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

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

A comparative investigation of the anatomical characters through a microscopical examination of the prepared transverse sections of the stem was carried out. Six plates with 32 photomicrographs were provided to convincingly show the considerable variations of anatomical characters within the nine examined species. The matrix of 18 anatomical characters which included nine quantitative and nine qualitative was applied for the clustering analysis (CA) followed by the principal component analysis (PCA) using the Multivariate Analysis of Ecological Data, PC-ORD.
The results exhibited significant variations among the species resulting in the construction of an artificial key; this key accurately represents a sufficient tool to display the

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.

An experiment was carried out on the fields of the college of Agriculture - Abu Ghraib, of a silty clay loam soil that has moisture of 15-16%, to study the effect of plowing and pulverization systems on some plant indicators of onion. The experiment included plowing systems with three levels (plowing with a moldboard plow, plowing by chisel plow and zero tillage plowing) as a primary factor. The second factor was that pulverization for only one time and repeating the pulverization twice through the use of the rotary tiller. The plant indicators of onion that are studied: plant length, onion diameter, onion weight and onion neck diameter. The experiment has carried out according to SPLIT PLOT design according to RCBD design by three replicat