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 .

Pseudomonas aeruginosa readily binds to different kind of abiotic surfaces and form biofilm. The ability of the bacterial species to form biofilm onto polyvinyl chloride (PVC) is associated with several economic, health and environmental problems. The effect of kind of water on ability of this bacterium to form biofilm is scanty in literature. In present study, the ability of different environmental isolates of P. aeruginosa to form biofilm onto polystyrene microtiter plate was evaluated. Furthermore, the effect of waters that collected from different sources on biofilm formation of this bacterium onto PVC was studied. Spectrophotometric method was used to check the ability of bacteria to form biofilm and evaluated the role of waters onto a

This paper deals with the problem of the mechanics of the operation of cinematography in the development of museum exhibition halls. In the first chapter, the researcher dealt with the problem and presented it to reach the goals and purpose of the research, which was represented in using and developing the methods and mechanisms of the presentation to keep pace with what is happening in the world of technology and access to the presented model to new formula and vision declares aesthetical and cognitive measure, thus the search constitutes an importance in absorbing Scenography dimensions in the theater and moved to the idea of the museum and the development of the display models and using them in drawing and representation of perception

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

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 discussion in this paper gives several theorems and lemmas on the Sums of Squares of  consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of  consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.

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

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