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 .

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 inhibitive action of Phenyl Thiourea (PTU) on the corrosion of mild steel in strong Hydrochloric acid, HCl, has been investigated by weight loss and potentiostatic polarization. The effect of PTU concentration, HCl concentration, and temperature on corrosion rate of mild steel were verified using 2 levels factorial design and surface response analysis through weight loss approach, while the electrochemical measurements were used to study the behavior of mild steel in 5-7N HCl at temperatures 30, 40 and 50 °C, in absence and presence of PTU. It was verified that all variables and their interaction were statistically significant. The adsorption of (PTU) is found to obey the Langmuir adsorption isotherm. The effect of temperature on th

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STAG proteins, which are part of the cohesin complex and encoded by the STAG genes, are known as Irr1/Scc3 in yeast and as SA/STAG/stromalin in mammals. There are more variants as there are alternate splice sites, maybe three open reading frames (ORFs) code for three main proteins, including: SA1 (STAG1), SA2 (STAG2) and SA3 (STAG3). The cohesin protein complex has various essential roles in eukaryotic cell biology. This study compared the expression of the STAG1 gene in four different breast cancer cell lines, including: MCF-7, T-47D, MDA-MB-468, and MDA-MB-231 and normal breast tissue. RNA was extracted from these cell lines and mRNA was converted to cDNA, and then expression of the STAG1 gene was quantified by three sets of specific prim

PKE Sharquie MD, PDPAA Noaimi MD, DDV, FDSM Al-Ogaily MD, IOSR Journal of Dental and Medical Sciences (IOSR-JDMS), 2015

Dylan Thomas (1914-1953) is a modern poet belongs to the apocalyptic movement of the 1940's.This movement is influenced by the doctrines and techniques of surrealism.

              Poetry for him should not be primarily concerned with man in society, but with the celebration of spiritual truth. It should bring to light the hidden causes, hence  his personal interest is to strip darkness and explore the inward motives. To do this he uses a cluster of images: a constant building up and breaking down of images. His poetry depends on the romantic spontaneity, suggestiveness of the Symbolists and the the surrealists' mysterious liberation of the unconsciousness and

Many approaches have been developed over time to counter the bioavailability limitations of poorly soluble drugs. With advances in nanotechnology in recent decades, this issue has been approached through the formulation of drugs as nanocrystals. Nanocrystals consist of pure drug(s) and a minimum of surface active agent(s) required for stabilization. They are carrier-free submicron colloidal drug delivery systems with a mean particle size typically in the range of 200 - 500 nm. By reducing particle size to nanoscale, the surface area available for dissolution is increased, and thus bioavailability is enhanced. Drug nanocrystals constitute a versatile formulation approach to enhance the pharmacokinetic and pharmacodynamic properties of poorly

Dylan Thomas (1914-1953) is a modern poet belongs to the apocalyptic movement of the 1940's.This movement is influenced by the doctrines and techniques of surrealism. Poetry for him should not be primarily concerned with man in society, but with the celebration of spiritual truth. It should bring to light the hidden causes, hence his personal interest is to strip darkness and explore the inward motives. To do this he uses a cluster of images: a constant building up and breaking down of images. His poetry depends on the romantic spontaneity, suggestiveness of the Symbolists and the the surrealists' mysterious liberation of the unconsciousness and the emotional involvement in the dynamics of life. In "Light Breaks

The ability to produce load-bearing masonry units adopting ACI 211.1 mix design using (1:3.2:2.5) as (cement: fine aggregate: coarse aggregate) with slump range (25-50mm) which can conform (dimension, absorption, and compressive strength) within IQS 1077/1987 requirements type A was our main goal of the study. The ability to use low cement content (300 kg/m3) to handle our market price products since the most consumption in wall construction for low-cost buildings was encouraging. The use of (10 and 20%) of LECA as partial volume replacement of coarse aggregate to reduce the huge weight of masonry blocks can also be recommended. The types of production of the load-bearing masonry units were A and B for (