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 .

planning is among the most significant in the field of robotics research.  As it is linked to finding a safe and efficient route in a cluttered environment for wheeled mobile robots and is considered a significant prerequisite for any such mobile robot project to be a success. This paper proposes the optimal path planning of the wheeled mobile robot with collision avoidance by using an algorithm called grey wolf optimization (GWO) as a method for finding the shortest and safe. The research goals in this study for identify the best path while taking into account the effect of the number of obstacles and design parameters on performance for the algorithm to find the best path. The simulations are run in the MATLAB environment to test the

The research aimed to identify the effects of the modern of technology on translating the media term from English language to Arabic. and try to identify the use of the impact of foreign media terminologies on the Arabic media term, and to know the effect of the translation process on Arabic media terminologies.

This research is considered an analytical study by using survey study for 111 items and the results for the study as following:

1.High percentage of the (use of foreign terms work to low the level of production) was (68.13%) and average 3.55

2.The percentage of (The multiplicity of translation of the foreign term into Arabic effects on the opinions and cognitive ideas of the Arab researcher and affects the

This age and the third millennium is the dominance of information technology on most of the administrative work in the developed world and the need for the so-called electronic marketing- and need our developing society to the development of our work to transform the traditional management and routine of it to the electronic management in order to save effort, time and cost They are the backbone speed to complete the work, The principle applications of electronic management to achieve the maximum possible benefit from the implementation of the administrative work of the society and institutions and the private sector the government in the state. The use of electronic management makes us safe from

وضع (woodruff and siddoway, 1965) معادلة لتقدير مفقودات التربة بواسطة التعرية الريحية تدعى (معادلة التعرية الريحية (WEQ، إذ يعطي حل هذه المعادلة الكمية القصوى للتعرية الريحية تحت ظروف حقلية معينة، وتعتبر دليل في تحديد الأساليب الضرورية لمعالجة التعرية الريحية في تلك الظروف (الطيف وآخرون، 1991). تهدف هذه الدراسة إلى معرفة مدى تأثير التغيرات المناخية في منطقة السماوة جنوب العراق وبغداد وسط العراق طوال فترة 34 سنة في قيم مفقودات

Extraction and Description of Urease Enzyme Produced from Staphylococcus saprophyticus and study of its effect on kidney and bladder of white mice

In this paper, the generalized inverted exponential distribution is considered as one of the most important distributions in studying failure times. A shape and scale parameters of the distribution have been estimated after removing the fuzziness that characterizes its data because they are triangular fuzzy numbers. To convert the fuzzy data to crisp data the researcher has used the centroid method. Hence the studied distribution has two parameters which show a difficulty in separating and estimating them directly of the MLE method. The Newton-Raphson method has been used.

The study aimed to evaluate the antimicrobial activity using different concentrations of aqueous and alcoholic extracts of dried lemongrass leaves. Chemical phytochemical tests were performed for aqueous and alcoholic extracts of lemongrass. Antimicrobials activity was tested using agar disc diffusion method against Escherichia coli and Staphylococcus aureus. The results of the study showed that the aqueous extract of dried lemon leaves was highly effective (P≤0.05) against S. aureus, as the inhibition diameter was 22 mm for 50 dilution, while the inhibition diameter decreased to 15 mm for concentration 100. As for the alcoholic extract only, the diameter of inhibition decreased significantly (P≤0.0

المستخلص
ى A ي تعن A ات الت A والدراس (Genre Analysis) يA وع الادب A ل الن A ي تحلی A ات ف A دث الاتجاھ A ع اح A جاماً م A انس
ن AA ابني ونكرس AA ھ-جی AA ون ١٩٩٨ ، بارجلی AA انس و ج AA ودلي-ایف AA ال (دی AA رة الاعم AA الات دائ AA ال الاتص AA ي مج AA اب ف AA بالخط
ر A یل اكث A وبتفاص .(Annual Reports) ١٩٩٩ ) یركز ھذا البحث على نوع مالي معین وھو التقاریر السنویھ
ھ AA ھ بحت AA ا مالی AA ف بكونھ A ي تتص AA نویھ الت AA اریر الس AA ة التق A ان طبیع AA ار بش AA ع الانتش AA اد ا

The comparison of double informative priors which are assumed for the reliability function of Pareto type I distribution. To estimate the reliability function of Pareto type I distribution by using Bayes estimation, will be  used two different kind of information in the Bayes estimation; two different priors have been selected for the parameter of Pareto  type I distribution . Assuming distribution of three double prior’s chi- gamma squared distribution, gamma - erlang distribution, and erlang- exponential distribution as double priors. The results of the derivaties of these estimators under the squared error loss function with two different double priors. Using the simulation technique, to compare the performance for