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 .

Abstract

            Itraconazole is a triazole antifungal given orally for the treatment of oropharyngeal and vulvovaginal candidiasis, for systemic infections including aspergillosis, candidiasis,  and for the prophylaxis of fungal infections in immunocompromised patients.

           The study aimed to formulate a practical water-insoluble Itraconazole, with insufficient bioavailability as nanosuspension to increase aqueous solubility and improve its dissolution and oral bioavailability.

          Itraconazole nanosuspension was produced by a

Resistance spot welding (RSW) aluminum alloys has a major problem of inconsistent quality from weld to weld, because of the problems of the non-uniform oxide layer. The high resistivity of the oxide causes strong heat released which influence significantly on the electrode lifetime and the weld quality. Much effort has been devoted experimentally to the study of the sheet surface characteristics for as-received sheet and surface pretreatment sheet by pickling in NaOH and glassblasted with three thicknesses (0.6, 1.0, and 1.5 mm) of AA1050. Three different welding process parameters energy setup as a low, medium, and high were carried. Tensile-shear strength tests were performed to indicate the weld quality. Moreover, microhardness tests,

Core decompression is one of the commonest used techniques in the handling of osteonecrosis of the pre-collapsed head of the femur. Core decompression had succeeded in preserving the hip joint and delaying the requisite for total hip replacement, but it had failed in the induction of osteogenesis in the necrotic area, thus augmenting core decompression with biological agents to induce osteogenic activity. To assess the effects of platelet-rich plasma in non-traumatic avascular necrosis of the hip joint (early stage) after core decompression. Interventional comparative study for twenty-four patients (32 hip joints) with AVN of the head of the femur was involved in this prospective study, and they were separated into two groups of 16

BACKGROUND: Femoral shaft fracture is a common fracture in pediatric age group reaching 62% of all fracture shaft femur in children in spite of rapid union rate and successful conservative treatment but some cases need surgical intervention and one of the methods using plate and screw by the lateral approach. AIM: This study aims to compare functional outcome fixation of mid-shaft femur fracture in children by plate and screws between (subvastus lateralis and transvastus lateralis) regarding infection, union, and limitation of knee movement. PATIENT AND METHOD: The study was done on 30 children who had diaphyseal fracture femur in Al-Kindy Teaching Hospital in period (April 2018–April 2020) with 6 months follow-up, and the pa

Aim: The reduction in the amount of marginal bone is the most important demand for the long term success of dental implants. This prospective clinical study was aimed to investigate the marginal bone loss of early loaded SLActive implants with different dimensions and surgical approaches. Materials and methods Fifteen patients aged from 18 to 60 years were divided into 2 groups (flapped and flapless approach) that underwent delayed implant placement protocol with SLActive implants. The marginal bone level was estimated by cone-beam computed tomography during three different periods: preoperatively, 8 weeks after surgery and 24 weeks after loading of the prosthesis. Results: The mean value of marginal bone level was not significantly chan

In this study, stabilization of expansive soils using waste materials namely; Cement Kiln Dust (CKD), and waste plastic bottles (WPB) was experimentally investigated. Using CKD and WPB are exponentially increasing day by day, due to their capability to solve both environmental and geotechnical problems successfully. Expansive soils were collected from locations with a wide range of plasticity index (PI) (15 - 27) and liquid limit (LL) (35% - 64%). Stabilizer percentages were varied from 0% to 20%, and curing durations for CKD cases were 7 and 28 days. Results showed the best percentages of CKD and WPB are 12% of each one respectively. LL, plastic limit (PL), and swelling percent (SP) loss were observed, which are 46%, 55%, and 96% respec

Pablo Neruda's artistic distinctiveness can be considered in two ideas or attitudes of romanticism. First, the imagination, which is the result of conduct and spirituality, and second, the individualism, which is a collection of mysterious mysteries from the texts of individuality based on philosophical sonnets. His collection of poems points out the ethereality and indescribability of life, employing the reality of life at the level of human perception in a symbolic language. In other words, Pablo Neruda recreates the meanings in poetry through the three ideas of reduction, interpretation, and analysis. "What is the essential connection between individualism and the symbolic language of Pablo Neruda's imagination and What are the reason