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 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

The - mixing ratios of -transitions from levels in populated in the reactions are calculated in present work using - ratio, constant statisticalTensor and least squares fitting methods The results obtained are in general, in good agreement or consistent, within the associated uncertainties, with these reported in Ref.[9],the discrepancies that occurs are due to inaccuracy existing in the experimental data The results obtained in the present work confirm the –method for mixed transitions better than that for pure transition because this method depends only on the experimental data where the second method depends on the pure or those considered to be pure -transitions, the same results occur in – method

Over application courier company (DHL) to keep the quality of service to achieve customer satisfaction the adoption of precedence delivery time - A prospective study))

Become attention to quality is a global phenomenon, and I took organizations and governments around the world attaches special attention, but we can say that quality has become the first function for many organizations, and has become a management philosophy

One of the important differences between multiwavelets and scalar wavelets is that each channel in the filter bank has a vector-valued input and a vector-valued output. A scalar-valued input signal must somehow be converted into a suitable vector-valued signal. This conversion is called preprocessing. Preprocessing is a mapping process which is done by a prefilter. A postfilter just does the opposite.

The most obvious way to get two input rows from a given signal is to repeat the signal. Two rows go into the multifilter bank. This procedure is called “Repeated Row” which introduces oversampling of the data by a factor of 2.

 For data compression, where one is trying to find compact transform representations for a

The pumping station became widely used in many fields. Free surface vortices at intakes of pumps are not favorable. It may cause noise, excessive vibration, damage to the pumping structure, reduction in efficiency and flow for hydro-turbines, etc. One of the important problems encountered during the pump intake design is the depth of submergence and other design parameters to avoid strong free-surface vortices formation. This study aims to compute the critical submergence depth with some geometrical and hydraulic limitations by using Computational Fluid Dynamic (CFD) package. The mathematical model was validated with a laboratory model that had been conducted. The model of three intake pipes was investigated under five d

The study aimed to reveal the extent of the first intermediate grade science curriculum focus on the national values, health, environmental, economic values, in the light of the education policy in the Kingdom of Saudi Arabia, in addition to present a proposed vision to strengthen it in the science curriculum for the first intermediate grade. The study was applied to the two books student and the two books of activity on the first-second semesters for the academic year 1441 AH. To analyze the curriculum content, the study used a verified card prepared by the researchers and a criterion for interpreting percentages. The study reached the following results: environmental values ranked first with a concentration of (43%), i.e. with an avera

Throughout Agriculture has mostly relied on the use of natural fertilizers throughout human history, which are compounds that increase the nitrogen levels in the soil. Modern agriculture was made possible by the introduction of synthetic fertilizers at the end of the 19th centuryproduction of agriculture. Their application enhanced crop yields and sparked an agricultural revolution unlike anything the world had ever seen.In the near future, synthetic fertilizers are anticipated to continue to have a significant impa ct on human life, both positively and negatively. They are frequently utilized for producing all t ypes of crops and are essential to plant growth. The significance of synthetic fertilizers is their ability to provide the soil w