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 .

The object of this study was to evaluate the efficiency of safranin O (SFO), dye removal with application of Thuja orientalis as a low-cost biosorbent. The biosorption equilibrium level was determined as a function of pH, adsorbent dose, contact time and temperature. Surface area and pore size distribution were measured for the adsorbent. Thuja has a good removal effeciency for SFO dye. The adsorption kinetics data were best fit for the pseudo-second order kinetic (the regression coefficient = 0.999). The experimental equilibrium adsorption data are tested for the Langmuir, freundlich,Temkin and Dubinin-Radushkevich isotherm modles. From the values of the regression coefficient the results indicate the following order to fit the isotherm

A simple ,accurate and sensitive spectrophotometric method has been developed the determination of Cobalt(II) and Cupper (II) .The method is based on the chelation of Co(II) and Cu(II) ions with 4-(4´-pyrazolon azo) -2-Naphthol(APAN) in aqueous medium . The complexes have a maximum absorption at (513) and (506) nm and ? max 0.531×10 4 and 0.12×10 5 L.mol -1.cm -1 for Co(II) and Cu(II) respectively .The reagent and two complexes have been prepared in ethanolic solution.The stoichiometry of both complexes were found to be 1:2 (metal :legend) .The effects of various cations and anions on Co(II) and Cu(II) determination have been investigated .The stability constants and standard deviations for Co(II) and Cu(II) 0.291 x107 ,0.909X108 L.mol

This study was conducted to examine the anatomical aspects of Carissa macrocarpa, of stem, leaf and leaf venation. The results obtaind showed that the tissue of the studied parts have important anatomical characteristics in terms of the shape of the cross-sectional of stem and vertical-sectional of leaves. The stem section appeared in circular and the midrib was crescent shape and the stomata appeared on the upper surface of the leaf only, Tetracytic in type. Druses crystals and Aleurone granules appeared on both surfaces of leaves. The venation type was Brochidodromous in which the secondary veins do not end at the edge of the leaf, and each secondary race is connected with the higher rac

The fouling depositions of crude oil stream were studied theoretically in a shell and tube heat exchanger to investigate the effect of depositions on the heat transfer process. The employed heat exchanger was with steam flowing in the inner tubes and crude oil in the shell at different velocities and bulk temperatures. It is assumed that fouling occurs only on the heated stream side (crude oil). The analysis was carried out for turbulent flow heat transfer conditions with wide range of Reynolds number, bulk temperature and time. Many previously proposed models for fouling resistance were employed to estimate a new model for fouling rate. It is found that the fouling rate and consequently the heat transfer coefficient were affected by Rey

Human cutaneous leishmaniasis (CL) is caused by Leishmania sp. parasite and endemic in Iraq. The current study was including analysis of available database from Iraqi CDC to determine the distribution of CL cases for the period (2008-2015 years) in Iraq. Total reported cases for this period were 17001 (range 2.9-10.5 per 100,000 individuals). Highest reported cases were recorded in the year 2015 (4000 cases). Male infections cases of CL (50.8%) were more than female infections (49.2%). Highest infections of CL were observed in the age group (5-14yr.) as (34.6%), While the lowest infection of CL were observed in the age group (>1yr.) as (4.3%). Highest infection case of CL was observed in the middle and west of Iraq (53%). In contrast,

Samples (4th) reviewed are deposited and stored in the Iraqi Natural History Museum (INHM), and there are 4th of them. Sciurus anomalous (Güldenstädt, 1785) species are preserved and mummified. It is a Caucasian squirrel (S. anomalus) that was medium in size, with a grayish-to-chestnut color, a golden gray back, and a golden tail. It is found in the forests of East and Southeast Asia. The variety possessed for the study was previously registered in the vertebrate literature by several authors and was stored by scientific methods in the museum. As a result of the multiplication and growth of these species, and to know the environmental changes that occurred in them, they were compared with models and samples found throughout Iraq

The sol-gel preparation technique of transparent silica monoliths containing up to 0.5 M of samarium have been described. The sol-gel processing parameters are: acid catalyzed hydrolysis and controlled drying. The prepared monoliths are analyzed by X-ray diffraction, pycnometer measurements, Fourier transformation infrared spectroscopy and optical spectroscopy. The oscillator strengths of the Sm3+ ions in the silica monoliths are calculated. The results show a linear concentration dependence of some Sm3+ transitions in UV/Vis absorption spectra and formation of Sm3+ clusters inside the pores structure of silica monoliths at high Sm3+ concentration

   The current study included collection for many fresh specimens, the observation of specimens in some Iraqi herbaria have been studied, although morphological characters of roots, stems, flowers, inflorescences and fruits were included in this work, however indumentums  and pollen grains were studied