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 .

Abstract

Agricultural Bank is an important source of funding Specialist His role in lending to farmers, it imposes a great job in providing the necessary head for any developmental process in the agricultural sector money. The ACB of ancient Iraqi banks, and that because of its importance to the advancement of the national economy and contribute to the development and regulation of the economic sector through the support and the assignment of the Iraqi agricultural sector in various agricultural activities because it is responsible

for the process of granting agricultural loans to farmers bank.

The aim of the internal control in the agricultural banks to

The energy density state are the powerful factor for evaluate the validity of a material in any application. This research focused on examining the electrical properties of the Se6Te4- xSbx glass semiconductor with x=1, 2 and 3, using the thermal evaporation technique. D.C electrical conductivity was used by determine the current, voltage and temperatures, where the electrical conductivity was studied as a function of temperature and the mechanical electrical conduction were determined in the different conduction regions (the extended and localized area and at the Fermi level). In addition, the density of the energy states in these regions is calculated using the mathematical equations. The constants of energy density states are det

Gypsum Plaster is an important building materials, and because of the availabilty of its raw materials. In this research the effect of various additives on the properties of plaster was studied , like Polyvinyl Acetate, Furfural, Fumed Silica at different rate of addition and two types of fibers, Carbon Fiber and Polypropylene Fiber to the plaster at a different volumetric rate. It was found that after analysis of the results the use of Furfural as an additive to plaster by 2.5% is the optimum ratio of addition to that it improved the flexural Strength by 3.18%.
When using Polyvinyl Acetate it was found that the ratio of the additive 2% is the optimum ratio of addition to the plaster, because it improved the value of the flexural stre

Energy efficiency is a significant aspect in designing robust routing protocols for wireless sensor networks (WSNs). A reliable routing protocol has to be energy efficient and adaptive to the network size. To achieve high energy conservation and data aggregation, there are two major techniques, clusters and chains. In clustering technique, sensor networks are often divided into non-overlapping subsets called clusters. In chain technique, sensor nodes will be connected with the closest two neighbors, starting with the farthest node from the base station till the closest node to the base station. Each technique has its own advantages and disadvantages which motivate some researchers to come up with a hybrid routing algorit

Structure of unstable 21,23,25,26F nuclei have been investigated
using Hartree – Fock (HF) and shell model calculations. The ground
state proton, neutron and matter density distributions, root mean
square (rms) radii and neutron skin thickness of these isotopes are
studied. Shell model calculations are performed using SDBA
interaction. In HF method the selected effective nuclear interactions,
namely the Skyrme parameterizations SLy4, Skeσ, SkBsk9 and
Skxs25 are used. Also, the elastic electron scattering form factors of
these isotopes are studied. The calculated form factors in HF
calculations show many diffraction minima in contrary to shell
model, which predicts less diffraction minima. The long tail

Background: Bone mineral density has been assessed using Dual-Energy X-Ray Absorptiometry. Bone mineral density is measured according to the results of the Dual-Energy X-Ray Absorptiometry examination of the vertebral column and pelvis. Although diabetes mellitus type II (DM) is known to affect bone mineral density, at the present time this particular relationship is not clear. Objective: The aim of current study was to evaluate the effects of type II diabetes mellitus on bone mineral density of the upper and lower limbs as well as gender differences. Patients and Methods: This study involved 165 patients complaining of bone pain (85 males and 80 females), 85 patients of who suffered from diabetes, involving both genders. In addition,

The Atmospheric Infrared Sounder (AIRS) on EOS/Aqua satellite provides diverse measurements of Methane (CH₄) distribution at different pressure levels in the Earth's atmosphere. The focus of this research is to analyze the vertical variations of (CH₄) volume mixing ratio (VMR) time-series data at four Standard pressure levels SPL (925, 850, 600, and 300 hPa) in the troposphere above six cities in Iraq from January 2003 to September 2016. The analysis results of monthly average CH₄VMR time-series data show a significant increase between 2003 and 2016, especially from 2009 to 2016; the minimum values of CH₄ were in 2003 while the maximum values were in 2016. The vertical distribution of CH_4<