In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

ABSTRACT

Impkact  of  Knowledge  sharing  on  organizational  innovation  Impriscal  study in Arabic company . 

of  Knowledge Management is  the  main  component  Knowledge  sharing  system, it mean the exchange if  Knowledge, ideas, and good  practice with  another  individual . Knowledge sharing between persons, then its values can growth .

It is vry important because it can provide us with the contention between virus peoples . the interaction among the people can pass all kind of Knowledge among them. the connection and interaction and interaction enabl

Abstract

Objective: the idea of this study to improve transdermal permeability of Methotrexate using eucalyptus oil, olive oil and peppermint oil as enhancers.
Method: eucalyptus oil (2% and 4%), peppermint oil (2% and 4%) and olive oil (2% and 4%) all used as natural enhancers to develop transdermal permeability of Methotrexate via gel formulation. The gel was subjected to many physiochemical properties tests. In-vitro release and permeability studies for the drug were done by Franz cell diffusion across synthetic membrane, kinetic model was studied via korsmeyer- peppas equation.
Result: the results demonstrate that safe, nonirritant or cause necrosis to rats' skin and stable till 60 days gel was successfully formulated.<

Oilwell cementing operations are crucial for drilling and completion, preserving the well's productive life. However, weak and permeable formations pose a high risk of cement slurry loss, leading to failure. Lightweight cement, like foamed cement, is used to avoid these difficulties. This study is focused on creating a range of foamed slurry densities and examining the effect of gas concentration on their rheological properties. The foaming agent and foam stabilizer are tested, and the optimal concentration is determined to be 2% and 0.12%, respectively, by the weight of the cement.

Furthermore, the construction of samples of foam cement with different densities (0.8, 1.0, 1.2, 1.4, and 1.6) g/cc is performed to f

An innovative two-step noncatalytic esterifcation technique was proposed to synthesize alkyl esters from free fatty acids simulated in waste cooking oil, as a pretreatment process for biodiesel production, without adding any catalyst under normal conditions of pressure and temperature. The efect of methanol:oil molar ratio, reaction time, mixing rate, and reaction temperature were investigated. The results confrmed that the conversion of the reaction was increased when increasing the methanol molar ratio and decreased in prolonged reaction temperature. High conversion (94.545%) was successfully achieved at optimized conditions of 115:1, 65:1 methanol:oil molar ratio in the frst step and second step, respectively, other conditions i

In this study NiO - CoO bimetallic catalysts are prepared with two Ni/Co ratios (70:30 and 80: 20) using the precipitation method of nitrate salts. The effects of Ni /Co ratio and preparation methods on the catalyst are analyzed by using different characterization techniques, i.e. atomic absorption (AA) , XRD, surface area and pore volume measurements according to the BET method . The results indicate that the best catalyst is the one containing the percentage of Ni :Co ( 70 : 30 ). Experiments indicate that the optimal conditions to prepare catalyst are stirring for three hours at a temperature of 60oC of the preparation , pH= (8-9) , calcination temperature at 400oC for two hours

    The research aims to shed light on the impact of the application of the electronic services system on electronic banking activities in a sample of Iraqi banks, as investment in technology is the most important factor for the success and future growth of administrative companies in general, and banking in particular, as global economic developments in the field of Technology has led the majority of banking sectors in the world to undergo deep reforms and radical changes in the entity of their systems and mechanisms to confront competition and keep pace with economic changes, as the concept of banking services and its diversity changed with it, especially since persistence in the traditional approach no longer gi

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.

Ti6Al4V alloy is widely used in aerospace and medical applications. It is classified as a difficult to machine material due to its low thermal conductivity and high chemical reactivity. In this study, hybrid intelligent models have been developed to predict surface roughness when end milling Ti6Al4V alloy with a Physical Vapor Deposition PVD coated tool under dry cutting conditions. Back propagation neural network (BPNN) has been hybridized with two heuristic optimization techniques, namely: gravitational search algorithm (GSA) and genetic algorithm (GA). Taguchi method was used with an L27 orthogonal array to generate 27 experiment runs. Design expert software was used to do analysis of variances (ANOVA). The experimental data were