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 concept of deficit in public budget becomes a chronic economic phenomenon in most of the world, whether the advanced countries or developing countries. Despite  the difference in the visions of the economic schools to accept or reject the deficit in public budget but the opinion that prevailed is the necessity of the state to reduce the public spending which led to a continuous deficits in the public budget which consequently increased the government borrowing ,increase income taxes and wealth, consequently this weakened the in motivation in private investment which contributed to the increase of in factionary stagnation , so that governments have to cover the lack of local funding sources which become difficult to be eq

     Cloth simulation and animation has been the topic of research since the mid-80's in the field of computer graphics. Enforcing incompressible is very important in real time simulation. Although, there are great achievements in this regard, it still suffers from unnecessary time consumption in certain steps that is common in real time applications.   This research develops a real-time cloth simulator for a virtual human character (VHC) with wearable clothing. This research achieves success in cloth simulation on the VHC through enhancing the position-based dynamics (PBD) framework by computing a series of positional constraints which implement constant densities. Also, the self-collision and collision wit

The results of the study showed the statistical significant difference (P≥0.05) for each of the relative weight of the yolk and egg whites, the relative weight of the shell and the Hauh unit, which is affected positively by the addition of ground fenugreek seed and Laurels leave to the quail bird's diet. There is also a statistically significant difference positively for each of the percentage of ash, protein and carbohydrates for qualis egg, while there is no significant difference for both the percentage of moisture and fat. The results of the mineral estimation showed an increase in each of the elements of iron, copper and cadmium from the addition of fenugreek and laurels leave, while there was no significant difference for

Objective of the research This study aimed to manufacture an innovative device that enables the player to walk after the operation and improves functional efficiency through improvement in the range of motion as well as improvement in the size of the muscles working on the knee joint Imposing research There are statistically significant differences between the pre and posttests of the experimental and control groups, there are Statistically significant differences between the post-tests between the experimental group and the control group in favor of the experimental group of the research sample. The researchers used the experimental approach by designing the control and experimental groups with a test (pre-post) for the suitabili

In this study, plastic wastes named (PET and PVC) were used to prepare polymer matrix composite (PMC) which can be used in different applications. Composite materials were prepared by mixing unsaturated polyester resin (UP) with plastic wastes, two types of plastic waste were used in this work included polyethylene-terephthalate (PET) and Polyvinyl chloride (PVC) with various weight fractions (0, 5,10,15, 20 and 25%) added as a filler in flakes form. In this work, some of the tests that were carried out included (tensile, bending, and compressive strength) as mechanical tests, in addition to (thermal conductivity and water absorption) as physical tests. The values of tensile, compressive strength and Young's modulus of UP increased after

A field experiment was conducted at the experimental field of botanical garden, faculty of science, university of Baghdad, in order to study the effect of plant density on growth and yield of two local cultivars of sunflower (Sin Althieb and Shumose). The densities used were 4.4 and 8.8 plant/m². The results showed difference between cultivars in their agronomic traits and their yields. There was a significant increase in plant height and leaf area index by increasing the plant density, while head diameter, number of seeds and leaf area decreased. But the most significant effect was the increasing in yield and biological yield by increasing the plant density. There was an increase by 72% and 58% in the yield and 79% an

The study aimed to identify the degree of commitment of social workers working in the Ministry of Social Development to the professional principles of the social work profession in light of the Corona pandemic, and the sample consisted of (135) specialists. The study reached several results: the most important one is  the degree of commitment of social workers working in the Ministry of Social Development to the professional principles of social service was great. The other result is the absence of statistically significant differences according to the variables of sex and place of residence. Moreover, the results also showed the absence of statistically significant differences in the principles of ( Acceptance o

This study involved the effect of the aqueous extracts of two plants, Origanum vulgare L.(1), Trigonella Foenum Graecum L. (Fenugreek) seeds(2) on the growth of cancer cell lines. Rhabdomyo sarcomas (RD) of human cell line and female intestine cells of Albino mice (L20B) in vitro System. These extracts were compared with the known anticancer drug Cis-platinum(Cis-Pt) as a positive control. The phytochemical tests were used for screening the active compounds in plants. The inhibition activity assay was used as a parameter of the cytotoxic effect of these extracts. Cancer cell lines were treated with four concentrations of Cis-platin, 31.25, 62.5, 125 and 250 ?g/ml for 72 hour exposure time. The same concentrations were used for the other ext

Background: Mineral Trioxide Aggregate (MTA) and BiodentineTM cements are new materials with numerous exciting clinical applications. Both have appreciable properties which include good physical properties and the ability to stimulate tissue regeneration as well as good antibacterial effects. The aim of this study was to investigate and compare the antibacterial effects of MTA and BiodentineTM, when they were mixed with different concentrations of aqueous solutions of Black Seed extract, against Enterococcus faecalis. Materials and methods: MTA and BiodentineTMwere prepared according to the manufacturer’s instructions. The method of Mawlood was followed to prepare the Black Seed aqueous solution. Agar diffusion method on Brain Heart