The Rivest–Shamir–Adleman (RSA) and the Diffie-Hellman (DH) key exchange are famous methods for encryption. These methods  depended on selecting the primes p and q in order  to be secure enough . This paper shows that the named methods used the primes which are found by some arithmetical function .In the other sense, no need to think about getting primes p and q and how they are secure enough, since the arithmetical function enable to build the primes in such complicated way to be secure. Moreover, this article   gives  new construction  of the  RSA  algorithm and DH key  exchange using the

primes p,qfrom areal number x.

Background: The world health organization estimates that worldwide 2 billion people still have iodine deficiency Objectives: Is to make comparison between the effect of identification of recurrent laryngeal nerve (RLN) and non-identification of the nerve on incidence of recurrent laryngeal nerve injury (RLNI) in different thyroidectomy procedures.

Type of the study: cross –sectional study.

Methods: 132 patients with goiters underwent thyroidectomy .Identification of RLN visually by exposure were done for agroup of them and non-identification of the nerves for the other group. The outcomes of RLNI in the two groupsanalyzed statistically for the effect of

This paper deals with the F-compact operator defined on probabilistic Hilbert space and gives some of its main properties.

Abstract

     In this research, a study of the behavior and correlation between sunspot number (SSN) and solar flux (F10.7) have been suggested. The annual time of the years (2008-2017) of solar cycle 24 has been adopted to make the investigation in order to get the mutual correlation between (SSN) and (F10.7). The test results of the annual correlation between SSN & F10.7 is simple and can be represented by a linear regression equation. The results of the conducted study showed that there was a good fit between SSN and F10.7 values that have been generated using the suggested mutual correlation equation and the observed data.

The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.

    Natural Language Processing (NLP) deals with analysing, understanding and generating languages likes human. One of the challenges of NLP is training computers to understand the way of learning and using a language as human.  Every training session consists of several types of sentences with different context and linguistic structures. Meaning of a sentence depends on actual meaning of main words with their correct positions. Same word can be used as a noun or adjective or others based on their position. In NLP, Word Embedding is a powerful method which is trained on large collection of texts and encoded general semantic and syntactic information of words. Choosing a right word embedding generates more efficient result than others

  In this paper, we introduce and study the concept of S-coprime submodules, where a proper submodule N of an R-module M is called S-coprime submodule if M N is S-coprime Rmodule. Many properties about this concept are investigated.

  Let L be a commutative ring with identity and let W be a unitary left L- module. A submodule D of an L- module W is called  s- closed submodule denoted by  D ≤sc W, if D has   no  proper s- essential extension in W, that is , whenever D ≤ W such that D ≤se H≤ W, then D = H. In  this  paper,  we study  modules which satisfies  the ascending chain  conditions (ACC) and descending chain conditions (DCC) on this kind of submodules.

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

The global food supply heavily depends on utilizing fertilizers to meet production goals. The adverse impacts of traditional fertilization practices on the environment have necessitated the exploration of new alternatives in the form of smart fertilizer technologies (SFTs). This review seeks to categorize SFTs, which are slow and controlled-release Fertilizers (SCRFs), nano fertilizers, and biological fertilizers, and describes their operational principles. It examines the environmental implications of conventional fertilizers and outlines the attributes of SFTs that effectively address these concerns. The findings demonstrate a pronounced environmental advantage of SFTs, including enhanced crop yields, minimized nutrient loss, improved nut