Search

In this contribution we propose a novel steganographic method based on several orthogonal polynomials and their combinations. The steganographic algorithm embeds a secrete message at the first eight coefficients of high frequency image. Moreover, this embedding method uses the Beta chaotic map to determine the order of the blocks where the secret bits will be inserted. In addition, from a 128-bit private key and the steps of a cryptography algorithm according to the Advanced Encryption Standard (AES) to generate the key expansion, the proposed method generates a key expansion of 2560 bits, with the purpose to permute the first eight coefficients of high frequency before the insertion. The insertion takes eventually place at the first eight high frequency coefficients in the transformed orthogonal moments domain. Before the insertion of the message the image undergoes a series of transformations. After the insertion the inverse transformations are applied to the original transformations in reverse order. The experimental work on the validation of the algorithm consists of the calculation of the Peak Signal-to-Noise Ratio (PSNR), the Universal Image Quality Index (UIQI), the Image Fidelity (IF), and the Relative Entropy (RE), comparing the same characteristics for the cover and stego image. The proposed algorithm improves the level of imperceptibility and security analyzed through the PSNR and RE values, respectively., Comment: 30 pages, 23 figures

Inspired by the results of Rhin and Viola (2001), the purpose of this work is to elaborate on a series representation for $\zeta \left( 3\right)$ which only depends on one single integer parameter. This is accomplished by deducing a Hermite-Pad\'e approximation problem using ideas of Sorokin (1998). As a consequence we get a new recurrence relation for the approximation of $\zeta(3)$ as well as a corresponding new continued fraction expansion for $\zeta(3)$, which do no reproduce Ap\'ery's phenomenon, i.e., though the approaches are different, they lead to the same sequence of diophantine approximations to $\zeta \left( 3\right) $. Finally, the convergence rates of several series representations of $\zeta(3)$ are compared.

This paper deals with a hyperbolic system of two nonlinear conservation laws, where the phase space contains two contact manifolds. The governing equations are modelling bidisperse suspensions, which consist of two types of small particles that are dispersed in a viscous fluid and differ in size and viscosity. For certain parameter choices quasi-umbilic points and a contact manifold in the interior of the phase space are detected. The dependance of the solutions structure on this contact manifold is examined. The elementary waves that start in the origin of the phase space are classified. Prototypic Riemann problems that connect the origin to any point in the state space and that connect any state in the state space to the maximum line are solved semi-analytically., Comment: 35 pages, 5 figures