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 .

The electrospun nanofibers membranes have gained considerable interest in water filtration applications. In this work, the fabrication and characterization of the electrospun polyacrylonitrile-based nonwoven nanofibers membrane are reported. Then, the membrane's performance and antifouling properties were evaluated in removing emulsified oil using a cross flow filtration system. The membranes were fabricated with different polyacrylonitrile (PAN) concentrations (8, 11, and 14 wt. %) in N, N-Dimethylformamide (DMF) solvent resulted in various average fiber sizes, porosity, contact angle, permeability, oil rejection, and antifouling properties. Analyses of surface morphology of the fabricated membranes before and after oil removal revealed

Introduction and Aim: The pro-inflammatory cytokine IL-39, a member of the IL-12 family plays a key role in the inflammatory response by modulating immune cell activity and inflammation. A literature search shows no study undertaken for the effect of IL-39's on arthritis so far. Hence, the purpose of this study was to investigate the role of IL-39 in rheumatoid arthritis. Materials and Methods: This study involved 80 patients with rheumatoid arthritis registered at the Rheumatology Clinic at Baghdad teaching hospital. The patients were divided into three groups based on treatments received. Group 1 included patients who were not on any treatment for arthritis, Group 2 with patients on hydroxychloroquine and or prednisone treatment,

This research utilized natural asphalt (NA) deposits from sulfur springs in western Iraq. Laboratory tests were conducted to evaluate the performance of an asphalt mixture incorporating NA and verify its suitability for local pavement applications. To achieve this, a combination of two types of NA, namely soft SNA and hard HNA, was blended to create a binder known as Type HSNA. The resulting HSNA exhibited a penetration grade that adhered to Iraqi specifications. Various percentages of NA (20%, 40%, 60%, and 80%) were added to petroleum asphalt. The findings revealed enhanced physical properties of HSNA, which also satisfied the requirements outlined in the Iraqi specifications for asphalt cement. Consequently, HSNA can serve as an

Background: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, and evaluating its effect as a separating medium on some mechanical properties such as (indentation hardness and transverse strength) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separating medium. Materials and M

60 patients diagnosed as having urticaria were included in the study ; 30 patients were effected with acute urticaria and 30 patients were affected with chronic urticaria. In addition, 30 healthy adult volunteers were selected as control group .The patients and control groups sera were examined with enzyme linked immunosorbent assay ( ELISA) to detect total level IgE and radial immunodiffusion (RID) to detect levels of IgG , IgA and IgM . The total level of IgE in acute urticaria ( 1.45±0.13) IU/mL and chronic urticaria (2.12 ± 0.10) IU/mL patients were significantly higher than the control groups ( 0.85 ± 0.10)IU/mL (p<0.05). The level of IgG in acute urticaria ( 12.5± 0.42) g/L and chronic (13.16±0.40) g/L patients , IgA in acute (2.

     Pregnancy and delivery are physiological conditions that are marked by abrupt alterations to hormones, immunological and molecular characters. The current study aimed to evaluate oxytocin (OT), prolactin (PRL), cortisol and insulin growth factor-2 (IGF-2) levels as physiological biomarkers; programmed cell death protein-1 (PD-1), programmed cell death ligand-1 (PD-L1),interleukin-6 (IL-6) as immunological biomarkers, and single nucleotide polymorphisms (SNPs; rs53576 and rs2254298) of oxytocin receptor gene OXTR as molecular factors in samples of Iraqi women undergoing caesarean section (CS) and normal delivery (ND). Blood samples were collected from 96 pregnant women at term with ages ranging between 16-43 years. Regarding

Buckling analysis of composite laminates for critical thermal (uniform and linear) and mechanical loads is reported here. The objective of this work is to carry out theoretical investigation of buckling analysis of composite plates under thermomechanical loads, and experimental investigation under mechanical loads. The analytical investigation involved certain mathematical preliminaries, a study of equations of orthotropic elasticity for classical laminated plate theory (CLPT), higher order shear deformation plate theory (HSDT) , and numerical analysis (Finite element method), then the equation of motion are derived and solved using Navier method and Levy method for symmetric and anti-symmetric cross-ply and angle-ply laminated plates t

Trickle irrigation is a system for supplying filtered water and fertilizer directly into the soil and water and it is allowed to dissipate under low pressure in an exact predetermined pattern. An equation to estimate the wetted area of unsaturated soil with water uptake by roots is simulated numerically using the HYDRUS-2D/3D software. In this paper, two soil types, which were different in saturated hydraulic conductivity were used with two types of crops tomato and corn, different values of emitter discharge and initial volumetric soil moisture content were assumed. It was assumed that the water uptake by roots was presented as a continuous sink function and it was introduced into Richard's equation in the unsaturated z

In this study, concentrations of radon and uranium were measured for twenty six samples of soil. The radon concentrations in soil samples measured by registrant alpha-emitting radon (²²²Rn) by using CR-39 track detector. The uranium concentrations in soil samples measured by using registrar fission fragments tracks in CR-39 track detector that caused by the bombardment of U with thermal neutrons from ²⁴¹ Am-Be neutron source that has flux of 5 ×10³n cm^-2 s^-1.
The concentrations values were calculated by a comparison with standard samples The results show that the radon concentrations are between (91.931-30.645Bq/m³).
The results show that also the uranium concentrat