Classification of j-maximal spacelike affine translation surfaces in the Minkovski space i31 with density

An affine translation surface is a graph of a function introduced by Liu and Yu in 2013. The article considers the spacelike affine translation surfaces in the Minkowski space with density establishing the Lagrange’s equation type for -maximal surface, classifying -maximal spacelike affine translation surfaces. The result obtains two parameters and . From that, the Calabi – Bernstein theorem in this space is not true because two function and are defined on

Weighted minimal affine translation surfaces in Euclidean space with density

The aim of this work is to study affine translation surfaces in the Euclidean 3-space with density. We completely classify affine translation surfaces with zero weighted mean curvature.

A Robust Image Watermarking Method based on Contourlet Transform for Correcting Geometric Attacks

A watermarking technique is proposed using Discrete Wavelet Transform (DWT), Discrete Cosine Transform (DCT), and Singular Value Decomposition (SVD) techniques to implement information hiding. Embedding can be done by dividing the host image into four rectangular segments which are non-overlapping called sub-images using hybrid scheme. Redundancy reduces cropping attack. The main aim is to reduce the effect of geometric bouts, such as rotation, translation, and affine translation using synchronization technique. Watermarks can be a binary random sequence of different lengths. Data replication and hamming code are two error modification methods utilized in the proposed scheme. Achieved results show comparable robustness against geometric attacks and signal processing. Contourlet transform can be used to improve the visual feature of the image. After embedding the image or data, contourlet transform is applied in the frequency domain to improve robustness. The optimal mapping function is obtained using contourlet transform which increases Peak Signal to Noise Ratio (PSNR) and hiding capacity with low distortion.

Polynomial affine translation surfaces in Euclidean 3-space

In this paper we study the polynomial affine translation surfaces in E3with constant curvature. We derive some non-existence results for suchsurfaces. Several examples are also given by figures.