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 .

A reliable and environmental analytical method was developed for the direct determination of tetracycline using flow injection analysis (FIA) and batch procedures with spectrophotometric detection. The developed method is based on the reaction between a chromogenic reagent (vanadium (III) solution) and tetracycline at room temperature and in a neutral medium, resulting in the formation of an intense brown product that shows maximum absorption at 395 nm. The analytical conditions were improved by the application of experimental design. The proposed method was successfully used to analyze samples of commercial medications and verified throughout the concentration ranges of 25–250 and 3–25 µg/mL for both FIA and batch procedures, respecti

The issue of intellectual capital is a critical issue in the success and excellence of organizations, especially if it is linked to the management of customer experience, and because of the characteristic of the Iraqi environment, which affected all sectors, including the banking sector, it was important to discuss the types of intellectual capital and its relationship to the management of customer experience, especially when managers private banks, the importance of research lies in the linking of its variables to build the strategic capabilities of banks to achieve excellence and sustainability, it aims to diagnose the extent of interest in the types of intellectual capital and management of customer experience in the Iraqi ban

The research aims to shed light on the role of artificial intelligence in achieving Ambidexterity performance, as banks work to take advantage of modern technologies, artificial intelligence is an innovation that is expected to have a long-term impact, as well as banks can improve the quality of their services and analyze data to ensure that customers' future needs are understood. . The Bank of Baghdad and the Middle East Bank were chosen as a community for the study because they had a role in the economic development of the country as well as their active role in the banking market. A sample of department managers was highlighted in collecting data and extracting results based on the checklist, which is the main tool for the stu

       Iraq is one of the most important countries in the world that has received its share of terrorist acts by the terrorist organization the Islamic State of Iraq and al-Sham (ISIS), which has caused instability, especially during the period of ISIS's control of seven Iraqi provinces (2014-2017). This stage has caused a decline in the levels of human and economic development and its inconsistency with the capabilities and needs of the Iraqi population. Therefore, this study aims to investigate the hypothesis that there is a close relationship between the decline in development in Iraq and the brutal practices of ISIS that it committed during his period of control over many Iraqi cities and regions. This study used several method

Aquatic Oligochaeta is an important group of Macroinvertebrates that has been very remarkable as bioindicators for assessing water pollution and determining its degree in water bodies. Hence, the idea of the current study aims at studying the impact of Baghdad effluents on the Tigris River by using oligochaetes community as bioindicators . For this purpose, four sites along the inside of Baghdad has been chosen. Site S1 has been located upstream, site S2 and S3 has been at midstream and site S4 at the downstream of the River.This investigation has used different types of biological indicators, including the  percentage of oligochaeta  within benthic invertebrates, which ranged from 49.2-51.28%. The highest percentage of the tubificid w

Consuming of by-product or waste materials in highway engineering is significant in the construction of new roads and/or in renovations of the existing ones. Pulverised Fuel ash (PFA), which is a by-product material of burning coal in power stations, is one of these materials that might be incorporated instead of mineral filler in hot asphalt mixtures.

Two types of surface course mixtures have been prepared one with conventional mineral filler i.e. ordinary Portland cement (OPC) while the second was with PFA. Several testings have been conducted to indicate the mechanical properties which were Marshall Stability and Indirect Tensile Strength tests. On the other hand, moisture damage and ageing have been evaluated

The inhibitory effect of acetone, ethanol, and aqueous extracts of ten medicinal plants on β-lactamase from Staphylococcus sciuri and Klebsiella pneumoniae was investigated in vitro by starch-iodine agar plate method. The results revealed the success of starch-iodine method for the detection of the inhibition of β-lactamase activity by the various extracts of each individual plant. The acetone extracts of Catharanthus roseus, Eucalyptus camaldulensis, and Schinus terebinthifolius induced an inhibitory effect on β-lactamase from Staphylococcus sciuri. On the other hand, acetone extracts from only Eucalyptus camaldulensis, and Schinus

The ability to produce load-bearing masonry units adopting ACI 211.1 mix design using (1:3.2:2.5) as (cement: fine aggregate: coarse aggregate) with slump range (25-50mm) which can conform (dimension, absorption, and compressive strength) within IQS 1077/1987 requirements type A was our main goal of the study. The ability to use low cement content (300 kg/m3) to handle our market price products since the most consumption in wall construction for low-cost buildings was encouraging. The use of (10 and 20%) of LECA as partial volume replacement of coarse aggregate to reduce the huge weight of masonry blocks can also be recommended. The types of production of the load-bearing masonry units were A and B for (