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 .

Maximum likelihood estimation method, uniformly minimum variance unbiased estimation method and minimum mean square error estimation, as classical estimation procedures, are frequently used for parameter estimation in statistics, which assuming the parameter is constant , while Bayes method assuming the parameter is random variable and hence the Bayes estimator is an estimator which minimize the Bayes risk for each value the random observable and for square error lose function the Bayes estimator is the posterior mean. It is well known that the Bayesian estimation is hardly used as a parameter estimation technique due to some difficulties to finding a prior distribution.

The interest of this paper is that

Polymethylmethacrylate film (PMMA) of thickness 75 μm was evaluated Spectrophotometrically for using it as a low-doses gamma radiation dosimeter. The doses were examined in the range 0.1 mrad-10 krad. Within an absorption band of 200-400 nm, the irradiated films showed an increase in the absorption intensity with increasing the absorbed doses. Calibration curves for the changes in the absorption differences were obtained at 218, 301, and 343 nm. At 218 nm the response for the absorbed doses is a linear in the range 10 mrad- 10 krad. Hence it is recommended to be adopted as an environmental low doses dosimeter

Bioaccumulation of heavy metals in the terrestrial invertebrates in Al-Jadriyia district Baghdad- Iraq were investigated. Forth terrestrial invertebrates snails, slug, isopods, and diplopods , were selected for this study. The results showed that all invertebrate groups have the ability in accumulate considerable amounts of heavy metals. Higher levels of zinc and copper were observed in the isopods specimens, it's about ( 60.50±0.58 ) and ( 96.00±0.58 ) ppm respectively , while higher levels of lead were observed in the diplopods specimens ,it's about ( 23.00±1.15 ) ppm ,but the higher levels of both iron and cadmium were observed in snail specimens , it's about ( 590.00±1.15 ) and ( 9.50±1.15 ) ppm respectively .but the

Systemic lupus erythematosus (SLE) is an autoimmune disease with polymorphic expression. B cells have an essential contribution in immune system activation via the production of different cytokines and functioning as potent antigen-presenting cells. Therefore, a drug that particularly targets B cells may represent an ideal therapeutic approach for SLE. Rituximab (RTX), an anti-CD20 monoclonal antibody causing transient B-cell depletion, has been used to manage SLE. This study aims to assess Rituximab effects on lupus nephritis (LN) patients when added to conventional immunosuppressants. Twenty four patients, 15-32 years old, with class III/IV/V LN were involved in this study. All were on steroids before lupus nephritis occurrence. They were

Systemic lupus erythematosus (SLE) is an autoimmune disease with polymorphic expression. B cells have an essential contribution in immune system activation via the production of different cytokines and functioning as potent antigen-presenting cells. Therefore, a drug that particularly targets B cells may represent an ideal therapeutic approach for SLE. Rituximab (RTX), an anti-CD20 monoclonal antibody causing transient B-cell depletion, has been used to manage SLE. This study aims to assess Rituximab effects on lupus nephritis (LN) patients when added to conventional immunosuppressants. Twenty four patients, 15-32 years old, with class III/IV/V LN were involved in this study. All were on steroids before lupus nephritis occurrence. They were

Background Osteoarthritis is a chronic degenerative disorder with rising prevalence. Early detection of structural damage is difficult. Consequently, there is a pressing demand for reliable biomarkers that enable an earlier diagnosis of osteoarthritis. The aim is to investigate the level of serum fibulin-3 in patients with primary knee osteoarthritis and its correlation with disease severity. Subjects and methods A case–control study was conducted at the Baqubah Teaching Hospital from November 2023 to January 2024. One hundred twenty persons participated in this study (eighty females with the diagnosis of knee osteoarthritis in its early and late stages, and forty age-matched, apparently healthy control. Serum fibulin-3, ESR, CRP, and cal

Salmonella enteritidis one of more important as epidemiological bacteria between other salmonella types. It is very important pathologically that cause food poising and gastrointestinal tract infections. This study includes some of immunological changes that appear by ELISA test and antibiotic sensitivity test against these bacteria in mice. ELISA test results appears high immunological response happen after 3 days of inoculation, mean titration readings beginning 0.198 and the maximum mean titration after 15 days of inoculation 1.538 and begin to decrease after this time slowly to remain about 0.297 after 40 days of inoculation. An antibiotics sensitivity test result appears, this bacteria sensitive to Chloramphenicol, Ceftriaxone,

        The experimental and theoretical methods were studied for inhibition of the corrosion titanium in HCl by using neomycin sulfate drug. The results of neomycin sulfate drug had good corrosion protection for titanium in hydrochloric acid and the inhibition efficiency (%IE) increasing with increasing concentration of drug because the neomycin sulfate drug had adsorption from acid solution on surface of titanium metal. The program of hyperchem-8.07 was used for theoretical study of the drug by molecular mechanics and semi-empirical calculations. Quantum chemical was studied drug absorption and electron transferred from the drug to the Titanium metal, also inhibition potentials of drug attachment with the (LUMO-HOMO) energy gap,