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 .

It is known that the oral administration of ibuprofen caused an irritation of stomach as a side effect due to its carboxylic moiety. Ibuprofen ester was synthesized by linking the carboxylic moiety of ibuprofen and the hydroxylic group of paracetamol to reduce its side effect. Study the kinetic hydrolysis of prepared ester was examined at different values of physiological pH (1.0, 5.8, 6.4 and 7.4) at 37 ± 0.1 of 1 hour period. Measurements of absorbance were carried out by UV-Visible spectrophotometer to follow the stability of ester, it showed Pseudo first order hydrolysis. The pH- apparent rate profiles of ester was exhibited a good stability at pH 1.0 and pH 5.8. Pharmacological activity in vivo of prepared ester was evaluated in re

The focus of this article, reviewed a generalized  of contraction mapping and nonexpansive maps and recall some theorems about the existence and uniqueness of common fixed point and coincidence fixed-point for such maps under some conditions. Moreover, some schemes of different types as one-step schemes ,two-step schemes and three step schemes (Mann scheme algorithm, Ishukawa scheme algorithm, noor scheme algorithm, .scheme algorithm,  scheme algorithm Modified  scheme algorithm arahan scheme algorithm and others. The convergence of these schemes has been studied .On the other hands, We also reviewed the convergence, valence and stability theories of different types of near-plots in convex metric space.

Liver is considered as the first target for the toxic effects of toxins and other xenobiotics, and this can be attributed to its role as a site which receive all absorbed xenobiotics from the gastrointestinal tract and its role as a major site for biotransformation of xenobiotics. The present study was designed to evaluate the possible hepatoprotective effect of benfotiamine against CCl₄-induced hepatotoxicity in rats. The study was conducted on 48 male albino rats; the animals were allocated into 8 groups (6 rats in each group) and treated as follow: 4 groups treated with oral doses of either normal saline, benfotiamine (100 mg/kg), thiamine (100 mg/kg), N-acetylcystein (400 mg/kg) only without induction of hepatic damage. Th

Communication is one of the main elements of culture, it is the source of its formation and a factor of its development and spread. Communication is a 'dynamic' cultural process and is an integral part of the political, social, economic and cultural aspects of people. Therefore, mass communication means help in the course and movement of individuals and cultural communities. The relationship between media and culture according to this perspective is one of many key factors and influential forces that make it coherent and sometimes intertwined. It is a problematic relationship that leads to research and study in order to lay the right foundations in the orientation towards the audience.

Mass communication has many basic functions.

Based on the systematic scientific investigation of artistic achievement, researchers (critics) adhere to mechanisms based on epistemology, through which it is envisaged to reveal the meaning of the achievement as the product of three actors: the effectiveness of an artistic sense, the effectiveness of an idea, and the arousal of taste according to systematic criticism procedures that investigate the new artistic achievement. Or, in a specific way, the possibility of meaning in all the accomplished from the aesthetics of artistic presentation and the character of the self-accomplished by the "artist" and the critic invokes his critical tools with certain cognitive foundations. In defining its nature from the rest of the other cultural ac

Abstract: As human history is implicated in landscape or the natural history, it can be stated that the origins of the Caribbean writers' conflict, in general, are the colonial history of West India. That history which tells the story behind not only their fragmented identity, but also the problems connected to their language as well. Building on the arguments of the prominent Postcolonial ecoccritics such as Elizabeth DeLoughrey, George Handley, Helen Tiffin, and Graham Huggan, this research analyzes selected poems by Derek Walcott's which are bounded in his volume, Collected Poems. It shows how the Caribbean history has been erased due to the brutality of colonization offering landscape as a reliable source which has recorded that history

This study analyzes how to make use of the resources in the marshlands of Iraq and how to utilize them, especially after the water returns to these areas and they are revitalized. We take an example of AL- Saheen Marsh and plan an ideal tourist resort there. This example can further expand to include other parts of the marshlands. The resort will utilize the local environment and tourist characteristics as it will have a feel and architectural resemblance to the houses and buildings that are currently built there. In addition the transportation methods will be the same as those used by the locals. Yet the resort will still posses all the facilities required by a modern tourist resort that includes all the services that will make

Sansevieriatrifasciata was studied as a potential biosorbent for chromium, copper and nickel removal in batch process from electroplating and tannery effluents. Different parameters influencing the biosorption process such as pH, contact time, and amount of biosorbent were optimized while using the 80 mm sized particles of the biosorbent. As high as 91.3 % Ni and 92.7 % Cu were removed at pH of 6 and 4.5 respectively, while optimum Cr removal of 91.34 % from electroplating and 94.6 % from tannery effluents was found at pH 6.0 and 4.0 respectively. Pseudo second order model was found to best fit the kinetic data for all the metals as evidenced by their greater R2 values. FTIR characterization of biosorbent revealed the presence of carboxyl a