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 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

Background: The aim of the study was to investigate the effect of surface treatments of zirconia (grinding and sandblast with 50μm, 100 μm) on shear bond strength between zirconia core and veneering ceramic. Material and methods: Twenty-eight presintered Y-TZP ceramic specimens (IPS e.max ZirCAD, Ivoclar vivadent) were fabricated and sintered according to manufacturer’s instructions. The core specimens were divided randomly in to 4 groups, group 1: no surface treatment, group2: zirconia specimens were ground with silicon carbide paper up to1200 grit under water cooling, group3: zirconia specimens were ground and sandblast with 100 μm alumina, group 4: zirconia specimens were ground and sandblast with 50 μm alumina. Surfa

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

     The research aimed to identify the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information. Such goal includes a set of sub-goals: Knowing the reasons for media offices' reliance on the information provided by the Cabinet's website; and revealing the benefit derived from relying on the Cabinet's website.

The researcher used the survey method to screen and comprehend the extent to which the media offices in the ministries depend on the website of the Iraqi Council of Ministers as a source of information.

The mechanism of comprehensive account of the limits of research wa

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

Background; Perforated duodenal ulcer (PDU) is a common surgical emergency that is associated with high mortality and morbidity. Early diagnosis and prompt surgical treatment is required to prevent grave complications.
Objective; The study was designed to evaluate the diagnostic accuracy of different radiological investigations in the diagnosis of perforated duodenal ulcer.
Methods; A prospective study of 185 pts with PDU at al kindy teaching hospital, Baghdad, Iraq from June 2008- august 2010. patients were examined clinically and investigated by blood test, chest x ray, plain X ray of the abdomen. Ultrasonography (U/S) and CT scanning done for those patients with negative X- ray finding. Resuscitation by intravenous fluid and ant

     In the present work, a kinetic study was performed to the extraction of phosphate from Iraqi Akashat phosphate ore using organic acid. Leaching was studied using lactic acid for the separation of calcareous materials (mainly calcite). Reaction conditions were 2% by weight acid concentration and 5ml/gm of acid volume to ore weight ratio. Reaction time was taken in the range 2 to 30 minutes (step 2 minutes) to determine the reaction rate constant k based on the change in calcite concentration. To determine value of activation energy when reaction temperature is varied from 25 to 65 , another investigation was accomplished. Through the kinetic data, it was found that selective leaching was controlled by