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 .

The selective information broadcasting service is one of the important services in libraries and information centers, as it is the link between the source and the beneficiary and between related sources, as it links similar sources through keywords and then sends them to beneficiaries, which contributes to reducing the time and effort spent by beneficiaries in obtaining sources or information. Therefore, the application of this service is an important matter and gives a positive indicator in the progress of the library towards the integration of its services. From this standpoint, this research came to answer some questions, including: 1. What are the outlets for beneficiaries (the research community) in obtaining information sources? 2. Wh

The study included adding antimony oxide to mixtures of coating metal surfaces (Enameling), after it was selected ceramic materials used in the coating metal pieces of the type of steel and cast iron in two layers. The first is called a ground coat and the second is a cover coat.
Ceramic materials layer for ground coat have been melted down in
platinum crucible at a temperature of 1200oC to prepare the glass
mixture (Frit). It was coated on metals at a temperature of 780oC for
two minutes, while the second layer was prepared glass mixture
(Frit) at a temperature of 1200oC, but was coated at a temperature of
760oC for two minutes.
Underwent tests crystalline state of powders (Frits) and enameled samples using X-ray di

The downhole flow profiles of the wells with single production tubes and mixed flow from more than one layer can be complicated, making it challenging to obtain the average pressure of each layer independently.  Production log data can be used to monitor the impacts of pressure depletion over time and to determine average pressure with the use of Selective Inflow Performance (SIP). The SIP technique provides a method of determining the steady state of inflow relationship for each individual layer. The well flows at different stabilized surface rates, and for each rate, a production log is run throughout the producing interval to record both downhole flow rates and flowing pressure. PVT data can be used to convert measured in-situ r

The downhole flow profiles of the wells with single production tubes and mixed flow from more than one layer can be complicated, making it challenging to obtain the average pressure of each layer independently.  Production log data can be used to monitor the impacts of pressure depletion over time and to determine average pressure with the use of Selective Inflow Performance (SIP). The SIP technique provides a method of determining the steady state of inflow relationship for each individual layer. The well flows at different stabilized surface rates, and for each rate, a production log is run throughout the producing interval to record both downhole flow rates and flowing pressure. PVT data can be used to convert measured in-situ rates

A new Schiffbase derivative ligands [H4L1] and [H2L2] have been produced by condensed ophathaldehyde with ethylene diamine and [N1, N1'E, N1, N1'E)-N1, N1'-(1, 2-phenylenebis (methan-1-yl- 1ylidene)) diethane-1, 2-diamine] with 2-benzoyl benzoic acid. Schiffbase ligands have been separated and categorized by 1H, 13 C-NMR, (CHN) elemental analysis, UV-visible, mass spectroscopy and FTIR methods. Ten new coordination complexes were prepared and structurally diagnosed: [M(L1)Cl2] and [M2(L2)Cl2] where M(II) = Mn (II), Co(II), Ni(II), Cu(II) and Hg(II). The complexes have been typified by FTIR, UV-visble atomic absorption, molar conductance elemental analysis, and magnetic susceptibility. The details of the ligand (H4L1) compounds are getting a

In the present work, a study is carried out to remove chromium (III) from aqueous solution by: activated charcoal, attapulgite and date palm leaflet powder (pinnae). The effect of various parameters such as contact time, and temperature has been studied. The isotherm equilibrium data were well fitted by Freundlich and Langmuir isotherm models. The adsorption capacity of chromium (III) that was observed by activated charcoal, attapulgite and date palm leaflet powder (pinnae) increased with the rise of temperature when the concentrations of Cr (III) were 600, 700 and 100mg/L respectively. The greatest adsorption capacity ofactivated charcoal, attapulgite and date palm leaflet powder (pinnae) at 10°C was 7.51, 5.39 and 0.77mg.gˉ¹ respective

Simulation  of  the  Linguistic  Fuzzy Trust  Model  (LFTM)  over  oscillating  Wireless  Sensor Networks (WSNs) where the goodness of the servers belonging to them could change along the time is presented in this paper, and the comparison between the outcomes achieved with LFTM model over oscillating WSNs with the outcomes obtained by applying the model over static WSNs where the servers maintaining always the same goodness, in terms of the selection percentage of trustworthy servers (the accuracy of the model) and the average path length are also presented here. Also in this paper the comparison between the LFTM and the Bio-inspired Trust and Reputation Model for Wireless Sensor Network

were prepared by condensation of 6-R-2amino bcnzothiazol with Salicyldehyde.These Schiff bases were found to reach with maleic anhydride and citraconic to give