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 .

One of the most significant elements influencing weather, climate, and the environment is vegetation cover. Normalized Difference Vegetation Index (NDVI) and Normalized Difference Built-up Index (NDBI) over the years 2019–2022 were estimated based on four Landsat 8 TIRS’s images covering Duhok City. Using the radiative transfer model, the city's land surface temperature (LST) during the next four years was calculated. The aim of this study is to compute the temperature at the land's surface (LST) from the years 2019-2022 and understand the link, between LST, NDVI, and NDBI and the capability for mapping by LANDSAT-8 TIRS's. The findings revealed that the NDBI and the NDVI had the strongest correlation with the

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

That less duration takes larva mature into a virgin under field conditions is one day during Alguetrh from April to October and last longer to more than a day during Alguetrh from November to February and up to nine days in January when low minimum temperature to zero degreespercentage that these larvae can not be a high percentage in the field ranging from 90-100% reduced Hessian Alnsphaly 85% during the months of July and Cape

Three plant species were picked randomly and their alcoholic extracts have been screened to know their effects on the phagocytic capability and intracellular killing of yeast by human peripheral macrophages. Macrophage cultures were incubated with different concentration of each plant extract: for 15 min., 30 min .and 45 min. The phagocytes activity in Iresine herbstii extract was significantly (p?0.05) increased with increasing dose and time of incubation. In Mentha piperita extract, increasing in dose and time of incubation leads to elevate phagocytic capbility, especially in the dose of 20% and 25% of plant extract, perhaps because the antimicrobial and antiviral activities of this plant, as well as strong antioxidant and antitumor act

In this article, new Schiff base ligand LH-prepared Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Hg(II), Pd(II), and Pt(II) materials were analyzed using spectroscopy (1 Metal: 2 LH). The ligand was identified using techniques such as FTIR, UV-vis, 1H-13C-NMR, and mass spectra, and their complexes were identified using CHN microanalysis, UV-vis and FTIR spectral studies, atomic absorption, chloride content, molar conductivity measurements, and magnetic susceptibility. According to the measurements, the ligand was bound to the divalent metal ions as a bidentate through oxygen and nitrogen atoms. The complexes that were created had microbicide activity against two different bacterial species and one type of fungus. DPPH techniques were bei

The aim of the research is to reveal the reality of teacher performance evaluation in the Sultanate of Oman in light of some global models. The study followed a qualitative descriptive research design. Seven forms of teacher formative and summative assessments were analyzed. Besides, an analytical template was developed, consisting of six areas related to the teaching performance of teachers. These included: lesson planning and preparation, learning environment, education, professional development, student academic, and community and parental partnership. The study reached a number of results; the most notable is the lack of change of forms for more than a decade despite the rapid development of the educational system in the sultanate in

This study aims to evaluate drinking water quality at the Al Wahda plant (WTP) in Baghdad city. A conventional water treatment plant with an average flow rate of 72.82 MLD. Water samples were taken from the influent and effluent of the treatment plant and analyzed for some physicochemical and biological parameters during the period from June to November 2020. The results of the evaluation indicate that treated water has almost the same characteristics as raw water; in other terms, the plant units do not remove pollutants as efficiently as intended. Based on this, the station appears to be nothing more than a series of water passage units. However, apart from Total dissolved solids, the mean values of all parameters in the study were

Treated effluent wastewater is considered an alternative water resource which can provide an important contribution for using it in different purposes, so, the wastewater quality is very important for knowing its suitability for different uses before discharging it into fresh water ecosystems. The wastewater quality index (WWQI) may be considered as a useful and effective tool to assess wastewater quality by indicating one value representing the overall characteristic of the wastewater. It could be used to indicate the suitability of wastewater for different uses in water quality management and decision making. The present study was conducted to evaluate the Al-Diwaniyah sewage treatment plant (STP) effluent quality based on wastewa

This study aims to evaluate drinking water quality at the Al Wahda plant (WTP) in Baghdad city. A conventional water treatment plant with an average flow rate of 72.82 MLD. Water samples were taken from the influent and effluent of the treatment plant and analyzed for some physicochemical and biological parameters during the period from June to November 2020. The results of the evaluation indicate that treated water has almost the same characteristics as raw water; in other terms, the plant units do not remove pollutants as efficiently as intended. Based on this, the station appears to be nothing more than a series of water passage units. However, apart from Total dissolved solids, the mean values of all parameters in th