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 .

Breastfeeding (BF) serves as a complete nutritional source for the first six months of infant’s life. Breast milk contains all essential nutrients that necessary for the physiological growth and development of infants. The aim of this study was to compare the physiological growth of infants including weight, height and head circumference who were exclusively breastfed for 6 months and those who were given bottle-fed or mixed fed and to find a percentage of exclusive breastfeeding among mothers who contributed in this study in Sulaimani city. This study was carried out in Sulaimani city/ Kurdistan region of Iraq and the cases were enrolled between the first of October 2018 and first of October 2019. The infants’ weight, height and hea

Some new complexes of 4-(5-(1,5-dimethyl-3-oxo-2-phenyl pyrazolidin-4- ylimino)-3,3-dimethyl cyclohexylideneamino) -1,5- dimethyl-2- phenyl -1H- pyrazol -3(2H) –one (L) with Mn(II), Fe(III), Co(II), Ni(II), Cu(II), Pd(II), Re(V) and Pt(IV) were prepared. The ligand and its metal complexes were characterized by phisco- chemical spectroscopic techniques. The spectral data were suggested that the (L) as a neutral tetradentate ligand is coordinated with the metal ions through two nitrogen and two oxygen atoms. These studies revealed Octahedral geometries for all metal complexes, except square planar for Pd(II) complex. Moreover, the thermodynamic activation parameters, such as ?E*, ?H, ?S, ?G and K are calculated from the TGA curves using Coa

Background: This study aimed to determine the value of Beta angle for a sample of Iraqi adults with class I skeletal and dental relations and to verify the existence of sexual dimorphism and to find out the relation between this angle and other craniofacial measurements. Materials and Methods: Sixty dental students (23 males and 37 females) with an age ranged between 20-31 years old and having class I skeletal and dental relations were chosen for this study. Each student was subjected to clinical examination and digital true lateral cephalometric radiograph. The radiographs were analyzed using AutoCAD 2007 computer program to measure the angular and linear variables. Descriptive statistics were obtained for the measurements for both genders

The preparation and characterization of innovative nanocomposites based on zinc oxide nanorods (ZNR) encapsulated by graphene (Gr) nanosheets and decorated with silver (Ag), and cupper (Cu) nanoparticles (NP) were studied. The prepared nanocomposites (ZNR@Gr/Cu-Ag) were examined by different techniques including Field Emission Scanning Electron Microscope (FESEM), Transmission electron microscopy (TEM), Atomic force microscopy (AFM), UV-Vis spectrophotometer and fluorescence spectroscopy. The results showed that the ZNR has been good cover by five layers of graphene and decorated with Ag and Cu NPs with particles size of about 10-15 nm. The ZNR@Gr/Cu-Ag nanocomposites exhibit high absorption behavior in ultraviolet (UV) region of sp

Background: Verrucous carcinoma (VSCC) is considered as a rare well differentiated carcinoma variant of SCC with no metastatic potential. The aim of this study is to evaluate the Immunohistochemical expression MMP-2, VEGF and D2-40 expression in OSCC and VSCC. Materials and methods: Thirty formalin fixed paraffin embedded tissue blocks of OSCC and another twelve VSCC were collected and Four micrometer thick sections were cut from each block and mounted on positively charged slides and stained immunohistochemically with monoclonal antibodies to MMP-2, VEGF and D2-40. Results: there is no statistical difference between SCC and VSCC regarding the immunoexpression of MMP-2 and VEGF. While the lymphatic vessels density were higher in SCC than V

   Decision-makers in each country work to define a list of internal and external interests, goals and threats to their countries according to the nature of their awareness of these interests, goals and threats. 

  Hence, Iraq is not an exception to this rule, and the process of evaluating its interests and the objectives of its foreign policy is subject to the pattern of awareness of decision-makers and the influencing forces in defining its basic interests, which often witness some kind of difference in defining them, evaluating their importance and determining the size of the threats they face. And among these interests and threats that have witnessed a difference in the assessment of their

Background: Prostatic adenocarcinoma is the most widely recognized malignancy in men and the second cause of cancer-related mortality encountered in male patients after lung cancer.

Aim of the study:  To assess the diagnostic value of diffusion weighted imaging (DWI) and its quantitative measurement, apparent diffusion coefficient (ADC), in the identification and localization of prostatic cancer compared with T2 weighted image sequence (T2WI).

Type of the study: a prospective analytic study

Patients and methods: forty-one male patients with suspected prostatic cancer were examined by pelvic MRI at the MRI department of the Oncology Teaching Hospital/Medical City in Baghdad