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 .

Background: Preparation of platelet-rich fibrin (PRF) is a simple, low cost and minimally invasive method to obtain a natural concentration of autologous growth factors that is widely used to accelerate soft and hard tissue healing, thus, PRF is used in different fields of medicine. The aim of this study was to evaluate the effect of local application PRF on stability of dental implants. Materials and methods: nineteen healthy patients with adequate alveolar bone with two or more adjacent missing teeth and/or bilaterally symmetric to the midline (split-mouth design) missing teeth participated in this study. Each patient received at least two dental implants (Dentium Co., Korea). After surgical preparation of the implant sockets, the PRF was

Leishmania is auxotroph to folic acid,antifolates drug inhibit the synthesis and conversion of folate derivatives. In this study, cytotoxic effect of methotrexate was investigated on the procyclic promastigotes proliferation of L. donovani. The results showed a significant (p ≥ 0.05) difference in growth of treated groups at high concentrations (1000, 500, 250, 125.5) μM after 24, 48 hrs., while at 72 hrs. significant difference was observed at all concentration. The IC50 values was measurable after 24, 48 and 72 hrs. and it was 174.238, 52.283 and 109.175 μM, respectively. The present study showed the cytotoxic effect of methotrexate on the proliferation of promastigotes of the visceral type of Leishmania.

This paper investigates the issue of surface-type effects on traffic noise in Baghdad. Since the raw materials for both flexible and rigid paving are available from local sources, the decision on selecting the type of paving which depends on the budget of the project and the road's importance and function. Knowing that for high traffic volumes and a high percentage of heavy vehicles, rigid pavement is more suitable compared to flexible pavement. In Baghdad, some highways consist of flexible pavement and others of combined pavement (flexible segments and rigid segments), so the study of the effect of surface type on traffic noise becomes an important matter. This study selected three highways: one with flexible pavement a

Widely present in the environment, arsenic trioxide has been identified as a genotoxic substance that poses a serious risk to public health. The genotoxic potential of arsenic at low allowable dosage levels is assessed in this study. Four groups of twelve adult rats each were created from the 48 total. Animals in Group I were used as controls Chromosome abnormalities found in bone marrow cells were used to assess the mutagenic potential of arsenic. Hematological parameters were also assessed. At 60 and 90 days, the percentage of microsomal degranulation in the hepatic fraction increased and the amounts of RNA and proteins considerably reduced (P < 0.01) in all three dosages given. was employed in order to assess hematological par

Permanent deformation (rutting) of asphalt mixtures is one of the major forms of distress. Aggregate gradation is one of the most important factors affecting the permanent deformation of asphalt mixtures. Other variables are also important to understand their effects on the mixture such as temperature, binder content and compaction level. For this purpose 6 different aggregate gradations have been chosen and each one of them has been manufactured / tested with different variables. The results showed that at relatively low temperature there is little effect of aggregate packing on the permanent deformation. However, as the temperature increases the effect of gradation becomes apparent, in that the better the packing the better the resistance

Laser beam has been widely used to improve the mechanical properties of the metals. It used for cutting, drilling, hardening, welding……etc. The use of Laser beam has many features in accuracy and speeding in work, also in the treatment of metals locally, and in the places that is hard to reach by traditional ways. In this research a surface treatment was done to medium carbon steel (0.4%C) which is common kind of steel that is used in industry. Pulsing Neodymium -YAG Laser has been used and 1.06 micrometer wave length and 5 msec and the distance is about 30 centimeter between the exit area of the Laser beam from the system and the piece that treated . We are going to check the fatigue resistance for samples that is

This paper investigates the issue of surface-type effects on traffic noise in Baghdad. Since the raw materials for both flexible and rigid paving are available from local sources, the decision on selecting the type of paving which depends on the budget of the project and the road's importance and function. Knowing that for high traffic volumes and a high percentage of heavy vehicles, rigid pavement is more suitable compared to flexible pavement. In Baghdad, some highways consist of flexible pavement and others of combined pavement (flexible segments and rigid segments), so the study of the effect of surface type on traffic noise becomes an important matter. This study selected three highways: one with flexible pavement and two with combined