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 sports field is one of the fields that are concerned with the various methods and methods because of their positive impact on the development of actual training, the investment of the exerted effort in time, and through the follow-up of the researcher in the field and academic field, I noticed that there is a weakness in explosive ability, which affects performance and skill level during training and competition Therefore, the researcher decided to prepare maximum physical exertion exercises according to the anaerobic threshold as a principle of development in many physical and skill variables because good physical performance leads to reaching the best achievements and since the skill of shooting by jumping high - either constitutes a

To study the qualitative changes in testis tissue after carbon tetrachloride (CCl4) administration and to determine whether citric acid (CA) has a protective effect against testis damage induced by CCl4. This study compared two types of CA by measuring the histoarchitecture of the testis and serum levels of progesterone, estrogen and testosterone on mice. One of the most produced organic acid is citric acid. In this study, CA produced by microbial fermentation using Aspergillus Niger 5mg/kg and derived from citrus limon 400mg/kg (lemon). Mice were treated with daily intraperitoneal (i.p.) injection for seven successive days after randomly separated into six groups: (1) control, (2) CCl4 (0.02%), (3) limon citric acid (400 mg/kg), (4) CCl4 (

The current research focuses on the extent to which the strategic orientation(entrepreneurial orientation, customer orientation, technology orientation, learning orientation, and investment orientation) affects the learning organization (building common vision, systemic thinking, personal dominance, mental models, team learning)The first hypothesis to test the connection relation between research variables and The second hypothesis was to test the relationship between these variables. In order to ascertain the validity of the hypotheses, the research was based on a questionnaire questionnaire prepared according to a number of In addition to building a fifth sub-variable for the strategic orientation (investment orientation) based

The experiment was carried out to study the effect of variety and gibberellic acid in concentration (0 and 50)mg.lat-1 and BL in five concentration (0, 0.50 ,1 ,2 and 3)mg.ltr-1 and their interaction in some chemical Characteristics and total chlorophyll for Dill plant . the experiment designed according Randomized Complete Block Design (RCBD) and three replicates per treatment, compared to the average using less significant difference at the level of probability (0.05) , the results showed the following:- The effect of brassinolide with it,s concentrations led to obtain a significant increase in all the studied characteristics, so the superiority of the concentration of 2 mg.L-1 of brassinolide in each of Ca, Mg,Fe, and total chlorophyll T

In this research work an attempt has been made to investigate about the Robustness of the Bayesian Information criterion to estimate the order of the autoregressive process when the error of this model,  Submits to a specific distributions and different cases of the time series on various size of samples by using the simulation,  This criterion has been studied by depending on ten distributions, they are (Normal, log-Normal, continues uniform, Gamma , Exponential, Gamble, Cauchy, Poisson, Binomial, Discrete uniform) distributions, and then it has been reached to many collection and recommendations related to this object , when the series residual variable is subject to each  ( Poisson , Binomial , Exponential , Dis

Background: Facial disfigurement can be the result of a congenital anomaly, trauma or tumor surgery, in many cases the prosthetic rehabilitation is indicated. Maxillofacial prosthetic materials should have desirable and ideal physical, aesthetic, and biological properties and those properties should be kept for long period of time in order to reach patient acceptance. Silicone elastomer are the most commonly used material for facial restoration because of its favorable properties mechanically and physically as the biocompatibility and good elasticity. Aim of this study: This study aimed to evaluate the effect of addition of Aluminum oxide (Al2O3) Nano fillers in different concentrations on tear strength and hardness of VST 50F room tempe

The technique of plant tissue culture has been used to In vitro micropropagation of Spilanthes acmella (L.) Murr. It is an ornamental and medicinal plant not cultivated in Iraq. Seeds were sterilized and cultuared on full strength Murashige and Skoog medium(1962)(MS). Naphthalene acetic acid (NAA), 6- furfuryl aminopurine (Kin.) growth regulators were used at the Initiation stage.The combination between IAA and Kin. was used in multiplication stage. IAA was used for rooting the shoots. Results showed that 1.5% sodium hypochlorite for 15 min was very effective for disinfecting and survival. Nodes exhibited relatively highest response as compared with apical meristems and leaflets culture. Supplying the culture medium with 1 mg/L.