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 effects of BaCl2 dopant on the optical properties of poly (vinyl alcohol) have been investigated. Pure and BaCl2 doped PVA films were prepared using solvent casting method. These films were characterized using UV/VIS technique in order to estimate the kind of transition which was found to be indirect transition. The value of the optical energy gap was decrease with increasing dopant concentration.
Refractive index, extinction coefficient and Urbach tail have been also investigated; it was found that all the above parameters affects by doping.

Porosity and permeability are the most difficult properties to determine in subsurface reservoir characterization. The difficulty of estimating them arising from the fact that porosity and permeability may vary significantly over the reservoir volume, and can only be sampled at well location. Secondly, the porosity values are commonly evaluated from the well log data, which are usually available from most wells in the reservoir, but permeability values, which are generally determined from core analysis, are not usually available. The aim of this study is: First, to develop correlations between the core and the well log data which can be used to estimate permeability in uncored wells, these correlations enable to estimate reservoir permeabil

The optical transmission and absorption spectra in UV-VIS were recorded in the wavelength range 350-800 nm for different glass compositions in the system: (CuO)x (PbO)50-x (Bi2O3)50 (x=2.5, 5.0, 7.5, 10.0, 12.5, 15.0, 20.0). Absorption coefficient {α (λ)}, optical energy gap (Eopt), refractive index (n), optical dielectric constant (ε`), Urbach energy (Ee), constant B and ratio of carrier concentration to the effective mass (N/m) have been reported. The effects of compositions of glasses on these parameters have been discussed. It has been indicated that a small compositional modification of the glasses lead to an important change in all the optical properties including non-linear behavior. The optical parameters were found to b

Several schottky diodes were fabricated from polyaniline/ Carbon nanotube (single and multiwalled) composites. These composites were synthesized with different concentration and two carbon nanotubes types, Single and Multi-Walled Carbon Nanotubes (SWCNT & MWCNT). Aluminum and silver paste were chosen as schottky and ohmic contact respectively. physical and electrical were used to studied these composite by using Atomic Force Microscopy (AFM) and electrical measurements. The Root Mean Square RMS surface roughness of the composite samples was found to be around 4nm. The currentvoltage characteristic were measurements for all samples in the bias range ±15V at room temperature. The results shows the increasing in carbon nanotubes concentration

Cowpea is a very important legume in Nigeria that is being utilized to Substitute high-cost animal protein for low-income people. The knowledge of some physical properties of various moisture contents is of utmost importance in the design of its handling and processing equipment and machinery, which is the aim of this work, which studied the physical properties of IT99K-573-1-1 (SAMPEA14) variety of Cowpea within 8.77 to 21.58 % db moisture content. The properties studied include Major, Intermediate, and Minor diameters, Sphericity, Surface area, Specific gravity, Volume, Bulk density, 50-tap density, 100-tap density, 1250-tap density, seed mass, Angle of repose, Geometric mean diameter, and Arithmetic mean diameter. The

    First principle calculations are performed to theoretically predict the physical properties of hexagonal aluminium arsenide planar and buckled monolayers. The structural characteristics showed that the buckled parameter is about 0.32 A°. Cohesive energies have favourable values and it indicates the fabrication possibility. Phonon dispersion properties indicated that the planar aluminium arsenic monolayers are dynamically unstable, while the buckled is less dynamically unstable. The elastic constant parameters achieved the required characteristics of stable hexagonal monolayer structures. The study of electronic band structure prefers to indirect semiconductor band gaps, and the density of states showed strong orbital hybridizati

In this work 2-hydrazino pyrimidine (1) was prepared from 2-mercapto pyrimidine with hydrazine hydrate. Treatment of (1) with active methylene compounds gave 2-(3,5-dimethyl -1 H – Pyrazole-1-yl) pyrimidine , whereas the reaction of (1) with carboxylic anhydride namely maleic anhydride or 1,2,3,6-tetra hydro phthalic anhydride yielded 1-Pyrimidine-2-yl-1,2-dihydro pyridazine-3,6-dione (3) and 2 – Pyrimidin -2-yl -2,3,4 a ,5,8 a – hexahydro phthalazine 1,4 – dione (4) . Reaction of (1) with phenyl isothiocyanate and ethyl chloro acetate afforded 3-Phenyl-1,3-thiazolidine-2,4-dione-2( pyrimidine -2- yl hydrazone (6) Azomethine (7-10) were prepared through condensation of (1) with aromatic aldehydes or ketones, then comp

The effect of adding different volume of coumarin dye (5, 15, 25 and 35) ml on optical properties of Poly (Methyl Meth Acrylate) was studied. Films of pure PMMA and PMMA with different volume of coumarin dye (5, 15, 25 and 35) ml were prepared using the casting technique. Transmission and absorption of the films were measured by using UV-VIS spectrometer technique type (100 Conc), in order to assess the type of transmission which was found an indirect transition. An optical energy gap of pure PMMA is (4.95e v) and after adding coumarin with volume (25, 35) ml, the energy gap for PMMA decrease by (0.05) compere to pure PMMA films and addition energy gap appear equal to (4.1 e v). It was found that the absorption coefficient, extinction coeff