一种可用于图像置乱的新型变换矩阵

以图像信息安全为背景,构造了一种新型变换矩阵W,证明了其周期性,并给出了其周期与Arnold矩阵变换周期的比较.理论分析表明,W-矩阵在二阶和三阶情况下具有比Arnold矩阵更大的周期,因此,在图像置乱处理中具有比Arnold矩阵更大的优势.实验仿真结果验证了这一结论.     

基于Arnold变换的图像逆置乱算法

针对Arnold变换的周期依赖于图像的阶数这一特性,提出了一种反变换算法.该算法通过分析加密图像任一点处两坐标分量间关系,得到原图像相应点的坐标,从而实现图像的解密.该反变换也可作为图像置乱的正变换,相应的反变换就是Arnold变换.在此基础上,把二维反变换算法推广到m维的情形.实验结果表明,对于已应用Arnold变换进行预处理的置乱图像,在无须计算原图像变换周期的前提下可快速实现图像的逆置乱,该过程具有确定性,其迭代次数与预处理置乱次数相等.     

Paul Ehrenfest’s Rough Road to Leiden: A Physicist’s Search for a Position, 1904–1912

Paul Ehrenfest (1880–1933) received his Ph.D. degree at the University of Vienna in 1904 and moved with his wife and young daughter to St. Petersburg in 1907, where he remained until he succeeded Hendrik Antoon Lorentz (1853–1928) in the chair of theoretical physics at the University of Leiden in 1912. Drawing upon Ehrenfest’s correspondence of the period, we first examine Ehrenfest’s difficult and insecure years in St. Petersburg and then discuss his unsuccessful attempts to obtain a position elsewhere before he was appointed as Lorentz’s successor in Leiden. Pim Huijnen is writing a doctoral dissertation in history; the present paper is based upon his Master’s Thesis, “‘Die Grenze des Pathologischen’: Het leven van fysicus Paul Ehrenfest, 1904–1912,” University of Groningen, 2003. A.J.Kox is Pieter Zeeman Professor of History of Physics at the University of Amsterdam.     

Arnold diffusion in the elliptic restricted three-body problem

In this paper, we show the existence of the Arnold diffusion in the elliptic restricted three-body problem. This gives one of the very few examples of Arnold diffusion in real physical systems. The construction is based on the transversal homoclinic orbits in the circular restricted three-body problem ([6, 7, 14]). We prove that the small perturbations to the horseshoe maps in the neighborhood of the homoclinic orbits creates the Arnold diffusion. The existence of the Arnold diffusion also shows that the elliptic restricted three-body problem is non-integrable.     

A blind DCT based color watermarking algorithm for embedding multiple watermarks

Multiple watermarking based techniques are receiving more attention in recent times for its wide variety of applications in different fields. To protect the copyright ownership and validate the authenticity of multiple owners, in this paper a color multiple watermarking method based on DCT (Discrete Cosine Transform) and repetition code is proposed and simulated. Initially, green and blue components of color host image are selected for inserting multiple watermarks. Then, each green and blue component of the image is decomposed into non overlapping blocks and subsequently DCT is employed on each block. In this technique, a binary bit of watermark is embedded into green/blue component’s transformed block by modifying some middle significant AC coefficients using repetition code. During multiple watermarks embedding in green and blue components of the proposed method, DC and some higher AC coefficients are kept intact after zigzag scanning of each DCT block to ensure the imperceptibility of the watermarked host image. The proposed scheme is experimented to establish the validity by extracting adequate multiple watermark data from the restructured cover image after applying common geometric transformation attacks (like rotation, cropping, scaling and deletion of lines/columns etc.), common enhancement technique attacks (like lowpass filtering, histogram equalization, sharpening, gamma correction, noise addition etc.) and JPEG compression attacks.     

The weakly dissipative version of the Kolmogorov-Arnold-Moser theory and practical calculations

The weakly dissipative version of the Kolmogorov-Arnold-Moser theory deals with the dynamics of systems that are a weakly dissipative perturbation of Hamiltonian systems. In the framework of this approach, both regular (asymptotically stable (unstable) periodic motions) and stochastic (Arnold’s web) dynamic properties are combined in the phase space. In this case, computer calculations are considerably simplified for the regular dynamics, which makes it possible to estimate physical parameters for stochastic components. A simple example of this approach is presented.     

Codimension one and two bifurcations of a discrete stage-structured population model with self-limitation

In this paper, the bifurcations of a discrete stage-structured population model with self-limitation between the two subgroups are investigated. We explore all possible codimension-one bifurcations associated with transcritical, flip (period doubling) and Neimark-Sacker bifurcations and discuss the stabilities of the fixed points in these non-hyperbolic cases. Meanwhile, we give the explicit approximate expression of the closed invariant curve which is caused by the Neimark-Sacker bifurcation. After that, through the theory of approximation by a flow, we explore the codimension two bifurcations associated with 1:3 strong resonance. We convert the nondegenerate condition of 1:3 resonance into a parametric polynomial, and determine its sign by the theory of complete discrimination system. We introduce new parameters and utilize some variable substitutions to obtain the bifurcation curves around 1:3 resonance, which are returned to the original variables and parameters to express for easy verification. By using a series of complicated approximate identity transformations and polar coordinate transformation, we explore 1:6 weak resonance. Moreover, we calculate the two boundaries of Arnold tongue which are caused by 1:6 weak resonance and defined as the resonance region. Numerical simulations and numerical bifurcation analyzes are made to demonstrate the effective of the theoretical analyzes and to present the relations between these bifurcations. Furthermore, our theoretical analyzes and numerical simulations are explained from the biological point of view.     

Frequency modulation indicator, Arnold’s web and diffusion in the Stark-Quadratic-Zeeman problem

We notice that the fundamental frequencies of a slightly perturbed integrable Hamiltonian system are not time-constant inside a resonance but frequency modulated, as is evident from pendulum models and wavelet analysis. Exploiting an intrinsic imprecision inherent to the numerical frequency analysis algorithm itself, hence transforming a drawback into an opportunity, we define the Frequency Modulation Indicator, a very sensitive tool in detecting where fundamental frequencies are modulated, localizing so the resonances without having to resort, as in other methods, to the integration of variational equations. For the Kepler problem, the space of the orbits with a fixed energy has the topology of the product of two 2-spheres. The perturbation Hamiltonian, averaged over the mean anomaly, has surely a maximum and a minimum, to which correspond two periodic orbits in physical space. Studying the neighbourhood of these two elliptic stable points, we are able to define adapted action-angle variables, for example, the usual but “SO(4)-rotated” Delaunay variables. The procedure, implemented in the program KEPLER, is performed transparently for the user, providing a general scheme suited for generic perturbation. The method is then applied to the Stark-Quadratic-Zeeman problem, displaying very clearly the Arnold web of the resonances. Sectioning transversely one of the resonance strips so highlighted and performing a numerical frequency analysis, one is able to locate with great precision the thin stochastic layer surrounding a separatrix. Another very long (10⁸ revolutions) frequency analysis on an orbit starting here reveals, as expected, a well defined pattern, which ensures that the integration errors do not eject the point out of the layer, and moreover a very slow drift in the frequency values, clearly due to Arnold diffusion.     

空域和小波域相结合的一种综合水印技术

提出了一种结合空域和小波域的综合水印算法,并对此算法进行了性能分析.结果表明,在不降低水印算法鲁棒性的前提下,极大地提高了水印信息的安全性,在工业和商业等领域有一定的应用价值.     

基于纠错编码和扩频调制的彩色图像水印算法

提出一种基于纠错编码和码分多址(CDMA)的彩色图像水印算法,先后将秘密信息进行Arnold置乱,纠错编码,扩频调制.提取宿主图像的绿色分量,对其进行离散余弦变换,将预处理的水印嵌入到变换后的部分中频区域.水印提取部分,首先对待测图像的绿色分量做离散余弦变换,其次提取中频部分的水印信息,将提取的值和由密钥得到的Gold...