Adiabatic Invariant for Dynamic Systems on Time Scale

Perturbation to Noether symmetry and adiabatic invariants for Birkhoffian system,Hamiltonian system and Lagrangian system with delta derivative are investigated,respectively. Firstly,the definition and some related properties of time scale calculus are listed simply as preliminaries. Secondly,the Birkhoffian system with delta derivative is studied. Based on the differential equation of motion as well as Noether symmetry and conserved quantity,perturbation to Noether symmetry and adiabatic invariant are investigated. Thirdly,adiabatic invariants for the Hamiltonian system and the Lagrangian system are presented through some transformations. And finally,an example is given to illustrate the methods and results.     

Discrete Fractional Lagrange Equations of Nonconservative Systems

In order to study discrete nonconservative system,Hamilton's principle within fractional difference operators of Riemann-Liouville type is given. Discrete Lagrange equations of the nonconservative system as well as the nonconservative system with dynamic constraint are established within fractional difference operators of Riemann-Liouville type from the view of time scales. Firstly,time scale calculus and fractional calculus are reviewed.Secondly,with the help of the properties of time scale calculus,discrete Lagrange equation of the nonconservative system within fractional difference operators of Riemann-Liouville type is presented. Thirdly,using the Lagrange multipliers,discrete Lagrange equation of the nonconservative system with dynamic constraint is also established.Then two special cases are discussed. Finally,two examples are devoted to illustrate the results.     

一类分数阶薛定谔方程孤立解的对称性研究

在有界环形区域上,研究了一类分数阶薛定谔方程孤立解的对称性问题。首先将分数阶薛定谔方程转化为包含Bessel位势和Riesz位势的积分方程组,然后利用移动平面法和Hardy-Littlewood-Sobolev不等式,证明了当方程边值为常数时,环形区域必为同心球,方程正解是径向对称的,且随着到对称点的距离增大而单调递减。     

Noether Theorem for Generalized Birkhoffian Systems with Time Delay

The Noether symmetries and the conserved quantities for generalized Birkhoffian systems with time delay are studied.Firstly,the generalized Pfaff-Birkhoff principle with time delay is proposed,and the generalized Birkhoff's equations with time delay are obtained.Secondly,the generalized Noether quasi-symmetric transformations of the system are defined,and the criterion of the Noether symmetries is established.Then the Noether theorem for generalized Birkhoffian systems with time delay is established.Finally,by imposing restrictions of constraints on the infinitesimal transformations,the Noether theorem of constrained Birkhoffian systems with time delay is established.One example is given to illustrate the application of the results.     

Arnoldi Projection Fractional Tikhonov for Large Scale Ill-Posed Problems

It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth for ill-posed problems,so fractional Tikhonov methods have been introduced to remedy this shortcoming.And Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining apartial Arnoldi decomposition of the given matrix.In this paper,we propose a new method to compute an approximate solution of large scale linear discrete ill-posed problems which applies projection fractional Tikhonov regularization in Krylov subspace via Arnoldi process.The projection fractional Tikhonov regularization combines the fractional matrices and orthogonal projection operators.A suitable value of the regularization parameter is determined by the discrepancy principle.Numerical examples with application to image restoration are carried out to examine that the performance of the method.     

图象匹配中的仿射透视近似

提出了在图象匹配中使用的一些新的仿射透视近似投影不变量。文中引进了点的仿射透视近似的概念，分析了线段的透视投影与其仿射透视近似间的最大相对误差，获得了一个有实用价值的距离三角形误差判决准则。基于此准则，研究了物体上同一空间平面中，平行线段长度比，同底面积比等仿射不变量，近似用作透视不变量的可能性。实验结果证实了分析的可靠性。     

抗几何攻击的数字图像版权保护算法

为了在保证图像质量的前提下实施图像的版权保护,提出了一种基于Krawtchouk矩和标识信息的零水印算法.该方法利用从图像中提取的特征信息来构造水印,从而达到版权保护的目的.主要步骤为,首先计算原始图像的Krawtchouk低阶矩不变量来构建水印信息,接着将水印信息和密钥信息在第三方登记注册并获得标识信息,最后通过标识信息确认版权所有者.水印提取过程简单,只需计算所得图像的几个低阶Krawtchouk矩不变量.文中给出了实验结果,并与传统几何矩不变量的算法进行了比较. 结果表明,该方法对旋转、缩放、剪切、组合攻击、平移和去掉行等几何攻击以及滤波、JPEG压缩等攻击具有更高的稳健性.     

广义经典力学系统动力学方程积分的Jacobi最终乘子法

研究动力学系统的积分问题,将Jacobi最终乘子法应用于积分广义经典力学系统的动力学方程。建立了广义经典力学系统的运动微分方程;定义了广义经典力学系统的Jacobi最终乘子;研究了系统的第一积分与Jacobi最终乘子的关系。研究表明:对于位形由n个广义坐标确定且拉格朗日函数含有广义坐标对时间的ω阶导数的广义经典力学系统,如果已知系统的(2ωn-1)个第一积分,则可利用Jacobi最终乘子给出系统的解。文末举例说明结果的应用。     

含橡胶隔振器振动系统动态特性研究

以APU隔振器为研究对象,提出采用五参数分数导数建立橡胶隔振器本构模型。推导了含橡胶隔振器振动系统的非线性动力学有限元方程式。分析了隔振器结构参数变化对传递率特性的影响。研究结果表明:文中的数值计算方法能更好地预测含橡胶隔振器振动系统的动态特性。     

单排圆柱孔射流气膜加热与气膜冷却方式的对比

为了揭示气膜加热和气膜冷却两种方式在影响规律机制上的异同,通过数值计算研究了两种方式单排圆柱孔在典型吹风比下(0.5,1.0和1.5)的射流-主流相干特征,并分析了热气流-冷气流温度比变化对气膜绝热加热或冷却效率的影响。研究结果表明:在相同的吹风比下,在气膜加热方式下喷注射流向主流的穿透趋向更为显著,引起喷注射流抬离壁面并在气膜孔出口附近诱导出尺度更大的卵形涡对;当温度比接近于1时,气膜绝热加热效率与气膜绝热冷却效率差异较小,随着温度比偏离1的程度加剧,气膜绝热加热效率与气膜绝热冷却效率差异显著增大。