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 .

Iron-Epoxy composite samples were prepared by added
different weight percentages (0, 5, 10, 15, and 20 wt %) from Iron
particles in the range of (30-40μm) as a particle size. The contents
were mixed carefully, and placed a circular dies with a diameter of
2.5 cm. Different mechanical tests (Shore D Hardness, Tensile
strength, and Impact strength ) were carried out for all samples. The
samples were immersed in water for ten weeks, and after two weeks
the samples were take-out and drying to conducting all mechanical
tests were repeated for all samples. The hardness values increased
when the Iron particle concentration increased while the Impact
strength is not affected by the increasing of Iron particles
c

Expansive soil spreads in Iraq and some countries of the world. But there are many problems can be occurred to the structures that built on, so we must study the characteristics of these soils due to the  problems that may be caused to these structures which built on these kinds of soil and then study the methods of treatment. The present study focuses on improving  the geotechnical properties of expansive soils by treating it Metakaolin(M). Metakaolin (M) has never been used before as an improvement material  for stabilizing the expansive soil . Metakaolin  is a pozzolanic material. It’s obtained by calcination of kaolinite clay at temperatures from 700°C to 800°C. Kaolin chemical composition is

Crystalline silicon (c-Si) has low optical absorption due to its high surface reflection of incident light. Nanotexturing of c-Si which produces black silicon (b-Si) offers a promising solution. In this work, effect of H₂O₂ concentrations towards surface morphological and optical properties of b-Si fabricated by two-step silver-assisted wet chemical etching (Ag-based two-step MACE) for potential photovoltaic (PV) applications is presented. The method involves a 30 s deposition of silver nanoparticles (Ag NPs) in an aqueous solution of AgNO₃:HF (5:6) and an optimized etching in HF:H₂O₂:DI H₂O solution under 0.62 M, 1.85 M, 2.47 M, and 3.7 M concentrations of H₂O<