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 .

Inhibition of T cell derived cytokine production could help suppress osteoclast differentiation in inflammatory skeletal disorders. Bisphosphonates are typically prescribed to prevent inflammatory bone loss but are not tolerated by all patients and are associated with an increased risk of osteonecrosis of the jaw. In light of this other anti-resorptives such as phytoestrogens are being considered. However the effect of phytoestrogens on T cell-induced osteoclast formation is unclear. The effect of genistein and coumestrol on activated T cell-induced osteoclastogenesis and cytokine production was therefore examined. Concentrations of genistein and coumestrol (10−7 M) previously shown to directly inhibit osteoclast formation also suppressed

In Iraq, the risk of soil pollution by petroleum products increases with the growth of oil exploration, production and shipping large quantities of oil through pipelines over thousands of kilometers. Numerous oil spills have been documented recently in many sites due to damage in the oil industry infrastructures, which have led to soil contamination causing serious environmental hazards and deterioration to the soil and its engineering properties. So, it is essential to investigate the impact of oil leakage through the soil stratum consequently, assessing the eligibility of the contaminated soil for construction projects or identifying the appropriate treatment method. The paper investigates the general behaviour and the associated variatio

This article describes how to predict different types of multiple reflections in pre-track seismic data. The characteristics of multiple reflections can be expressed as a combination of the characteristics of primary reflections. Multiple velocities always come in lower magnitude than the primaries, this is the base for separating them during Normal Move Out correction. The muting procedure is applied in Time-Velocity analysis domain. Semblance plot is used to diagnose multiples availability and judgment for muting dimensions. This processing procedure is used to eliminate internal multiples from real 2D seismic data from southern Iraq in two stages. The first is conventional Normal Move Out correction and velocity auto picking and

Owing to high antibacterial resistance of Pseudomonas aeruginosa, it could be considered as the main reason behind the nosocomial infections. P. aeruginosa has a well-known biofilm forming ability. The expression of polysaccharide encoding locus (pelA gene) by P. aeruginosa is essential for this ability. The purpose of the current research was to determine the biofilm formation in P. aeruginosa isolated from clinical samples and to evaluate the role of the selected PelA gene in biofilm formation using PCR method in Iraqi patients. Results revealed that 24 (96%) isolates were found to have the ability to form biofilm that was remarkably related to gentamicin resistance. Moreover, the pelA gene was found in all biofilm-producers. In c

The objective of the conventional well testing technique is to evaluate well- reservoir interaction through determining the flow capacity and well potential on a short-term basis by relying on the transient pressure response methodology. The well testing analysis is a major input to the reservoir simulation model to validate the near wellbore characteristics and update the variables that are normally function of time such as skin, permeability and productivity multipliers.

Well test analysis models are normally built on analytical approaches with fundamental physical of homogenous media with line source solution. Many developments in the last decade were made to increase the resolution of transient response derivation to meet the

    Examining of 80 feces samples showed that 31 samples of the house and stray cats harbored either single or mixed infection with eight species of parasites and protozoa with a total infection rate 38.75 %.The results on parasite classes are: Toxocara cati (5%), Ancylostoma tubeforme (3.75%), Capillaria felis(3.75%), Isospora sp.(10%), Cryptosporidium parvum(3.75%), Cryptosporidium muris (6.25%), Toxoplasma gondi (3.75%), Giardia sp.(2.5%) infection from feces of cats that showed single, double and triple infections. Our findings revealed the risk for public health, thus preventive measures should be implemented.

The aim of this study is to use style programming goal and technical programming goal fuzzy to study assessing need annual accurately and correctly depending on the data and information about the quantity the actual use of medicines and medical supplies in all hospitals and health institutions during a certain period where they were taking the company public for the marketing of medicines and medical supplies sample for research. Programming model was built goal to this problem, which included (15) variable decision, (19) constraint and two objectives:

1 - rational exchange of budget allocated for medicines and supplies.
2 - ensure that the needs of patients of medicines and supplies needed to improve