Let R be a commutative ring with unity .M an R-Module. M is called coprime module     (dual notion of prime module) if ann M =ann M/N for every proper submodule N of M   In this paper we study coprime modules we give many basic properties of this concept. Also we give many characterization of it under certain of module.

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The risk of significant concern is resistance to antibiotics for public health. The alternative treatment of metallic nanoparticles (NPs), such as heavy metals, effects on antibiotic resistance bacteria with different types of antibiotics of - impossible to treat using noval eco-friendly synthesis technique nanoparticles copper oxide (CuO NPs) preparation from S. epidermidis showed remarkable antimicrobial activity against S.aureus Minimum inhibitory concentra range (16,32,64,256,512) µg/ml via well diffusion method in vitro, discover those concentrations effected in those bacteria and the best concentration is 64 µg/ml, characterization CuO NPs to prove this included atomic force microscope, UV, X-ray Diffraction and TEM, and ant

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  In this paper, we introduce a new class of sets, namely , s*g--open sets and we show that the family of all s*g--open subsets of a topological space ) ,X(  from a topology on X which is finer than  . Also , we study the characterizations and basic properties of s*g-open sets and s*g--closed sets . Moreover, we use these sets to define and study a new class of functions, namely , s*g-  -continuous functions and s*g-  -irresolute functions in topological spaces . Some properties of these functions have been studied .

We study in this paper the composition operator that is induced by ?(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of C? and give some other partial results.

The relation between faithful, finitely generated, separated acts and the one-to-one operators was investigated, and the associated S-act of coshT and its attributes have been examined. In this paper, we proved for any bounded Linear operators T, VcoshT is faithful and separated S-act, and if a Banach space V is finite-dimensional, VcoshT is infinitely generated.

With the wide developments of computer science and applications of networks, the security of information must be increased and make it more complex. The most important issues is how to control and prevent unauthorized access to secure information, therefore this paper presents a combination of two efficient encryption algorithms to satisfy the purpose of information security by adding a new level of encryption in Rijndael-AES algorithm. This paper presents a proposed Rijndael encryption and decryption process with NTRU algorithm, Rijndael algorithm is important because of its strong encryption. The proposed updates are represented by encryption and decryption Rijndael S-Box using NTRU algorithm. These modifications enhance the degree of