub-millimeter wave experimental data on ³²SH⁻, ³³SH⁻, ³⁴SH⁻, and ³²SD⁻ yields accurate information on Born-Oppenheimer breakdown parameters. The potential constants of expansion of the potential function up to the sixth order were calculated. Differences between the construction of the potential function based on the Morse potential and that on the base of the power series expansion are shown.     

Instability of isolated equilibria of dynamical systems with invariant measure in spaces of odd dimension

We discuss the conjecture asserting that isolated equilibrium states of autonomous systems admitting invariant measures are unstable in spaces of odd dimension. This conjecture is proved for systems for which quasihomogeneous truncations with isolated singularities can be found. We consider a counterexample in the class of systems with infinitely differentiable right-hand sides and zero Maclaurin series at the equilibrium state. Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 674–680, May, 1999.     

二元直交多项式的不变因子与数值积分公式

A．H．Stroud给出了关于二元m^2点2m-1次求积公式存在性的充分条件,即两个m次直交多项式P1(x,y)和p2(x,y)存在m^2个不同的公共零点,并且都不是无穷远点。本文用不变因子的方法给出了当m=2时这种直交多项式对的一种选取方法．另外,本文最后给出了一些2m-1次积分公式．     

关于矩阵方程X+A*X-1A=P的解及其扰动分析

考虑非线性矩阵方程X＋A^＊（X^-1）A=P其中A是n阶非奇异复矩阵,P是n阶Hermite正定矩阵．本文给出了Hermite正定解和最大解的存在性以及获得最大解的一阶扰动界,改进了文[5,6]中的部分结论．     

基于形状特征的水声图像小目标识别方法

为了抑制背景噪声,提高目标识别准确率,该文提出一种基于形状特征的水声图像小目标识别方法.对含有目标的水声图像进行非局部均值去噪处理后,使用OTSU算法自适应选取阈值对去噪图像进行二值化分割,结合形态学处理获得分割后的目标区域;提取目标区域的矩形度、圆形度、几何不变矩等各项形状参数,将目标的特征向量输入随机森林分类器实现...     

Perturbation and Adiabatic Invariants of Mei Symmetry for Nonholonomic Mechanical Systems

Based on the concept of adiabatic invariant, the perturbation and adiabatic invariants of the Mei symmetry for nonholonomic mechanical systems are studied. The exact invariants of the Mei symmetry for the system without perturbation are given. The perturbation to the Mei symmetry is discussed and the adiabatic invariants of the Mei symmetry for the perturbed system are obtained.