Throughout this paper R represents commutative ring with identity and M is a unitary left R-module. The purpose of this paper is to investigate some new results (up to our knowledge) on the concept of weak essential submodules which introduced by Muna A. Ahmed, where a submodule N of an R-module M is called weak essential, if N ? P ? (0) for each nonzero semiprime submodule P of M. In this paper we rewrite this definition in another formula. Some new definitions are introduced and various properties of weak essential submodules are considered.

Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if  for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph K_n, Complete bipartite graph K_m,n and Complete tripartite graph K_l,m,n. It has also been studied how the lucky number changes whi

This search include the synthesis of some new 1,3-oxazepine derivatives have been prepared, starting from reaction of L-ascorbic acid with dry acetone in presence of dry hydrogen chloride afforded the acetal (I). Treatment of the latter with p-nitrobenzoyl chloride in dry pyridine yielded the ester (II) which was dissolved in (65%) acetic acid in absolute ethanol yielded the glycol (III). The reaction of the glycol (III) with sodium periodate in distilled water at room temperature produced the aldehyde (IV). The compound (V) [2-amino-5-mercapato-1,3,4-thiadiazole] was prepared through the reaction of thiosemicarbazide with carbon disulphide (CS2) in entity of anhydrous (Na2CO3) in (abs. ethanol ). Compound (VI) [2-(5-mercapto-1,3,4-thiadiaz

Background: Saliva plays an important role in oral health. Several salivary proteins are involved in the antimicrobial defence mechanism and are able to eliminate or inhibit bacterial growth in the oral cavity. Secretory IgA (SIgA) is one of the principal antibodies present in saliva, could help oral immunity by preventing microbial adherence, neutralizing enzymes and toxins. The aim of this study was to investigate the relationship between salivary Streptococcus Mutans (SM) count and S IgA in stimulated whole saliva in children with primary dentition compared to those with permanent teeth in relation to some oral hygiene parameters. Material and methods: Stimulated whole saliva was collected from 50 children (25 with primary dentation and

In general, the importance of cluster analysis is that one can evaluate elements by clustering multiple homogeneous data; the main objective of this analysis is to collect the elements of a single, homogeneous group into different divisions, depending on many variables. This method of analysis is used to reduce data, generate hypotheses and test them, as well as predict and match models. The research aims to evaluate the fuzzy cluster analysis, which is a special case of cluster analysis, as well as to compare the two methods—classical and fuzzy cluster analysis. The research topic has been allocated to the government and private hospitals. The sampling for this research was comprised of 288 patients being treated in 10 hospitals. As t

A new ligand 2,3-dihydrobenzo [d] thiazole-2-carboxylic acid (L) has been prepared from the reaction of ortho amino phenyl thiol with dichloroacetic acid in mole ratio (1:1). It has been characterized by elemental analysis (C.H.N.), IR, UV- Vis.spectraand 1H, 13C-NMR. A new series complexes of the bivalent ions (Co, Ni, Cu, Pd, Cd, Hg and Pb) and the trivalent (Cr) have been prepared and characterized too. The structural has been established by elemental analysis (C.H.N.), IR, UV-Vis. spectra, molar conductivity, atomic absorption and magnetic susceptibility measurements. The synthesized complexes were prepared in (1:2) ratio correspond to (Co(II), Ni(II), Cu(II), Pd(II), Cd(II), Hg(II) and Pb(II) complexes while in case Cr(III) complex is

Parkinson’s disease (PD) consider as a progressive ageing neurodegenerative disease, Parkinson’s consider as a heterogenous disease, with mainly initiate through correlation between genetic and epigenetic by inducing of different factors on some related genes, these factors like (environmental, toxicants, nutrition, heavy metals, pesticides, some drugs) and also(trauma on head ,strokes) in addition to unknown reasons which cause an idiopathic PD .Current study aims to focusing on specific related PD gene called SNCA by single nucleotides polymorphism (rs2619363) as a risk factor for PD initiation disease in PD patients in addition to study the effect of polymorphisms on random Iraqi patients with different gastrointestinal

Many studies of the relationship between COVID-19 and different factors have been conducted since the beginning of the corona pandemic. The relationship between COVID-19 and different biomarkers including ABO blood groups, D-dimer, Ferritin and CRP, was examined. Six hundred (600) patients, were included in this trial among them, 324 (56%) females and the rest 276 (46%) were males. The frequencies of blood types A, B, AB, and O were 25.33, 38.00, 31.33, and 5.33%, respectively, in the case group. Association analysis between the ABO blood group and D-dimer, Ferritin and CRP of COVID-19 patients indicated that there was a statistically significant difference for Ferritin (P≤0.01), but no-significant differences for both D-dimer and CRP.

n this study new derivatives of Schiff bases (5-10) were synthesized from the new starting material 1 . Which has been synthesized by the reaction of (1 mol.) of dichloroacetic acid with two moles of morpholine, in the presence of potassium hydroxide, Ester derivatives 2 and 3 were synthesized by the reaction of 1 with methanol or ethanol respectively in the presence of sulphuric acid as catalyst . Compound 2 was also prepared from dimethylsulphate with high yield , 2 and 3 was used to synthesized 2,2-dimorpholinylacetohydrazide 4 via reaction with NH2NH2.H2O 80% .Imines (5-10) were synthesized via the reaction of 4 with appropriate aromatic aldehydes in the presence of G.A.A as a catalyst . Derivatives compounds (1-10) were identifie