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 .

Biodiesel is an environmentally friendly fuel and a good substitution for the fossil fuel. However, the purity of this fuel is a major concern that challenges researchers. In this study, a calcium oxide based catalyst has been prepared from local waste eggshells by the calcination method and tested in production biodiesel. The eggshells were powdered and calcined at different temperatures (700, 750, 800, 850 and 900 °C) and periods of time (1, 2, 3, 4 and 5 hr.). The effect of calcination temperature and calcination time on the structure and activity of the solid catalyst were examined by X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM), and Brunaure-Emmett-Teller (BET). The optimum catalyst performance was obtained at 900 °C

Catalytic reduction is considered an effective approach for the reduction of toxic organic pollutants from the environment, but finding an active catalyst is still a big challenge. Herein, Ag decorated CeO2 catalyst was synthesized through polyol reduction method and applied for catalytic reduction (conversion) of 4-nitrophenol (4-NP) to 4-aminophenol (4-AP). The Ag decorated CeO2 catalyst displayed an outstanding reduction activity with 99% conversion of 4-NP in 5 min with a 0.61 min−1 reaction rate (k). A number of structural characterization techniques were executed to investigate the influence of Ag on CeO2 and its effect on the catalytic conversion of 4-NP. The outstanding catalytic performances of the Ag-CeO2 catalyst can be assigne

Background: Parkinson's disease (PD) is a neurodegenerative aging disease, with idiopathic PD being most common. Gastrointestinal tract disorders (GITD) and microbiota changes may trigger idiopathic PD. Neurotoxins from microbiota can travel from the gut to the brain via the brain-gut axis (BGA), leading to α-syn protein misfolding and dopaminergic neuron death. Methods: The aim of the current study was to investigate the link between PD and GITD by measuring several biochemical and immunological markers in 142 patients. The biochemical markers measured were vitamins B6, B12, and D, calcium, serotonin, ghrelin, dopamine, and α-syn protein. The immunological markers included transforming growth factor-beta (TGF-β), tu

The present study reports the effect of temperature and liquid hourly space velocity (LHSV) on the cumene cracking reaction rate and selectivity by using a laboratory continuous flow unit with fixed bed reactor operating at atmospheric pressure. The prepared HX zeolite was made from Iraqi kaolin with good crystallinity .The activity and selectivity of prepared HX-zeolite was compared with standard HY zeolite and HX zeolite catalysts in the temperature range of 673-823K and LHSV of 0.7-2.5 h-1 . It was found that the cumene conversion increases with increasing temperature and decreasing LHSV at 823K and LHSV of 0.7 h-1 the conversions 65.32, 42.88 and 59.42 mol% for HY, HX and prepared HX catalysts respectively and at LHSV of 2.5 h-1 and th

The American-European dispute is one of the important issues that dominated international relations during the nineteenth century in particular, although the previous period witnessed the emergence of a dispute over the right to control these colonies, which the United States of America, especially after the proclamation of the Monroe Doctrine in 1823, is a natural right and that It has the ability to prevent European countries from interfering in the affairs of the American continent, so the United States of America entered into continuous disputes with European countries, which were constantly directing their eyes towards the Spanish colonies in the American continent. But the American government had priority in controlling those colonies

Fingerprints are commonly utilized as a key technique and for personal recognition and in identification systems for personal security affairs. The most widely used fingerprint systems utilizing the distribution of minutiae points for fingerprint matching and representation. These techniques become unsuccessful when partial fingerprint images are capture, or the finger ridges suffer from lot of cuts or injuries or skin sickness. This paper suggests a fingerprint recognition technique which utilizes the local features for fingerprint representation and matching. The adopted local features have determined using Haar wavelet subbands. The system was tested experimentally using FVC2004 databases, which consists of four datasets, each set holds

Due to the high mobility and dynamic topology of the FANET network, maintaining communication links between UAVs is a challenging task. The topology of these networks is more dynamic than traditional mobile networks, which raises challenges for the routing protocol. The existing routing protocols for these networks partly fail to detect network topology changes. Few methods have recently been proposed to overcome this problem due to the rapid changes of network topology. We try to solve this problem by designing a new dynamic routing method for a group of UAVs using Hybrid SDN technology (SDN and a distributed routing protocol) with a highly dynamic topology. Comparison of the proposed method performance and two other algorithms is simula

The accounting system of government is considered an important tool to follow up the financial transactions that reflect the activities of governmental units and by which the useful information for estimating governmental annual revenues and expenditures are provided through the state public budget because it is an information system that provides detailed past performance, as well as measures the efficiency of the governmental agencies performance in implementing the budget, and the of success governmental units is measured through the type of services and programs offered, their size and the possibility of achieving the objectives assigned to them. The medical evacuation program is one of the medical and curative health services provid