Let R be  commutative Ring , and let T be  unitary left .In this paper ,WAPP-quasi prime submodules are introduced as  new generalization of Weakly quasi prime submodules , where  proper submodule C of an R-module T is called WAPP –quasi prime submodule of T, if whenever 0≠rstϵC, for r, s ϵR , t ϵT, implies that either  r tϵ C +soc   or  s tϵC +soc  .Many examples of characterizations and basic properties are given . Furthermore several characterizations of WAPP-quasi prime submodules in the class of multiplication modules are established.

    We introduce in this paper the concept of approximaitly semi-prime submodules of unitary left -module  over a commutative ring  with identity as a generalization of a prime submodules and semi-prime submodules, also generalization of quasi-prime submodules and approximaitly prime submodules. Various basic properties of an approximaitly semi-prime submodules are discussed, where a proper submodule  of an -module  is called an approximaitly semi-prime submodule of  , if whenever , where ,  and , implies that . Furthermore the behaviors of approximaitly semi-prime submodule in some classes of modules are studied. On the other hand several characterizations of this concept are

In this paper, a new class of nonconvex sets and functions called strongly -convex sets and strongly -convex functions are introduced. This class is considered as a natural extension of strongly -convex sets and functions introduced in the literature. Some basic and differentiability properties related to strongly -convex functions are discussed. As an application to optimization problems, some optimality properties of constrained optimization problems are proved. In these optimization problems, either the objective function or the inequality constraints functions are strongly -convex. 

Voting is one of the most fundamental components of a democratic society. In 2021 Iraq held the Council of Representatives (CoR) elections in 83 electoral constituencies in 19 governorates. Nonetheless, several significant issues arose during this election, including the problem of logistics distribution, the excessively long period of ballot counting, voters can't know if their votes were counted or if their ballots were tampered with, and the inconsistent regulation of vote counting. Blockchain technology, which was just invented, may offer a solution to these problems. This paper introduces an electronic voting system for the Iraq Council of Representatives elections that is based on a prototype of the permission hyperledger fabr

Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

Objectives: Small field of view gamma detection and imaging technologies for monitoring in vivo tracer uptake are rapidly expanding and being introduced for bed-side imaging and image guided surgical procedures. The Hybrid Gamma Camera (HGC) has been developed to enhance the localization of targeted radiopharmaceuticals during surgical procedures; for example in sentinel lymph node (SLN) biopsies and for bed-side imaging in procedures such as lacrimal drainage imaging and thyroid scanning. In this study, a prototype anthropomorphic head and neck phantom has been designed, constructed, and evaluated using representative modelled medical scenarios to study the capability of the HGC to detect SLNs and image small organs. Methods: An anthropom

From 50 stool samples collected from children with diarrhea of both sexes who visited various hospitals in Baghdad, 26 isolates of E.coli were found to belong to the phylogenetic group E. The findings revealed that the percentage of E.coli for thephylogenetic group E is (52%) , making it the dominant group among the other phylogenetic groups. The findings demonstrated that 100% of the E.coli isolates from phylogenetic group E are resistant to penicillin, and only 15% are resistant to imipenem. Multi-drug resistance (MDR) was found to be 15%, while XDR reached 85%. The results of thephylogenetic group for the remaining species of isolates in this study were group A (2/50 and by 4%), gr

The literature shows conflicting outcomes, making it difficult to determine how e-learning affects the performance of students in higher education. The effect of e-learning was studied and data has been gathered with the utilization of a variety of qualitative and quantitative methods, especially in relation to students' academic achievements and perceptions in higher education, according to literature review that has been drawn from articles published in the past two decades (2000-2020). The development of a sense of community in the on-line environment has been identified to be one of the main difficulties in e-learning education across this whole review. In order to create an efficient online learning community, it could be claim

<p>There is an Increasing demand for the education in the field of E-learning specially the higher education, and to keep contiuity between the user and the course director in any place and time. This research presents a proposed and simulation multimedia network design for distance learning utilizing ATM technique. The propsed framework determines the principle of ATM technology and shows how multimedia can be integrated within E- learning conteext. The first part of this research presents a theoretical design for the Electricity Department, university of technology. The purpose is to illustrate the usage of the ATM and Multimedia in distance learning process. In addition, this research composes two entities: Software entity