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 .

Granulation Technique for Gamma Alumina Catalyst Support was employed in inclined disk granulator (IDG), rotary drum granulator (RD) and extrusion – spheronization equipments .Product with wide size range can be produced with only few parameters like rpm of equipment, ratio of binder and angle of inclination. The investigation was conducted for determination the optimum operating conditions in the three above different granulation equipments.
Results reveal that the optimum operating conditions to get maximum granulation occurred at ( speed: 31rpm , Inclination:420 , binder ratio:225,300% ) for the IDG,( speed: 68rpm , Inclination: 12.50 , binder ratio: 300% ) for the RD and ( speed:1200rpm , time of rotation: 1-2min )for the Caleva

This work studies the performance of zeolite permeable reactive barrier in removing cadmium from a contaminated shallow aquifer. Batch tests have been performed to characterize the equilibrium sorption properties of the zeolite in cadmium-containing aqueous solutions. A 1D numerical finite difference model has been developed to describe pollutant transport within groundwater taking pollutant sorption on the permeable reactive barrier (PRB), which is performed by Langmuir equation, into account. Numerical results show that the PRB starts to saturate after a period of time (~120 h) due to reduction of the retardation factor, indicating a decrease in the percentage of zeolite functionality. However, a reasonable agreement between model predict

A method has been demonstrated to synthesise effective zeolite membranes from existing crystals without a hydrothermal synthesis step.

      Nanocrystalline ZnO/Zeolite type A composite was prepared by simple method of operation by . the precipitation of zinc oxide and loading on zeolite 5A in one step. Characterization was made by X-ray diffraction (XRD), X-ray fluorescence(XRF), N2  adsorption- desorption for BET surface area, and Atomic force microscopy (AFM). Results showed that zinc oxide was loaded on zeolite as noticed by the characteristic peaks and was of nano scale having an average diameter of 88.57nm. The percentage loading of ZnO on zeolite A was 28.37% and the surface area was 222m2/g. The activity of the prepared catalyst was examined in the desulfurization of double hydrogenated diesel fuel. The process was investigated in a

Low grade crude palm oil (LGCPO) presents as an attractive option as feedstock for biodiesel production due to its low cost and non-competition with food resources. Typically, LGCPO contains high contents of free fatty acids (FFA), rendering it impossible in direct trans-esterification processes due to the saponification reaction. Esterification is the typical pre-treatment process to reduce the FFA content and to produce fatty acid methyl ester (FAME). The pre-treatment of LGCPO using two different acid catalysts, such as titanium oxysulphate sulphuric acid complex hydrate (TiOSH) and 5-sulfosalicylic acid dihydrate (5-SOCAH) was investigated for the first time in this study. The optimum conditions for the homogenous catalyst (5-SOCAH) wer

Recent research has examined the improvement of physical and dielectric properties of BaTiO₃ ceramic material by small addition of excess TiO₂ or BaCO₃. The prepared samples sintered at different temperatures and varying soaking time. The results show that increasing the sintering temperature within 1350°C and soaking time of 10 hrs give better electrical and physical properties, which indicate the reaction is complete at higher temperature and period.

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