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 .

Background: Adjustment of any premature occlusal contact of any zirconia restoration requires its polishing or glazing in order to restore the smoothness of the restoration. The objective of this in vitro study was to evaluate the effects of different polishing systems and glazing on the surface roughness of full-contour zirconia. Material and methods: Forty disks (diameter: 8 mm, thickness: 6.4 mm) were prepared from pre-sintered full-contoured zirconia block; they were colored and sintered in a high-temperature furnace at 1500ËšC for 8 hours. The specimens were then leveled and finished using grinding and polishing machine and adjusted using diamond disk. The specimens were then randomly divided into four groups (n=10), group I involves

The study aimed to find out the degree of practicing Arabic language teachers in the preparatory stage of higher-order thinking skills from their point of view in the first, second and third Baghdad Rusafa directorates of education. The descriptive survey method was used. The study population consisted of teachers of the Arabic language in the directorates of Baghdad, Rusafa, First, Second and Third, and the sample number was (284) teachers. A questionnaire was built on higher-order thinking skills. The validity and reliability of the tool were verified, after which the scale was applied to the research sample of (116) schools and (168) teachers who were randomly selected from the schools affiliated to the Baghdad Education Directorates Rus

Roller-Compacted Concrete (RCC) is a zero-slump concrete, with no forms, no reinforcing steel, no finishing and is wet enough to support compaction by vibratory rollers. Because the effectiveness of curing on properties and durability, the primary scope of this research is to study the effect of various curing methods (air curing, emulsified asphalt(flan coat) curing, 7 days water curing and permanent water curing) and different porcelanite (local material used as an Internal Curing agent) replacement percentages (volumetric replacement) of fine aggregate on some properties of RCC and to explore the possibility of introducing more practical RCC for road pavement with minimum requirement of curing. Cubes specimens were sawed from the slab

The toxicity effect of some heavy metals (Lead, Cadmium, Copper, and Zinc) on the growth of alga Scenedesmus dimorphus which belongs to the Division of Chlorophyta was studied and depended on the total cell number . The growth rate and doubling time were also calculated accordingly in present of absent of the the heavy metals . There were differences in toxic effects of the metals (p<0.05) . The growth was decreased gradually with alga when exposured to Lead at 15,20 and 25 mg/l in comparison with the control , mean while 30 mg/l caused an acute decrease in growth . Treating the alga with 0.05,0.1,0.5 mg/l concentration of Cadmium the number of cells decreased while at 1 mg/l the effect was more pronounced . As for Copper the conc

The sunflower plants are attacked by serious seed and soil-borne pathogens including charcoal rot disease that caused by Macrophomina phaseolina. This disease has serious damages to sunflower crop. This study aimed to assess the efficacy of Arbuscular mycorrhizal fungus against charcoal rot disease as fungicide alternative.

Abstract: In this research we study the of added NaCl with concentration (0.2, 0.02)M on the spectral of cationically charged dye (cresyl violet) and anionically charged surfactant (sodium dodecyl sulphate) with different concentration, the result show two peaks appearance the first attributed to micelle and the other formation of dye surfactant complex, in addition to the increase in the quantum efficiency of emission spectrum and shifted toward long wavelength (λmax=692.5nm-626nm).