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 .

In this paper, ARIMA model was used for Estimating the missing data(air temperature, relative humidity, wind speed) for mean monthly variables in different time series at three stations (Sinjar, Baghdad , AL.Hai) which represented different parts of Iraq from north to south respectively

Triump is a happy end and a positive outcome of any good deed on the part of a human
being, or of any competition or contest in any field. A human being’s life abounds with gain
and loss. If one succeeds one will be happy psychologieally, physieally, etc. if one the other
hard one loses, one wil be in a state. Between loss and gain there are many a step.
However humans work hard to be a great success and a read winner.The life of the world constitutes a huge race-track where people try hard to head towards
the hereafter. Therefore, we find people who succed and gain the Garden, and people whose
habitation is the fire, The Glorious Qur’an has shown us in many a surah the way to success
when Allah mentions ‘great

Twelve stations in the cities of Kufa and Mishkhab were selected for studying the geotechnical, including physical, engineering, chemical and mineralogical, properties of soils in the river banks along the Euphrates River. Grain size distribution of the bank soils showed higher silt than clay and sand percentages. Soil samples from the 12 stations were classified according to the USCS standards. Silt with low plasticity constituted 91% of the silt fraction, whereas that with high plasticity composed 9%. The saturated density values ranged between 1.75-2.073 g/cm³ with an average of 1.953 g/cm³, while the dry density values ranged between 1.307-1.740 g/cm³ with an average of 1.553 g/cm³. The val

Kurdish language multifunctional morphemes indicate the different functional morphological, syntactical, and semantic tasks of the morphemes. The present study discusses the multifunctional task of the Morpheme Le in Kurdish Language. The Morpheme Le has marginally been included in other studies, yet up to the present times, there has not been a research inclusively dedicated to thoroughly discuss and clarify its multifunctional aspects. The  present study is divided into two chapters:

       Chapter one discusses the theoretical aspect of chapter two that is entirely concerned with the practical aspect of the morpheme Le. The first part of chapte

This paper aims to study the chemical degradation of Brilliant Green in water via photo-Fenton (H2O2/Fe2+/UV) and Fenton (H2O2/Fe2+) reaction. Fe- B nano particles are applied as incrustation in the inner wall surface of reactor. The data form X- Ray diffraction (XRD) analysis that Fe- B nanocomposite catalyst consist mainly of SiO2 (quartz) and Fe2O3 (hematite) crystallites. B.G dye degradation is estimated to discover the catalytic action of Fe- B synthesized surface in the presence of UVC light and hydrogen peroxide. B.G dye solution with 10 ppm primary concentration is reduced by 99.9% under the later parameter 2ml H2O2, pH= 7, temperature =25°C within 10 min. It is clear that pH of the solution affects the photo- catalytic degradation

The aim of the current study was to develop a nanostructured double-layer for hydrophobic molecules delivery system. The developed double-layer consisted of polyethylene glycol-based polymeric (PEG) followed by gelatin sub coating of the core hydrophobic molecules containing sodium citrate. The polymeric composition ratio of PEG and the amount of the sub coating gelatin were optimized using the two-level fractional method. The nanoparticles were characterized using AFM and FT-IR techniques. The size of these nano capsules was in the range of 39-76 nm depending on drug loading concentration. The drug was effectively loaded into PEG-Gelatin nanoparticles (≈47%). The hydrophobic molecules-release characteristics in terms of controlled-releas