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 purpose of my thesis is to prepare four new ligands (L1-L4) that have been ‎used to prepare a series of metal complexes by reacting them with metal ions:‎ ‎ M=(Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Hg(II) ‎ ‎ Where succinyl chloride was used as a raw material for the preparation of ‎bi-dented ligands (L1-L4) by reacting it with potassium thiocyanate as a first ‎step and then reacting with (2-aminobenzothiazole, Benzylamine, 4-‎aminoantipyrine, Sulfamethoxazole) respectively as a second step with the use ‎of dry acetone as a solvent, the chemical formula of the four ligands prepared in ‎succession:‎ N1,N4-bis(benzo[d]thiazol-2-ylcarbamothioyl)succinamide (L1)‎ N1,N4-bis(benzylcarbamothioyl)succinami

The present research is descriptive and analytical by nature; it practically presents the method of implementing the standard pattern in an unconventional way using the bias-cut line. The study aims at investigating the variables of bias-cut and their suitability for fitting large-shaped Iraqi ladies. It also aims at exploring the artistic and innovative features of the bias-cut. Therefore, one needs to understand the rules and basics of clothing and the nature of the body to reach the maximum degree of control.Consequently, the study is to answer the following questions: What is the effectiveness of tailoring on the bias-cut in fitting a standard template of a large-shaped Iraqi ladies? Is it possible to obtain from the offered possibil

PPSU hollow fiber nanofiltration membranes are prepared by applying two concentrations and various extrusion pressures according to the phase inversion method. Cross-sectional area and outer structures were characterized by using scanning electron microscope (SEM) and atomic force microscopy (AFM). In additional to the pore size distribution, either the mean roughness or the mean pore size of the PPSU hollow fiber surfaces was evaluated by AFM. It was found that the morphology of the PPSU fibers had both sponge-like and finger-like structures through different extrusion pressures and PPSU concentrations. The mean pore size and mean roughness for inner and outer surfaces were seen to be decreased with the increase of extrusion pressure at

Sulphated zirconia (SZ) is one of the most important solid acid catalysts was synthesize at different operating conditions, different calcination temperature and sulfonating time has been used. The prepared catalyst was distinguished by X-ray Diffraction (XRD), particle size and morphology of catalyst were checked by atomic force microscopy (AFM) and scanning electron microscopy (SEM) respectively, in addition to analysis by (DTA) Differential thermally and Energy Dispersive X-Ray (EDX). Finally, the N2 adsorption-desorption was used to measure the surface area (BET) and pore volume. High degree of tetragonal crystallinity was obtained 90 %, and surface area of 169 m2/g and pore volume of 0.39 cm3g-1 at 600°C calcination temperature for 3

The aim of this work was to prepare zeolite type 13X from locally available kaolin and to study the effects of using some binding materials through the process of agglomeration of this zeolite. This study was focused on using kaolin binder in different weight percents (10,15,25,35 and 45%).Physical and mechanical properties of the agglomerates such as porosity , apparent density , pore volume, crushing strength , loss on attrition , surface area and finally the adsorption capacity had been measured and evaluated .The preparation step was achieved by mixing the reactants consisting of metakaolin , source of silica as ( sodium trisilicate ) and sodium hydroxide . The conditions was temperature of 70° C and time of mixing as 8, 10,24,34,50

In the present work, a D.C. magnetron sputtering system was
designed and fabricated. This chamber of this system includes two
coaxial cylinders made from copper .the inner one used as a cathode
while the outer one used as a node. The magnetic coils located on
the outer cylinder (anode) .The profile of magnetic field for various
coil current (from 2Amp to 14Amp) are shown. The effect of
different magnetic field on the Cu thin films thickness at constant
pressure of 7x10-5mbar is investigated. The result shown that, the
electrical behavior of the discharge strongly depends on the values
of the magnetic field and shows an optimum value at which the
power absorbed by the plasma is maximum. Furthermore, the
pl

Metronidazole therapy is recommended in the treatment of giardiasis,athough some clinical reports mention the resistance to this drug from many pathogens. Many studies were applied to show the effect of probiotic to prevent or to heal diseases of gastrointestine, but only few is known about probiotic activity against infections of protozoa. This study aims to evaluate the efficiency of Bifidobacterium against infection with Giardia lamblia   in experimental mice. It was found that daily application of viable Bifidobacterium cells with a single dose (0.1ml∕mice∕day) significantly reduced the shedding of Giardia lamblia parasite cysts in feces, and infection completely disappeared at the da

Recently, a great rise in the population and fast manufacturing processes were noticed. These processes release significant magnitudes of waste. These wastes occupied a notable ground region, generating big issues for the earth and the environment. To enhance the geotechnical properties of fine-grained soil, a sequence of research projects in the lab were conducted to analyze the impacts of adding sludge waste (SW). The tests were done on both natural and mixed soil with SW at various proportions (2%, 4%, 6%, 8%, and 10%) based on the dry mass of the soil used. The experiments conducted focused on consistency, compaction, and shear strength. With the addition of 10% of SW, the values of LL and PI decreased by 29.7% and 3

This study aimed to conduct a comparative analysis of seven calliphorid species of third- instar larvae that were collected from central Iraq. The purpose was to morphologically characterize these species and develop an identification key to differentiate them from closely related species. Scanning Electron Microscope (SEM) graphical images and high-resolution traditional optical microscopes were used to analyze the morphological characteristics of the species Calliphora vomitoria (Linnaeus, 1758), C. vicina Robineau-Desvoidy, 1830, Chrysomya albiceps (Widemann, 1819), Ch. rufifacies (Macquart, 1844), Ch. megacephala (Fabricius, 1794), Lucilia cuprina (Wiedemann, 1830), and L. sericata (Meigen, 1826). An identification key was const