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

     The present work aimed to examine the nature and degree of the cross-correlations among three different ionospheric indices: these are Optimum Working Frequency (OWF), Highest Probable Frequency (HPF), and Best Usable Frequency (BUF). VOCAP and ASASPS models were adopted to determine the datasets of the selected ionospheric indices. The determination was made for different transceiver stations that provide certain HF connection links during the minimum and maximum years of solar cycle 24, 2009 and 2014, respectively. Matlab program was implemented to produce the geodesic parameters for the selected transceiver stations. The determination was made for different path lengths (500, 1000, 1500, and 2000) Km and bearings (0o, 45

The present investigation is concerned primarily with sorting and identification of subfamily Tubificinae from River Tigris and some water surface in Baghdad /Iraq . For this purpose six study sites were chosen, including a Al- Kadhemyia drainage canal, North Baghdad; three sites on the shore of River Tigris; in addition to site in Al-Jaish canal , East Baghdad, finally the sixth site was from pond in Al-Zawra'a park , within the center of Baghdad .These sites were characterized by sediment rang from clay, silty-clay to silty with a percentage of organic matter ranged between 0.7% - 9.9% . According to water temperature, salinity and pH values, they were nearly identical in all study sites, the water temperature was ranged through the study

Background: The world health organization estimates that worldwide 2 billion people still have iodine deficiency Objectives: Is to make comparison between the effect of identification of recurrent laryngeal nerve (RLN) and non-identification of the nerve on incidence of recurrent laryngeal nerve injury (RLNI) in different thyroidectomy procedures.

Type of the study: cross –sectional study.

Methods: 132 patients with goiters underwent thyroidectomy .Identification of RLN visually by exposure were done for agroup of them and non-identification of the nerves for the other group. The outcomes of RLNI in the two groupsanalyzed statistically for the effect of

Urine proteomics have been an area of interest and recently in Kala-azar as an alternative sample type for serum or plasma. Because of simplicity, noninvasiveness of collection and simpler matrix.  Many studies had detected an increased protein excretion in the urine of patients with active Kala-azar due to renal involvement particularly by an immunological related mechanism(s). This study have demonstrated the presence of three different protein profiles in Iraqi children (Patients: including 60 children aged 4-60 months) with defined Kala-azar using the conventional SDS-PAGE on urine samples. Urine protein profile in Kala-azar patients revealed three groups of banding patterns: group-1(33.4)% of the patients show the pattern of 5

Soil water retention curves (SWRCs) are crucial for characterizing soil moisture dynamics and are particularly relevant in the context of irrigation management. A study was carried out to obtain the SWRC, inflection point, S index, pore size distribution curve, macro porosity, and air capacity from samples submitted to saturation and re-saturation processes. Five different-texture disturbed soil samples Sandy Loam, Loam, Sandy Clay Loam, Silt Loam, and Clay were collected. After obtaining SWRC, each air-dried soil samples were submitted to particle size distribution and clay dispersed in water analyses to verify the soil lost clay. The experimental design was completely randomized with three replications using two processes of SWRC (saturat