this paper, we will prove the following theorem, Let R be a ring with 1 having
a reverse derivation d ≠ 0 such that, for each x R, either d(x) = 0 or d(x) is
invertible in R, then R must be one of the following: (i) a division ring D, (ii) D 2 ,
the ring of 2×2 matrices over D, (iii) D[x]/(x ) 2
where char D = 2, d (D) = 0 and
d(x) = 1 + ax for some a in the center Z of D. Furthermore, if 2R ≠ 0 then R = D 2 is
possible if and only if D does not contain all quadratic extensions of Z, the center of
D.

The purpose of this paper is applying the robustness in Linear programming(LP) to get rid of uncertainty problem in constraint parameters, and find the robust optimal solution, to maximize the profits of the general productive company of vegetable oils for the year 2019, through the modify on a mathematical model of linear programming when some parameters of the model have uncertain values, and being processed it using robust counterpart of linear programming to get robust results from the random changes that happen in uncertain values ​​of the problem, assuming these values belong to the uncertainty set and selecting the values that cause the worst results and to depend buil

     Playfair cipher is a substitution scheme. The classical playfair scheme has a limited matrix size  containing only uppercase letters, so it is prone to hackers and cryptanalysis. To increase the resistance of playfair cipher, a new encipherment and decipherment method is proposed in this work, which depends on the permutation and its inverse, respectively. In addition, a modified  key matrix is utilized, which includes capital and small Alphabets, numbers, and 38 special characters collected from ASCII codes. In the proposed method, both substitution and transposition schemes are used, where the first stratum of the cipher is a substitution by using  key matrix and the second stratum is a transposi

Background: Listeria monocytogenes, a member of the genus Listeria, is widely distributed in agricultural environments, such as soil, manure and water. The genus of Listeria bacteria is about 15-17 species. It is a pathogenic bacterium that can cause a rare but dangerous infection called listeriosis.

Objectives: Studying the rate of salads contaminated with Listeria bacteria. and Listeria monocytogenes according to International, Arabic and Iraqi specifications and finding the correlation between commitments of restaurants to standard health conditions with contamination with these bacteria

Methods: The study included

Estimation of elements: Pb, Zn, Mn, Cd, and Cu, which were conducted seasonally from October-2021 till March-2022 in residential areas of Baghdad City using Geoaccumulation index (Igeo), enrichment factor ratios (EF), the factor of contamination (CF), contamination degree (Cd), index of pollution load (PLI) and index of potential ecological risk (Eif). The overall contamination factor in the research area is limited from low contamination with Cu, Mn, and Zn, moderately contaminated to very high contamination with Pb and Cd, while the assessment according to the I-geo index shows categories that vary from a slightly polluted to unpolluted by those examined heavy metals. The pollution load index indicates that the soils in some resi

The current research includes several axes, which determine the basic professional skills among kindergarten teachers and government civil Balraudhat and their relationship to educate kindergarten children with life skills teacher Albaiah.boattabar his career. And this profession imposes upon that possesses special skills, qualify him to do his roles. The teacher experimenter, researcher and owner of philosophy and organizer and director of the positions and educational director of the interactions of classroom and non-classroom. And educational systems that are responsible for the preparation of the emerging needs constant review in order to improve internal Kvaiadtha select the best input consistent with the reality of education, so as

Helicobacter pylori (H. Pylori) is one of the most common infectious human pathogens. H. pylori could induce inflammation, that causes illnesses and disorders of upper gastrointestinal which including peptic ulcer diseases, dyspepsia, gastroesophageal reflux disease and gastric mucosa-associated lymphoid tissue (MALT) lymphoma. It is important to use a better tolerated and greatly effective eradication regimen. In this study, 75 newly diagnosed adult patients with H. pylori infection were included and completed the study, they were allocated into three groups with three different treatment regimens for H. pylori eradications; Group A (25 patients) received oral standard clarithromycin-based tr

Background: The patient's vital signs must stay stable pre a pulmonary function test since the approach demands the patient to breathe slowly and deeply and exhale quickly. However, events that cause variations in normal vital signs may impact the patient. Many strategies can be utilized to stabilize vital signs, including music treatment. The purpose of this study is to compare the effectiveness of music therapy on the vital signs of client's pre a pulmonary function test. Methods: An experimental design study with an application (pre-test, post-test), to determine the effectiveness of music therapy for clients pre pulmonary function test for 106 clients in Al-Diwaniyah, Al-Shamiya, and Al- Hamza public hospitals In Iraq. Parti