Journal of Al-Qadisiyah for Computer Science and Mathematics

Let R be a commutative ring with identity and P a unital left R-module . The purpose
of this paper is to introduce and study the concept of WAPP-prime submodules as a generalization
of weakly prime submodules , where a proper submodule L of an R-module P is called a WAPPprime , if whenever 0≠re ϵ L for rϵR , eϵP , implies that either e∈

n this paper we invention all the principle indecomposablespin(projective)
characters of the symmetric group

n this paper R stand for commutative ring with identity ,and E is a unitary left R-module. The concept of weakly quasi-2-Absorbing submodule has been generalized in this research to a Wpq-2-Absorbing submodules ,where a paper submodule H of an R-module E is a Wpq-2-Absorbiming if 0≠abcyεH ,for a,b,cεR, yεE , implies that either abyεH+Soc(E) or acyεH+Soc(E) or bcyεH+Soc(E) .Several characterizations ,examples and basic properties of this concept are introduced .Moreover characterizations of Wpq-2-Absorbing submodules in some types of modules are given .Keywords: Weakly quasi-2-Absorbing submodules, Wpq-2-Absorbing submodules, socel of modules ,multiplication modules ,Z-regular modules ,non-singular modules

The numerical solution of a Singularly Perturbed Delay Differential Equations (SPDDE)is defined as a very charged problematic of computational becouse to the non-local nature of this type of differential Equations. Prove that parallelism can be used to overawed these problems for this purpose we suggest the application of parallel processors as the best solution to overcome the difficulties of the perturbed that occurs in Perturbed Delay Differential Equations on a matching processer. Allowing to several latest publications, this process has been effectively applied to a big number of SPDDE rising from a change of application fields. The exact quality of the conception of parallelism is argued in fact and several examples are presented to demonstrate the feasibility of our approach

Because of the rapid development and use of the Internet as a communication media emerged
to need a high level of security during data transmission and one of these ways is
"Steganography". This paper reviews the Least Signification Bit steganography used for
embedding a variety of related binary images in a single grayscale image rather than
traditional methods of embedding information which is embedded one image in another
image (cover image). First three images represent the secret images which are used for hiding
from unauthorized users while other images used for making more difficult and more secret
watermark. In this paper, we have merged both methods of hiding and watermark. Instead of
either creating a watermark or hiding secret data in a grayscale image, we can use both of
them at the same image to take advantage of both the hiding and watermark properties at the
same time. The findings of the research were the results as a new watermark composed of
multiple related binary images and hidden secret multiple binary images inside.