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 .

     In this study, oxidative desulfurization of dibenzothiophene (DBT) with H2O2 as an oxidant was studied, whereas the catalyst used was zirconium oxide supported on Activated carbon (AC). Zirconium oxide (ZrO2) was impregnated over prepared activated carbon (AC) and characterized by various techniques such as XRD, FTIR, BET, SEM, and EDX. This composite was used as a heterogeneous catalyst for oxidation desulfurization of simulated oil. The results of this study showed that ZrO2/AC composite exhibited significant catalytic activity and stability, effectively lowering sulfur content under mild conditions. Factors such as reaction temperature (30, 40, 50, 60°C), time (5, 10, 15,20,30,60, 80 100 min), catalyst dose (0.3, 0.5,

Geologic modeling is the art of constructing a structural and stratigraphic model of a reservoir from analyses and interpretations of seismic data, log data, core data, etc. ‎[1].

   A static reservoir model typically involves four main stages, these stages are Structural modeling, Stratigraphic modeling, Lithological modeling and Petrophysical modeling ‎[2].

   Ismail field is exploration structure, located in the north Iraq, about 55 km north-west of Kirkuk city, to the north-west of the Bai Hassan field, the distance between the Bai Hassan field and Ismael field is about one kilometer ‎[3].

   Tertiary period reservoir sequences (Main Limestone), which comprise many economica

The study deals with the issue of multi-choice linear mathematical programming. The right side of the constraints will be multi-choice. However, the issue of multi-purpose mathematical programming can not be solved directly through linear or nonlinear techniques. The idea is to transform this matter into a normal linear problem and solve it In this research, a simple technique is introduced that enables us to deal with this issue as regular linear programming. The idea is to introduce a number of binary variables And its use to create a linear combination gives one parameter was used multiple. As well as the options of linear programming model to maximize profits to the General Company for Plastic Industries product irrigation sy

ENGLISH

in this paper the notion of threshold relations by using resemblance relation are introduced to get a similarity relation from a resemnblance relation R

The parliamentary election is one of the features of democratic systems that give individuals the right to participate in government and political election-making. Typically, the process of parliamentary elections received wide attention from media, as well as attention from large segments of the public because they understand the vast importance to assume political positions and associated fates of people and their destinies. Its importance comes from the fact that it allows citizens the right to participate in managing the public affairs by granting their confidence and voices to the elected president or his representatives in the parliamentary.
Media task is to emerge democratic societies, in particular, in the mission of urging p

Abstract\

The value chain analysis is main tools to achieve effective and efficient cost management; it requires a depth and comprehensive understanding for all internal and external activities associated with creating value.  Supply chain as apart of value chain, that means managing it in active and efficient can achieve great results when adopting a comprehensive and integrated performance for these two chains activities. The research aims to identify possible ways to integrate the performance of value and supply chains of the sample" Kufa-cement plant" and determine the effect of this integration in enhancing customer value. The research arrival that logical and integrated analysis of value and supply chains helps