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 .

It is known that the oral administration of ibuprofen caused an irritation of stomach as a side effect due to its carboxylic moiety. Ibuprofen ester was synthesized by linking the carboxylic moiety of ibuprofen and the hydroxylic group of paracetamol to reduce its side effect. Study the kinetic hydrolysis of prepared ester was examined at different values of physiological pH (1.0, 5.8, 6.4 and 7.4) at 37 ± 0.1 of 1 hour period. Measurements of absorbance were carried out by UV-Visible spectrophotometer to follow the stability of ester, it showed Pseudo first order hydrolysis. The pH- apparent rate profiles of ester was exhibited a good stability at pH 1.0 and pH 5.8. Pharmacological activity in vivo of prepared ester was evaluated in re

This study involves the synthesis of a new class of silicon polymers, designated as P1-P7, derived from dichlorodimethylsilane (DCDMS) in combination with various organic compounds (Schiff bases prepared from different amines and appropriate aldehydes or ketones) [I-V] through condensation polymerization. The structures of all monomers and polymers were characterization by FTIR and 1HNMR spectroscopy (for some polymers). The results of thermogravimetric analysis (TGA) and differential scanning calorimetry DSC test show stable thermal behaviour. Polymers with a higher concentration of aromatic rings in their repeating structural units exhibited a higher temperature for weight loss, indicating increased thermal stability. Thermal meas

This study aimed to IQ test standardization of Marten Lother Johan which used with childreen of the one stage at primary schools who aged (6) years old in Baghdad (Resafaa and Kharh).

 The importance of this study are :

1-The  importance of childhood and its role to develop the personality.

2-The importance of this age as the child will exposure to different kind of official teaching .

3-The capability for early detection of special category for early intervention in order to provide the necessary care .

4-Using the current test could consider as a predictive tool to screen the intelligent children .

In order to achieve the study aim, the researcher had followed the follow

This research presents a study for precipitating phosphorus (as phosphate ion) from simulated wastewater (5ppm initial concentration of phosphorus) using calcium hydroxide Ca(OH)₂ solution. The removal of phosphorus by Ca (OH)₂ solution is expected to be very effective since the chemical reaction is of acid-base type but Ca(OH)₂ forms complex compound with phosphate ions called. Hydroxyapatite Ca₅ (PO₄)₃OH. hydroxyapatite is slightly soluble in water. This research was directed towards sustainable elements as phosphorus. Kinetics of the dissolution reaction of hydroxyapatite was investigated to find the best factors to recover phosphorus. The effect of con

     In the present work, a kinetic study was performed to the extraction of phosphate from Iraqi Akashat phosphate ore using organic acid. Leaching was studied using lactic acid for the separation of calcareous materials (mainly calcite). Reaction conditions were 2% by weight acid concentration and 5ml/gm of acid volume to ore weight ratio. Reaction time was taken in the range 2 to 30 minutes (step 2 minutes) to determine the reaction rate constant k based on the change in calcite concentration. To determine value of activation energy when reaction temperature is varied from 25 to 65 , another investigation was accomplished. Through the kinetic data, it was found that selective leaching was controlled by

The species Vitex agnus-castus is an important medicinal plants and it is one of the cultivated and dicotyledon plants in Iraq. The anatomical of stem, petiole, midrib area, epidermis, veins, type of leaf stomata and seeds were studied by light microscope. In this research, shows the knowledge of anatomical characteristics of the studied plant, showing its importance as taxonomic characteristics through the sections of the stem, petiole, the midrib and the petals.

Microfinance Institutions (MFIs) offers small loans with easy repayment system and till now these institutions have served millions of needy people around the globe. This study highlights the hurdles influence the smooth working and growth of Microfinance institution in Egypt. The structured interviews were conducted from the top and mid-level managers of MFI's. This study revealed that interest rate, political and economic conditions, corruption, customer outreach, competition and technology are the important elements for MFI's success. It is evident that lack of use of technology and less importance drawn on customer outreach programs are the main challenges of MFI's in Egypt. This study provides a roadmap for practitioners and strategic

The current study is a taxonomic account of three gastrotrich species that belong to Chaetonotidae (Phylum Gastrotricha) namely Ichthydium auritum Brunson, 1950 Lepidodermella squamata (Dujardin, 1841) and Chaetonotus anomalus Brunson, 1950. These species are registered as a new record from Iraq and were collected from several locations along the main outfall drain (MOD) in south of Baghdad, from January to December 2020. The species described in this article were found to be related to Hydrilla and Ceratophyllum and prefer environments rich in detritus and decomposing organic matter. The worms preferred water that is salty, hard, alkaline, and had good oxygen content.