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.

Introduction: Although soap industry is known from hundreds of years, the development accompanied with this industry was little. The development implied the mechanical equipment and the additive materials necessary to produce soap with the best specifications of shape, physical and chemical properties. Objectives: This research studies the use of vacuum reactive distillation VRD technique for soap production. Methods: Olein and Palmitin in the ratio of 3 to 1 were mixed in a flask with NaOH solution in stoichiometric amount under different vacuum pressures from -0.35 to -0.5 bar. Total conversion was reached by using the VRD technique. The soap produced by the VRD method was compared with soap prepared by the reaction - only method which

Abstract: Iatrogenic furcal root perforations are serious complications during dental treatment. This study was aimed to compare the sealing ability of new bioceramic root repair material TotalFill® with the other perforation repair materials (GIC, MTA and Biodentine) using a dye- extraction method.Materials and Methods: Forty extracted, human mandibular molars with non-fused well developed root were collected. Artificial perforations were made from the external surface of the teeth. Then the teeth were randomly divided into 4 experimental groups (n= 10) according to the type of repair material used in this study; Medifil glass ionomercement, TotalFill® bioceramic root repair material, BiodentineTM and MTA Plus. The specimens were then im

Novel derivatives of 1-(´1, ´3, ´4, ´6-tetra benzoyl-β-D-fructofuranosyl)-1H- benzotriazole and 1-(´1, ´3, ´4, ´6-tetra benzoyl-β-D-fructofuranosyl)-1H- benzotriazole carrying Schiff bases moiety were synthesised and fully characterised. The protection of D- fructose using benzoyl chloride was synthesized, followed by nucleophilic addition/elimination between benzotria- zole and chloroacetyl chloride to give 1-(1- chloroacetyl)- 1H-benzotriazole. The next step was condensation reaction of protected fructose and 1-(1-chloroacetyl)-1H- benzotriazole producing a new nucleoside analogue. The novel nucleoside analogues underwent a second conden- sation reaction with different aromatic and aliphatic amines to provide new Schiff b

This study is concerned with the comparison of the results of some tests of passing and dribbling of the basketball of tow different years between teams of chosen young players in Baghdad. Calculative methods were used namely (Arithmetic mean, Value digression and T.test for incompatible specimens). After careful calculative treatments, it has been that there were abstract or no abstract differences in the find results of chestpass, highdribble and cross-over dribble. The clubs were: (Al-Khark, Air defence, Police and Al-Adamiyah) each one separate from the other for the year (2000-2001). After all that many findings were reached such as the lack of objective valuation (periodical tests) between one sport season and the other. In the light

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

Most companies use social media data for business. Sentiment analysis automatically gathers analyses and summarizes this type of data. Managing unstructured social media data is difficult. Noisy data is a challenge to sentiment analysis. Since over 50% of the sentiment analysis process is data pre-processing, processing big social media data is challenging too. If pre-processing is carried out correctly, data accuracy may improve. Also, sentiment analysis workflow is highly dependent. Because no pre-processing technique works well in all situations or with all data sources, choosing the most important ones is crucial. Prioritization is an excellent technique for choosing the most important ones. As one of many Multi-Criteria Decision Mak

The effects of nutrients and physical conditions on phytase production were investigated with a recently isolated strain of Aspergillus tubingensis SKA under solid state fermentation on wheat bran. The nutrient factors investigated included carbon source, nitrogen source, phosphate source and concentration, metal ions (salts) and the physical parameters investigated included inoculum size, pH, temperature and fermentation duration. Our investigations revealed that optimal productivity of phytase was achieved using wheat bran supplemented with: 1.5% glucose. 0.5% (NH4)2SO4, 0.1% sodium phytate. Additionally, optimal physical conditions were 1 × 105 spore/g substrate, initial pH of 5.0, temperature of fermentation 30˚C and fermentation dura

Activated carbon prepared from date stones by chemical activation with ferric chloride (FAC) was used an adsorbent to remove phenolic compounds such as phenol (Ph) and p-nitro phenol (PNPh) from aqueous solutions. The influence of process variables represented by solution pH value (2-12), adsorbent to adsorbate weight ratio (0.2-1.8), and contact time (30-150 min) on removal percentage and adsorbed amount of Ph and PNPh onto FAC was studied. For PNPh adsorption,( 97.43 %) maximum removal percentage and (48.71 mg/g) adsorbed amount was achieved at (5) solution pH,( 1) adsorbent to adsorbate weight ratio, and (90 min) contact time. While for Ph adsorption, at (4) solution pH, (1.4) absorbent to adsorbate weight ratio, and (120 min) contact