Using watermarking techniques and digital signatures can better solve the problems of digital images transmitted on the Internet like forgery, tampering, altering, etc. In this paper we proposed invisible fragile watermark and MD-5 based algorithm for digital image authenticating and tampers detecting in the Discrete Wavelet Transform DWT domain. The digital image is decomposed using 2-level DWT and the middle and high frequency sub-bands are used for watermark and digital signature embedding. The authentication data are embedded in number of the coefficients of these sub-bands according to the adaptive threshold based on the watermark length and the coefficients of each DWT level. These sub-bands are used because they a

  There are many researches deals with constructing an efficient solutions for real problem having Multi - objective confronted with each others. In this paper we construct a decision for Multi – objectives based on building a mathematical model formulating a unique objective function by combining the confronted objectives functions. Also we are presented some theories concerning this problem. Areal application problem has been presented to show the efficiency of the performance of our model and the method. Finally we obtained some results by randomly generating some problems.

The aim of this paper is to propose an efficient three steps iterative method for finding the zeros of the nonlinear equation f(x)=0 . Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is proved to establish its five order of convergence. Several examples are given to illustrate the efficiency of the proposed new method and its comparison with other methods.