一个大范围超混沌系统的生成和电路实现

在对一些已有的超混沌系统研究和分析的基础上,提出了一个新的四维自治的超混沌系统,这个超混沌系统是通过引入一个状态变量到一个三维自治混沌系统而生成的,它较已有的超混沌系统而言,不仅最大的Lyapunov指数要大一些,而且在参数变化时,呈现超混沌的参数范围也很大.在对该系统进行数值仿真和分形分析的同时,也通过模拟电路对其进行了验证,电路实验结果表明,在电路中分别呈现的周期、伪周期、混沌、超混沌特性与数值仿真中获得的结果是一致的. 关键词： 超混沌 分形分析 超混沌电路 Lyapunov指数     

The bifurcation threshold value of the chaos detection system for a weak signal＊

Recently, it has become an important problem to confirm the bifurcation threshold value of a chaos detectionsystem for a weak signal in the fields of chaos detection. It is directly related to whether the results of chaos detectionare correct or not. In this paper, the discrimination system for the dynamic behaviour of a chaos detection system fora weak signal is established by using the theory of linear differential equation with periodic coefficients and computingthe Lyapunov exponents of the chaos detection system; and then, the movement state of the chaos detection system isdefined. The simulation experiments show that this method can exactly confirm the bifurcation threshold value of thechaos detection svstem.     

Regularity results of the thin obstacle problem for the p(x)-Laplacian

We study thin obstacle problems involving the energy functional with $p(x)$-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent $p(x)$ is Hölder continuous.     

Interior gradient estimate for steady flows of electrorheological fluids

In this paper, we consider the equations of stationary motion of electrorheological fluids in any dimension $n\ge 2$. We show that the first gradient of local solutions to the system has optimal $L^q$-regularity with some $q>1$ with respect to the one of the external force. This is achieved by comparison principle and a good $\lambda$-estimate.     

Engel-4 Groups of Exponent 5

We show that if G is a group of exponent 5, and if G satisfiesthe Engel-4 identity [x,y,y,y,y]=1, then G is locally finite.By a result of Traustason, this implies that Engel-4 5-groupsare locally finite. We also show that a group of exponent 5is locally finite if and only if it satsifies the identity This result implies that a group of exponent 5 is locally finiteif its three generator subgroups are finite. 1991 MathematicsSubject Classification: 20D15, 20F45, 20F50.     

Analytical optimization of exponent values in protonic and deuteronic Gaussian‐type functions by elimination of translational and rotational motions from multi‐component molecular orbital scheme

To optimize the exponent values in protonic and deuteronic Gaussian‐type functions (GTF) by the elimination of translational and rotational motions, we have proposed the new scheme of an analytical gradient formula with respect to the exponent values in the multi‐component molecular orbital scheme, which can take into account the quantum effects of protons and deuterons, under the Hartree‐Fock level of theory. Numerical assessment of H₂ and D₂ molecules confirms that there is a clear difference between distributions of protonic and deuteronic orbitals following the elimination of translational and rotational motions. In particular, the d‐type GTF in the protonic orbital drastically improves the total energy. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Proposed sets of critical exponents for randomly branched polymers,using a known string theory model

The critical exponent ν for randomly branched polymers with dimensionality d equal to 3, is known exactly as 1/2. Here, we invoke an already available string theory model to predict the remaining static critical exponents. Utilizing results of Hsu et al. (Comput Phys Commun. 2005;169:114–116), results are added for d = 8. Experiment plus simulation would now be important to confirm, or if necessary to refine, the proposed values.     

Polygonal Approaches to the Circular Billiard: the Lyapunov Exponent

The Lyapunov exponents for three polygonal approaches to the circular billiard quasiperiodic approach, random approach and equilateral approach are calculated, the chaotic behavior in polygonal billiards is discussed. The role of singularity presented by vertex angles is quantitatively discussed. It is found that for the equilateral approach, the Lyapunov exponents vary with the side number N according to a Poisson law, i.e., λ(N) = aN exp(-βN).     

Relationship between Continuum of Hurst Exponents of Noise-like Time Series and the Cantor Set

In this paper, we have modified the Detrended Fluctuation Analysis (DFA) using the ternary Cantor set. We propose a modification of the DFA algorithm, Cantor DFA (CDFA), which uses the Cantor set theory of base 3 as a scale for segment sizes in the DFA algorithm. An investigation of the phenomena generated from the proof using real-world time series based on the theory of the Cantor set is also conducted. This new approach helps reduce the overestimation problem of the Hurst exponent of DFA by comparing it with its inverse relationship with α of the Truncated Lévy Flight (TLF). CDFA is also able to correctly predict the memory behavior of time series.