In this paper, we introduce the notion of a 2-prime module as a generalization of prime module E over a ring R, where E is said to be prime module if (0) is a prime submodule. We introduced the concept of the 2-prime R-module. Module E is said to be 2-prime if (0) is 2-prime submodule of E. where a proper submodule K of module E is 2-prime submodule if, whenever rR, xE, E, Thus xK or [K: E].

Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called special selfgenerator or weak multiplication module if for each cyclic submodule Ra of M (equivalently, for each submodule N of M) there exists a family {fi} of endomorphism of M such that Ra = ∑_i▒f_i (M) (equivalently N = ∑_i▒f_i (M)). In this paper we introduce a class of modules properly contained in selfgenerator modules called special selfgenerator modules, and we study some of properties of these modules.

Let R be a commutative ring with identity, and let M be a unitary left R-module. M is called Z-regular if every cyclic submodule (equivalently every finitely generated) is projective and direct summand. And a module M is F-regular if every submodule of M is pure. In this paper we study a class of modules lies between Z-regular and F-regular module, we call these modules regular modules.

   In this paper ,we introduce a concept of Max– module as follows: M is called a Max- module if ann N R is a maximal ideal of R, for each non– zero submodule N of M;       In other words, M is a Max– module iff (0) is a *- submodule, where  a proper submodule N of M is called a *- submodule if [ ] : N K R is a maximal ideal of R, for each submodule K contains N properly.       In this paper, some properties and characterizations of max– modules and  *- submodules are given. Also, various basic results a bout Max– modules are considered. Moreover, some relations between max- modules and other types of modules are considered.

The aim of the research is to estimate the hidden population. Here، the number of drug users in Baghdad was calculated for the male age group (15-60) years old ، based on the Bayesian models. These models are used to treat some of the bias in the Killworth method Accredited in many countries of the world.

Four models were used: random degree، Barrier effects، Transmission bias، the first model being random، an extension of the Killworth model، adding random effects such as variance and uncertainty Through the size of the personal network، and when expanded by adding the fact that the respondents have different tendencies، the mixture of non-random variables with random to produce

This paper presents the application of a framework of fast and efficient compressive sampling based on the concept of random sampling of sparse Audio signal. It provides four important features. (i) It is universal with a variety of sparse signals. (ii) The number of measurements required for exact reconstruction is nearly optimal and much less then the sampling frequency and below the Nyquist frequency. (iii) It has very low complexity and fast computation. (iv) It is developed on the provable mathematical model from which we are able to quantify trade-offs among streaming capability, computation/memory requirement and quality of reconstruction of the audio signal. Compressed sensing CS is an attractive compression scheme due to its uni