In this work, we introduced the Jacobson radical (shortly Rad (Ș)) of the endomorphism semiring Ș =  ( ), provided that  is principal P.Q.- injective semimodule and some related concepts, we studied some properties and added conditions that we needed. The most prominent result is obtained in section three

-If   is a principal self-generator semimodule, then (_ȘȘ) = W(Ș).

Subject Classification: 16y60

This study aims to develop a recommendation engine methodology to enhance the model’s effectiveness and efficiency. The proposed model is commonly used to assign or propose a limited number of developers with the required skills and expertise to address and resolve a bug report. Managing collections within bug repositories is the responsibility of software engineers in addressing specific defects. Identifying the optimal allocation of personnel to activities is challenging when dealing with software defects, which necessitates a substantial workforce of developers. Analyzing new scientific methodologies to enhance comprehension of the results is the purpose of this analysis. Additionally, developer priorities were discussed, especially th

Present study was conducted in order to assess Slabiaat water quality by measuring some physical and chemical factors of river water, the study included a choice of three stations along of Slabiaat River in Samawa city, water samples collected a monthly during the period from September 2013 August 2014. The study involved measuring the Air & water temperatures, pH, Electrical conductivity, Total dissolved solids, Dissolved oxygen, Total hardness, calcium hardness, magnesium, turbidity, and some types of bacteria in River water. The study results showed that the values of air & water temperatures have ranged between (20.1-36.6)?C , (10-21.8) in Slabiaat River, respectively . pH values ranged between (6.6-8.7). Electrical conductivity in

Heritage reflects peoples' memory and essence of nations. Thus, this divan was really the material and tool for writers in general and poets in specific both in their artificial innovations . Accordingly, modern writers have endeavored to bring heritage back in all its details and occurrences. Abdullwahab Al-Bayati's experience had reflected his innovative and strong link with the humanitarian heritage, in that heritage in view of Al-Bayati means both the humanitarian expertise and gains that are able to extend from past to future passing through the present.From this, the poet had not disconnected his strong link with the Arab poetic heritage .Thus, the poet had utilized the Arab poetic heritage in expressing on the Arab contrary realit

Background: Fractures of the humeral shaft
accounting for approximately 3% of all
fractures. There is a wide array of good
options for their treatment and controversy
over the best methods. Although good
techniques of osteosynthesis are available, the
aim of this article is toemphasize on the benefit
and good outcome of conservative treatment
for properly selected cases to decrease the cost
and avoid the complications of surgery.

Receipt date:3/13/2021 accepted date:5/26/2021 Publication date:12/31/2021

 This work is licensed under a Creative Commons Attribution 4.0 International License.

energy is one of the strategic resources within international politics, and this is through the existing competition between the international powers on it, and the global powers have begun to rely on interest in new areas, such as import, depending on new projects an

Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of Messengers, Muhammad and his family

The good and pure and after his companions

God Almighty said: ( ) Do they not contemplate the Qur’an? If it had been from other than God, they would have found in it much discrepancy. God Almighty has made the well-being of people and their lives linked to faith in it. So what is the need of people today to return to the Book of their Lord so that they may return to the right path that God intended for His servants so that they may attain sustenance? Security and the good life. How could it not be, when many of the nations of the world no longer see security or stability because their leaders and politic

According to the prevalence of multidrug resistance bacteria, especially Pseudomonas aeruginosa, in which the essential mechanism of drug resistance is the ability to possess an efflux pump by which extrusion of antimicrobial agents usually occurs, this study aims to detect the presence of mexB multidrug efflux gene in some local isolates of this bacteria that show resistance towards three antibiotics, out of five. Sensitivity test to antibiotics was performed on all isolates by using meropenem (10μg/disc), imipenem (10μg/disc), amikacin (30 μg/disc), ciprofloxacin (5μg/disc) and ceftazidime (30 μg/disc). Conventional PCR results showed the presence of mexB gene (244bp) in four isolates out of ten (40%). In addition,25, 50μg/ml of cur

The Research deals with the negative phenomena which appeared in the urban scenes of the  Iraqi cities after 2003, particularly trespassing the architectural design of the urban Individual houses.  Many academic researchers , critics, and cultural circles, drawn attention to the impact of  political and cultural variable change on such phenomena  without detailed  analysis . The research problem  is set according to central questions : If the phenomena is the trespass , what
are the sides which are being trespassed  in the division of the individual house? , If the diagnosis of the phenomena denotes perceived repetition of the cases , So what's size of this transposes on the architectural design of t

In this paper, the density of state (DOS) at Fe metal contact to Titanium dioxide semiconductor (TiO2) has been studied and investigated using quantum consideration approaches. The study and calculations of (DOS) depended on the orientation and driving energies. was a function of TiO2 and Fe materials' refractive index and dielectric constant. Attention has focused on the effect of on the characteristic of (DOS), which increased with the increasing of refractive index and dielectric constant of Fe metal and vice versa. The results of (DOS) and its relation with and values of system have been discussed. As for contact system is increased, (DOS) values increased at first, but the relation is disturbed later and transforms into an inve