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 .

Parasitological examination of gills of three species of sparid fishes in the territorial waters of Iraq was performed, two diplectanid monogenoids were isolated and described; Lamellodiscus indicus Tripathi, 1959 from both Haffara seabream Rhabdosargus haffara (Forsskål, 1775) and Goldline seabream R. sarba (Forsskål, 1775) and Protolamellodiscus senilobatus Kritsky, Jiménez-Ruiz and Sey, 2000 from King soldierbream Argyrops spinifer (Forsskål, 1775). The record of the parasites is considered new to the parasite fauna of Iraq. The redescription of L. indicus for the first time which is collected from a new distribution area (Arabian Gulf). R. haffara is considered a new host record .

This work deals with the production of light fuel cuts of (gasoline, kerosene and gas oil) by catalytic cracking treatment of secondary product mater (heavy vacuum gas oil) which was produced from the vacuum distillation unit in any petroleum refinery. The objective of this research was to study the effect of the catalyst -to- oil ratio parameter on catalytic cracking process of heavy vacuum gas oil feed at constant temperature (450 °C). The first step of this treatment was, catalytic cracking of this material by constructed batch reactor occupied with auxiliary control devices, at selective range of the catalyst –to- oil ratio parameter (  2, 2.5, 3 and 3.5) respectively.  The conversion of heavy vacuum gas

Gravity and magnetic data are used to study the tectonic situation of Kut- Dewania- Fajir and surrounding areas in central Iraq. The study includes the using of window method with different spacing to separate the residual from regional anomalies of gravity and magnetic data. The Total Horizontal Derivative (THD) techniques used to identify the fault trends in the basement and sedimentary rocks depending upon gravity and magnetic data. The obtained faults trends from gravity data are (N30W), (N60W) (N80E) and (N20E) and from magnetic data are (N30W), (N70E), (N20E),(N10W),(N40E). It is believed that these faults extend from the basement to the lower layers of the sedimentary rocks except the N60W trend that observed clearly in gravity in

The extraction of Eucalyptus oil from Iraqi Eucalyptus Camadulensis leaves was studded using water distillation methods. The amount of Eucalyptus oil has been determined in a variety of extraction temperature and agitation speed. The effect of water to Eucalyptus leaves (solvent to solid) ratio and particle size of Eucalyptus leaves has been studied in order to evaluate the amount of Eucalyptus oil. The optimum experimental condition for the Eucalyptus oil extraction was established as follows: 100 C extraction temperature, 200 rpm agitation speed; 0.5 cm leave particle size and 6: 1 ml: g amount of water to eucalyptus leaves Ratio.

The present research has investigated the effect of microwave energy on improving the flow properties of heavy crude oil. The fragmentation of crude oil molecules was carried out with and without using 1 and 10 wt. % concentration of various types of H-donors like tetralin, cyclohexane, and naphtha.  Microwave power of 320, 385, and 540 W and radiation time 1-9 min, and temperature were studied. The kinematic viscosity and asphaltene content were measured for evaluation the improving of heavy crude oil.

   Results show that viscosity of crude oil decreased with increase H-donor concentration, a maximum percentage of viscosity reduction was10.63 % for tetralin at 6 min radiation time, while 8.67%, and 7.34% for cycl

Oil from Brassca campestris (local variety) was extracted with hexane using Soxhlet. The extracted oil was characterized and its antimicrobial activity was determined as well. The content of extracted oil was 40% with 0.5% of volatile oil .Oil was immiscible with polar solvent such as ethanol, acetone and water, while it was easily miscible with chloroform due to its hydrophobicity. The result of organoleptic tests revealed that the oil is clear yellow in color and odorless with acceptable taste. The oil was stable at 4 -25 C? for a month. Refractive index (RI) of oil was 1.4723 with density of 0.914, [both at 4-25 C?]. Boiling point 386 C?. Infra red spectroscopy (IR) indicated the presence of different chemical groups (C=C

The current study was conducted on the southern part of Gharaf  River in   order to define the physical-chemical properties and the impact of the Tigris River’s floodplain water on its ecological characteristics during 2019. Four sites were selected along the southern part of the river. The findings showed a strong connection between the temperature of air and water at all sites. A value ranging from 4.85 - 84.65 NTU was reported for turbidity. The water was found to be oligohaline, low alkaline, and well ventilated due to high dissolved oxygen concentrations. Gharaf  River is considered to be of questionable clean water, according to the results of BOD5. The total a

The present study was undertaken to use individual terrestrial crustacean from Isopoda such as the species Porcellionides pruinosus (Brandt 1833) as environmental cleaner and that through the test of their abilities in decomposition of residues of some cellulosean wastes such as wood pieces which contain high ratio of urban wastes, and residue of Zea mays and particularly leaves as plant waste in agricultural fields and residue of Cynodon dactylon plants which compose the main wastes in most of gardens and parks. Experiments were conducted relatively in stable laboratory conditions to ensure environmental conditions similar to crustaceans' life. The results showed presence of good efficiency of these individuals in treating such wastes as