切换奇异系统的有限时间稳定

本文研究了一类连续切换奇异系统的有限时间稳定和状态反馈控制问题.首先,讨论了连续切换奇异系统解的存在条件,然后给出连续切换奇异系统有限时间稳定和有限时间有界的概念;其次,利用模型依赖平均驻留时间方法和Lyapunov函数方法,分别给出切换奇异系统是正则、脉冲自由且有限时间稳定和有限时间有界的充分条件,并设计状态反馈控制器,使得闭环系统有限时间稳定和有限时间有界且具有H∞性能指标γ;最后通过数值算例验证了本文方法的有效性.     

广义系统族的二次稳定与二次镇定

以系统族的方式描述了广义不确定系统的不确定性, 提出了广义系统“广义二次稳定锥”的概念. 利用矩阵不等式, 得到了广义系统族广义二次稳定和广义二次可镇定的充分必要条件. 关键词： 广义系统族 广义二次稳定 广义二次可镇定 矩阵不等式     

Compact-like discrete breather and its stability in a discrete monatomic Klein--Gordon chain

This paper studies a discrete one-dimensional monatomic Klein--Gordon chain with only quartic nearest-neighbor interactions, in which the compact-like discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. Introducing the trying method, it proves that compact-like discrete breathers exist in this nonlinear system. It also discusses the linear stability of the compact-like discrete breathers, when the coefficient (β) of quartic on-site potential and the coupling constant (K₄) of quartic interactive potential satisfy the given conditions, they are linearly stable.     

基于小波变换和奇异值分解的图像水印算法研究

利用小波变换频谱特性和图像奇异值分解特征,提出了一种结合人眼对比感知特性的图像水印算法。并通过结合人眼视觉特性,将置乱的水印以一定的强度嵌入到图像的奇异值矩阵中,采用其逆过程提取水印,通过仿真进行了验证。对其实施了压缩、剪切、高斯噪声和中值滤波攻击测试,与前人提出的8种水印算法的抗攻击性能进行对比分析。结果表明,在质量因子为20%的较强压缩攻击下,提取水印的NC值仍能达到0.8359,含水印图的PSNR和SSIM达到25.0908dB和0.8451,且比8种水印算法具有更好的鲁棒性。综合表明,提出的算法有效地解决了水印嵌入过程中鲁棒性、视觉透明性与水印嵌入量之间的平衡问题。     

离散Lagrange系统的Lie对称性

研究离散Lagrange系统的Lie对称性. 根据离散变分原理建立离散系统的运动方程. 给出离散运动方程Lie对称性的定义和确定方程. 举例说明结果的应用. 关键词： 离散Lagrange系统 离散变分原理 Lie对称性 确定方程     

Unified symmetry of non-holonomic singular systems

In this paper, the unified symmetry of non-holonomic singular systems is studied. The differential equations of motion of the systems are given. The definition and the criterion of the unified symmetry for the systems are presented. The Noether conserved quantity, the Hojman conserved quantity and the Mei conserved quantity are obtained. An example is given to illustrate the application of the results.     

Two new discrete integrable systems

In this paper,we focus on the construction of new(1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new(1+1)-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.     

Noether symmetries of discrete mechanico-electrical systems

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.     

Noether's theory of Lagrange systems in discrete case

In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the well-known Noether theory of Lagrange system in the continuous case. Then, we introduce some definitions and notations, such as the operators of discrete translation to the right and the left and the operators of discrete differentiation to the right and the left, and give the conditions for the invariance of the difference functional on the uniform lattice and the non-uniform one, respectively. We also deduce the discrete analog of the Noether-type identity. Finally, the discrete analog of Noether's theorem is presented. An example was discussed to illustrate these results.     

The discrete variational principle and the first integrals of Birkhoff systems＊

This paper shows that first integrals of discrete equation of motion for Birkhoff systems can be determined explicitly by investigating the invariance properties of the discrete Pfaffian. The result obtained is a discrete analogue of theorem of Noether in the calculus of variations. An example is given to illustrate the application of the results.     

一类非完整奇异系统的Lie对称性与守恒量

利用微分方程在无限小变换群下的不变性,研究一类非完整奇异系统的Lie对称性.给出Lie对称性的确定方程、限制方程、附加限制方程和结构方程,并给出守恒量的形式 关键词： 奇异系统 非完整约束 Lie对称性 守恒量     

ICF装置靶场结构总体稳定性设计

 通过分析光学元件的动力学响应,计算靶场每条光路的结构漂移误差,进行了靶场结构总体稳定性评估。神光主机装置单光路靶场结构漂移误差计算结果表明：其靶场结构设计满足稳定性要求,该方法可以应用在ICF装置靶场结构总体稳定性设计中,但所得的漂移误差的裕度应大于一个给定的合理值。     

Symmetries and variational calculation of discrete Hamiltonian systems

We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.     

Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems

This paper focuses on studying Lie symmetries and conserved quantities of discrete nonholonomic Hamiltonian systems. Firstly, the discrete generalized Hamiltonian canonical equations and discrete energy equation of nonholonomic Hamiltonian systems are derived from discrete Hamiltonian action. Secondly, the determining equations and structure equation of Lie symmetry of the system are obtained. Thirdly, the Lie theorems and the conservation quantities are given for the discrete nonholonomic Hamiltonian systems. Finally, an example is discussed to illustrate the application of the results.     

Structural stability and electronic properties of carbon star lattice monolayer

By means of the first-principles calculations, we have investigated the structural stability and electronic properties of carbon star lattice monolayer and nanoribbons. The phase stability of the carbon star lattice is verified through phononmode analysis and room temperature molecular dynamics simulations. The carbon star lattice is found to be metallic due to the large states across the Fermi-level contributed by pz orbital. Furthermore, the nanoribbons are also found to be metallic and no spin polarization occurs, except for the narrowest nanoribbon with one C12 ring, which has a ferromagnetic ground state. Our results show that carbon star lattice monolayer and nanoribbons have rich electronic properties with great potential in future electronic nanodevices.     

锥顶碳纳米管的结构稳定性与场致发射性能

运用密度泛函理论研究了锥顶碳纳米管的结构稳定性与电子场致发射性能.结果表明:在外电场作用下,该体系的结构稳定性明显优于碳纳米锥体、C₃₀半球封口的碳纳米管,且电子发射性能与锥角大小、锥顶构型密切相关,特别是锥角38.9°及棱脊型顶部的cone₁@(6,6)综合性能最优,用其作为场致发射源的阴极时可显著提高发射电流密度并延长器件的使用寿命. 关键词： 锥顶碳纳米管 电子场致发射 结构稳定性 密度泛函理论     

Nb原子链的结构稳定性和电子性质

使用基于密度泛函理论的第一性原理平面波赝势法，研究了Nb原子链的结构稳定性和电子结构性质.计算表明，Nb原子可以形成线性链，平面之字形，二聚化以及梯子形等一系列的一 维链式结构.结果也显示，其中之字形结构最为稳定，其他结构均为亚稳的.通过第一性原理 计算的电子结构和Jahn-Teller效应，讨论了这些结构的相对稳定性以及各链式结构的电子 能带、态密度和电荷密度等性质. 关键词： Nb原子链 结构稳定性 电子结构 从头计算     

Global exponential stability of mixed discrete and distributively delayed cellular neural network

This paper concernes analysis for the global exponential stability of a class of recurrent neural networks with mixed discrete and distributed delays. It first proves the existence and uniqueness of the balance point,then by employing the Lyapunov--Krasovskii functional and Young inequality, it gives the sufficient condition of global exponential stability of cellular neural network with mixed discrete and distributed delays,in addition, the example is provided to illustrate the applicability of the result.     

演示离散混沌系统分岔图的实验方法

将模拟器件和数字器件相结合,以一维Logistic映象和二维 Henon映象为例,介绍了在电路上实现离散系统分岔图的方法,实验结果与数值计算的结果非常一致.     

Noether-type theorem for discrete nonconservative dynamical systems with nonregular lattices

We investigate Noether symmetries and conservation laws of the discrete nonconserved systems with nonregular lattices. The operators of discrete transformation and discrete differentiation to the right and left are introduced for the systems. Based on the invariance of discrete Hamilton action on nonregular lattices of the systems with the nonconserved forces under the infinitesimal transformations with respect to the time and generalized coordinates, we give the discrete analog of generalized variational f...