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 fish assemblage in the East Hammar marsh was studied during December 2009 to May 2010. The fish fauna of the marsh consisted of 17 native, 23 marine (49%) and seven alien species. The dominant species were Liza abu (14.6%), Carassius auratus (13.4%) and Thryssa mystax (11.2%). The resident species formed 44.7%, occasional species 36.1% and seasonal species 19.2% of the total number of fish species. Fish species diversity index ranged from 1.28 to 2.61, richness from 1.98 to 4.50 and evenness from 0.45 to 0.78. Salinity ranged from 1.45 to 7.74‰. The increase in the proportion of marine species (49%) in the fish assemblage due to marine waters progress from Arabian Gulf had an impact on the values of ecological indices and the

Water pollution is an issue that can be exacerbated by drought as increased concentrations of unwanted substances are a consequence of lower water levels. Polluted water that flows into natural marshlands leads to the deposition of pollutants in the interior of the marsh. Here we present evidence that the interior of the Central Marsh (CM) in southern Iraq suffers from higher levels of pollution than areas closer to the source of water entering the marsh (the Euphrates River). A 1.7m embankment that halts the flow of the Euphrates is only infrequently breached and so the CM is effectively the terminal destination of the waters (and their associated pollutants and agricultural waste) flowing from the West of Iraq.

A range of water

One male specimen of the species Metapenaeus stebbingi Nobili, 1904 was first recorded in November 2021 from the Iraqi territorial waters, Northwest of the Arabian Gulf. Therefore, the investigated shrimp species nominally corresponds to the original description of M. stebbing through the main diagnostic features. It must be adopted in the spread and expansion of species, a new record of the area, and a distinctive addition to the species of commercial shrimp within the Iraqi marine waters.

Investigations made and soil samples brought from 14 sites in different areas, including Abu Ghraib and Al Anbar. Tests and measurements made in the Microbiology Laboratory at the College of Agriculture, University of Anbar. Department of Soil Sciences and water Resources, in order to isolate bio-fertilizers and test isolates fixing nitrogen in atmosphere and solvents for phosphorous compounds efficiency. The experiment included isolating and diagnosis of bacteria from rhizosphere soils of different plants that were brought from different agricultural areas, 74 isolates obtained by soils alleviation, and then the bio-chemical morphological and microscopic characteristics of these soils studied. The results showed that the most abundant and

This paper describes the development of a simple spectrophotometric determination of bismuth III with 4-(2-pyridylazo) resorcinol (PAR) in aqueous solution in the presence of cetypyridinium chloride surfactant at pH 5 which exhibits maximum absorption at 532 nm. Beer's law is obeyed over the range 5-200 µg/25 mL. i.e. 0.2-8 ppm with a molar absorptivity of 3×104 l.mol-1.cm-1 and Sandell's sensitivity index of 0.0069 µg.cm-2. The method has been applied successfully in the determination of Bi (III) in waters and veterinary preparation.

In this paper, we studied the spark corona discharge in tap and distillited waters. The results show the shape of cone that generated on the tip of capillary tube is different with conductivity of liquids. The blue glow appears at the end of capillary tube and the drop extends into a cone. In addition, the conducitivity is affected on the relationship between the appearance of the blue glow discharge with the applied voltage. The size of the cone decreases with an increase in applied voltage. The cone diameter at the base of capillary tube oscillates with period approximately 1 Sec. this oscillates in the cone diameters is due to the change distance between the liquid electrode and the surface of liquid. The intensity of spark corona dis

The Mishrif Formation is one of the most important geological formations in Iraq consisting of limestone, marl, and shale layers since it is one of the main oil producing reservoirs in the country, which contain a significant portion of Iraq's oil reserves. The formation has been extensively explored and developed by the Iraqi government and international oil companies, with many oil fields being developed within it. The accurate evaluation of the Mishrif formation is key to the successful exploitation of this field. However, its geological complexity poses significant challenges for oil production, requiring advanced techniques to accurately evaluate its petrophysical properties.

   This study used advanced well-logging analysi