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 Flanagan Aptitude Classification Tests (FACT) assesses aptitudes that are important for successful performance of particular job-related tasks. An individual's aptitude can then be matched to the job tasks. The FACT helps to determine the tasks in which a person has proficiency. Each test measures a specific skill that is important for particular occupations. The FACT battery is designed to provide measures of an individual's aptitude for each of 16 job elements.

The FACT consists of 16 tests used to measure aptitudes that are important for the successful performance of many occupational tasks. The tests provide a broad basis for predicting success in various occupational fields. All are paper and pen

The toxicity effect of some heavy metals (Lead, Cadmium, Copper, and Zinc) on the growth of alga Scenedesmus dimorphus which belongs to the Division of Chlorophyta was studied and depended on the total cell number . The growth rate and doubling time were also calculated accordingly in present of absent of the the heavy metals . There were differences in toxic effects of the metals (p<0.05) . The growth was decreased gradually with alga when exposured to Lead at 15,20 and 25 mg/l in comparison with the control , mean while 30 mg/l caused an acute decrease in growth . Treating the alga with 0.05,0.1,0.5 mg/l concentration of Cadmium the number of cells decreased while at 1 mg/l the effect was more pronounced . As for Copper the conc

Locking of the knee is a one of the commonest orthopedic outpatient presentation. This patient usually need magnetic resonance imaging (MRI) when there is suspected lesion in the soft tissue clinically. Meniscal tears is the first differential diagnosis when accompany with painful knee. (1, 2)
Giant cell tumor (GCT) is benign a localized nodular tenosynovitis often occur in the tendon sheath , Mostly involve the hand tendons in middle age group between 30 and 50 years old , female affect more than male.(3,4) The WHO defines two well-known kinds of giant cell tumor: (1) pigmented villonodular synovitis ( generalized type), which mainly involve the joints of the lower limb and (2) giant cell tumor of the tendon sheath ( localized type)

Liver is considered as the first target for the toxic effects of toxins and other xenobiotics, and this can be attributed to its role as a site which receive all absorbed xenobiotics from the gastrointestinal tract and its role as a major site for biotransformation of xenobiotics. The present study was designed to evaluate the possible hepatoprotective effect of benfotiamine against CCl₄-induced hepatotoxicity in rats. The study was conducted on 48 male albino rats; the animals were allocated into 8 groups (6 rats in each group) and treated as follow: 4 groups treated with oral doses of either normal saline, benfotiamine (100 mg/kg), thiamine (100 mg/kg), N-acetylcystein (400 mg/kg) only without induction of hepatic damage. Th

Carbon nanoparticles are prepared by sonication using carbon black powder. The surface morphology of carbon black (CB) and carbon nanoparticles (CNPs) is investigated using scanning electron microscopy (SEM). The particles size ranges from 100 nm to 400 nm for CB and from 10 nm to 100 nm for CNPs. CNPs and CB are mixed with silicon glue of different ratios of 0.025, 0.2, 0.05, and 0.1 to synthesis films. The optical properties of the prepared films are investigated through reflectance and absorbance analyses. The ratio of 0.05 for CNPs and CB is the best for solar paint because of its higher solar water heater efficiency and is then added to the silicon glue . Temperature of cold water and temperature of hot water in storage tank were ta

In this study, evaluate the impact of organic extracts of leaf butterfly Albzl in some aspects of life has been affected performance ratio destruction of eggs increased by 0.8% extract Alorat ethanol solvent, ethyl acetate and hexane, respectively ..

Pyrolysis of high density polyethylene (HDPE) was carried out in a 750 cm3 stainless steel autoclave reactor, with temperature ranging from 470 to 495° C and reaction times up to 90 minute. The influence of the operating conditions on the component yields was studied. It was found that the optimum cracking condition for HDPE that maximized the oil yield to 70 wt. % was 480°C and 20 minutes. The results show that for higher cracking temperature, and longer reaction times there was higher production of gas and coke. Furthermore, higher temperature increases the aromatics and produce lighter oil with lower viscosity.

In this work, MWCNT in the epoxy can be prepared at room temperature and thickness (1mm) at different concentration of CNTs powder. Optical properties of multi-walled carbon nanotubes (CNTs) reinforced epoxy have been measured in the range of (300-800)nm. The electronic transition in pure epoxy and CNT/epoxy indicated direct allowed transition. Also, it is found that the energy gap of epoxy is 4.1eV and this value decreased within range of (4.1-3.5)eV when the concentration of CNT powder increased from (0.001-0.1)% respectively.
The optical constants which include (the refractive index (n), the extinction coefficient (k), real (ε1) and imaginarily (ε2) part of dielectric constant calculated in the of (300-800)nm at different concent