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 research aimed to identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

Abstract: As human history is implicated in landscape or the natural history, it can be stated that the origins of the Caribbean writers' conflict, in general, are the colonial history of West India. That history which tells the story behind not only their fragmented identity, but also the problems connected to their language as well. Building on the arguments of the prominent Postcolonial ecoccritics such as Elizabeth DeLoughrey, George Handley, Helen Tiffin, and Graham Huggan, this research analyzes selected poems by Derek Walcott's which are bounded in his volume, Collected Poems. It shows how the Caribbean history has been erased due to the brutality of colonization offering landscape as a reliable source which has recorded that history

This research is an attempt to achieve the following objectives: 1. identifying the nature of the non-verbal communication skills practiced by educational counselors in individual guidance. 2. Identifying the significant differences between non-verbal communication skills exercised by educational counselors from their point of view in regard to their gender (male-female). The researcher used a questionnaire as a tool prepared based on exploratory questions of educational counselors and literature. It has consisted of (26) items over four domains applied to a sample of (50) educational counselors (male and female) who have been chosen randomly from schools located in Baghdad Education Directorate Rusafa / 2. It was treated statistically u

Twenty five vaginal swabs from outpatients' healthy women were collected from Kamal Al-Samarai Hospital, Baghdad, to isolate and identify of Lactobacillus acidophilus. Three isolates were diagnosed as L. acidophilus which represents 15% of the total number of lactic acid bacterial (LAB) isolates; other LAB types represent 65% (20 isolates).The ability of L. acidophilus to produce surlactin was detected after measuring its biological activity to inhibit the adhesion of biofilm formed by Pseudomonas aeruginosa to surfaces using test tube method. It was found that all isolates were able to produce surlactin but the activity of surlactin was varying in each isolate. Surlactin produced by isolates 1 and 13 was the most effective. Biological appl

This study aimed to see how allicin (45mg/kg BW) affected diabetic Mellitus in male rats (DM). Forty male rats were utilized, and they were split into four groups at random for 42 days. T2 was treated with 45 mg/kg B.W of allicin dissolved in 1 ml of D.W daily and injected with a single dose of sodium citrate buffer (0.5ml Intra-Peritoneal IP), DM was induced in T1 and T2 by injection of a single dose of streptozotocin 50 mg/kg B.W IP, T1 was assigned as a positive control, T3 received 45 mg/kg B.W. of allicin dissolved in 1 ml D.W. every day, and a single dose of sodium citrate buffer was injected (0.5ml IP). When diabetic rats treated with allicin in T2 were compared to diabetic rats in T1, the findings indicated a significant increase (P

Baqubah city has grown extremely rapidly. The rate of growth exceeds the growth of services that must grow side by side with the growth of population. There are natural features that affect the growth of Baqubah city such as Dieyala river, Alssariya river, in addition to agricultural areas .All these natural features affect the growth of Baqubah city in the running form being seen . In this research the remote sensing and geographic information system (GIS) techniques are used for monitoring urban expansion and forecasting the probable axes to the growth of the city, and found that the probability of Baqubah growth to east is preferred due to Baqubah growth to the east would never interfere with natural features. Also in this res