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

Background: The aim of the study was to investigate the effect of surface treatments of zirconia (grinding and sandblast with 50μm, 100 μm) on shear bond strength between zirconia core and veneering ceramic. Material and methods: Twenty-eight presintered Y-TZP ceramic specimens (IPS e.max ZirCAD, Ivoclar vivadent) were fabricated and sintered according to manufacturer’s instructions. The core specimens were divided randomly in to 4 groups, group 1: no surface treatment, group2: zirconia specimens were ground with silicon carbide paper up to1200 grit under water cooling, group3: zirconia specimens were ground and sandblast with 100 μm alumina, group 4: zirconia specimens were ground and sandblast with 50 μm alumina. Surfa

irrigation use at many stations along the Euphrates River inside the Iraqi lands and to try to correlate the results with the satellite image analyses for the purpose of making a colored model for the Euphrates that can be used to predict the quality classifications of the river for irrigation use at any point along the river. The Bhargava method was used to calculate the water quality index for irrigation use at sixteen stations along the river from its entrance to the Iraqi land at Al-Qaim in Anbar governorate to its union with the Tigris River at Qurna in Basrah governorate. Coordinates of the sixteen stations of the Euphrates River were projected at the mosaic of Iraq satellite image which was taken from LANDSAT satellite for bands 1, 2

This study aimed to IQ test standardization of Marten Lother Johan which used with childreen of the tow  stage at primary schools who aged (7) 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

The toxicity effect of some heavy metals (Lead, Cadmium, Copper, and Zinc) on the growth of alga Scenedesmus dimorphus which belongs to the Division of Chlorophyta was studied and depended on the total cell number . The growth rate and doubling time were also calculated accordingly in present of absent of the the heavy metals . There were differences in toxic effects of the metals (p<0.05) . The growth was decreased gradually with alga when exposured to Lead at 15,20 and 25 mg/l in comparison with the control , mean while 30 mg/l caused an acute decrease in growth . Treating the alga with 0.05,0.1,0.5 mg/l concentration of Cadmium the number of cells decreased while at 1 mg/l the effect was more pronounced . As for Copper the conc

This manuscript investigated the effect of anchorage CFRP wrapping sheets, bolts, and laminate interlock on increasing the efficiency of flexural strengthening for the post-tension girder using CFRP composites techniques longitudinal laminates at the soffit for partially damaged loss of about 14.3% from its area of prestressed concrete beams, and the impact on restoring the original flexural capacity of PC girder. Mitigating delamination of the soffit of horizontal laminates (CFRP). The texture of the laminate and anchorages influenced the stress of the laminate carbon fiber, the mode of crack propagation and failure, and consequently, the beam's attitude has been investigated in this manuscript. The experimental findi

The experiment was conducted using Potato( Solanum tuberosum L.) at the eastern Radwaniyah at private field during fall season 2020/2021 and spring 2021 to study the effect of nitrogen levels to 350, 275, 200 kg N h-1 ( N1, N2, N3) and phosphorous to 100, 180, 360 kg P2O5 h-1 ( P1, P2, P3) and potassium to 100, 200, 300 kg K2O h-1 ( K1, K2, K3) to vegetative growth and yield of industrial potato, The seeds of the hybrid potato Sinora, Class A, were planted in the fall season on 15/9/2020 and Elite in the spring season on 31/1/2021. The experimental fertilizers were added in four batches and in proportions according to the stages of plant age, Factorial experiment with RCBD using three replications. The results showed that changing t

Communication is one of the main elements of culture, it is the source of its formation and a factor of its development and spread. Communication is a 'dynamic' cultural process and is an integral part of the political, social, economic and cultural aspects of people. Therefore, mass communication means help in the course and movement of individuals and cultural communities. The relationship between media and culture according to this perspective is one of many key factors and influential forces that make it coherent and sometimes intertwined. It is a problematic relationship that leads to research and study in order to lay the right foundations in the orientation towards the audience.

Mass communication has many basic functions.

In this work, MWCNT in the epoxy can be prepared at room temperature and thickness (1mm) at different concentration of CNTs powder. Optical properties of multi-walled carbon nanotubes (CNTs) reinforced epoxy have been measured in the range of (300-800)nm. The electronic transition in pure epoxy and CNT/epoxy indicated direct allowed transition. Also, it is found that the energy gap of epoxy is 4.1eV and this value decreased within range of (4.1-3.5)eV when the concentration of CNT powder increased from (0.001-0.1)% respectively.
The optical constants which include (the refractive index (n), the extinction coefficient (k), real (ε1) and imaginarily (ε2) part of dielectric constant calculated in the of (300-800)nm at different concent