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 .

Based on the diazotization-coupling reaction, a new, simple, and sensitive spectrophotometric method for determining of a trace amount of (BPF) is presented in this paper. Diazotized metoclopramide reagent react with bisphenol F produces an orange azo-compound with a maximum absorbance at 461 nm in alkaline solution. The experimental parameters were optimized such as type of alkaline medium, concentration of NaOH, diazotized metoclopramide amount, order additions, reaction time, temperature, and effect of organic solvents to achieve the optimal performance for the proposed method. The absorbance increased linearly with increasing bisphenol F concentration in the range of 0.5-10 μg mL^-1 under ideal conditions, with a correlati

Soil water use and water storage vary by vegetative management practices, and these practices affect land productivity and hydrologic processes. This study investigated the effects of agroforestry buffers (AB), grass buffers (GB), and biofuel crops (BC), relative to row crops (RC) on soil water use for a claypan soil in northern Missouri, USA. The experiment located at the Greenley Memorial Research Center included RC, AB, GB, and BC established in 1991, 1997, 1997, and 2012, respectively. Soil water reflectometer sensors installed at 5‐, 10‐, 20‐, and 40‐cm depths monitored soil water from April to November in 2017 and 2018. Results showed significant differences in weekly volumetric water content (VWC) among treatments for all fou

In this research, Artificial Neural Networks (ANNs) technique was applied in an attempt to predict the water levels and some of the water quality parameters at Tigris River in Wasit Government for five different sites. These predictions are useful in the planning, management, evaluation of the water resources in the area. Spatial data along a river system or area at different locations in a catchment area usually have missing measurements, hence an accurate prediction. model to fill these missing values is essential.
The selected sites for water quality data prediction were Sewera, Numania , Kut u/s, Kut d/s, Garaf observation sites. In these five sites models were built for prediction of the water level and water quality parameters.

     In this article, the lattice Boltzmann method with two relaxation time  (TRT)  for the  D2Q9 model is used to investigate numerical results for 2D flow. The problem is performed to show the dissipation of the kinetic energy rate and its relationship with the enstrophy growth for 2D dipole wall collision. The investigation is carried out for normal collision and oblique incidents at an angle of . We prove the accuracy of moment -based boundary conditions with slip and Navier-Maxwell slip conditions to simulate this flow. These conditions are under the effect of Burnett-order stress conditions that are consistent with the discrete Boltzmann equation. Stable results are found by using this kind of boundary condition where d

The operative system of theatrical performance depends on the construction of the scenographic space, as it constitutes the most aesthetic effect of the recipient, and the body of the theatrical discourse that contains the signs of the show, and it comes as an embodiment of the directing vision of the show director, so most of the world directors resorted to attention to the output treatment to establish the scenographic space, and thus it possesses a contrast in The embodiment of the directing vision according to the stylistic and hermeneutical dimension of the director, so the two researchers found the importance of studying the topic, and the study came under the title (Directing Treatments of the Scenographic Space in the Iraqi Theat

Recently, several concepts and expressions have emerged that have often preoccupied the world . around the concept of environment and sustainability. This is due to the negative and irresponsible impact of man and his innovations in various industrial and technological fieldsthat have damaged the natural environment. Architecture and cities at the broader level are some of the man made components that caused these negative impacts and in the same time affected by them. What distinguishes architectural and urban projects is the consumption of large . quantities of natural resources and production larger amounts of waste and pollution, along the life of these projects. At the end of the twentieth century and the beginning of the twenty-fir

The public budget is on the same time an art and a science .As an accountable science it seeks balance between public income and public expenditure for an accountable year. And as an accountable art it seeks to achieve economic balance by distributing equitable income in order to reach sustainable development .This is the optimal use of all natural and human resources to address scarcity of natural resources facing the increase need of human resources by spending on education, health, environment, housing, agriculture and industry to achieve social justice for the current generation and future generations. Since the first budget in Iraq on 1921 an accounting budget, is balancing the sections and items has been adopted and since the publi

   To deduct the childhood status in Iraq, it was important manner to use statistical tools and approaches concerned with interpreting the causal relationships and their attitudes and use classification method for the important effects (variables) to draw an obvious picture of the phenomena under study in order to make it useful through investing, updating and improving it in by demographic studies in the future. Two statistical methods had been used in the field of analyzing data of multivariate analysis namely, Cluster Analysis and Factor Analysis.  

The present study focuses on four fundamental axes .The nutrition axis, health axis, Educational axis, and the social axis. The study has ca

The physical sports sector in Iraq suffers from the problem of achieving sports achievements in individual and team games in various Asian and international competitions, for many reasons, including the lack of exploitation of modern, accurate and flexible technologies and means, especially in the field of information technology, especially the technology of artificial neural networks. The main goal of this study is to build an intelligent mathematical model to predict sport achievement in pole vaulting for men, the methodology of the research included the use of five variables as inputs to the neural network, which are Avarage of Speed (m/sec in Before distance 05 meters latest and Distance 05 meters latest, The maximum speed achieved in t