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 present art icle discusses the prob lems of understanding and translating the lingu istic and cult ural aspect of a foreign lite rary text. The article considers the trans lation process through the pr ism of cult ural orientation. In the process of transl ation, the nati onal cultural iden tity should be expressed to the max imum extent, through all me ans of expre ssion that include imagery and inton ation. In addi tion to the author's sty le, special atte ntion should al so be pa id to tro pes, phraseological uni ts, colloquial wo rds and dial&n

Background: Hyperplastic polyps account for 30–93% of gastric polyps. Recently, there have been studies about the development of dysplasia in this type of polyp. Every cell in the body contains the p53 gene, which has anti-cancer properties. Objective: The sensitivity of immunohistochemical expression of p53 is evaluated among gastric hyperplastic polyps with and without dysplasia and gastric adenomatous polyps to know its usefulness as a diagnostic marker. Methods: A retrospective cross-sectional study was done on fifty formalin-fixed paraffin-embedded blocks of gastric polyps (44 hyperplastic polyps without dysplasia, 3 hyperplastic polyps with dysplasia, and 3 adenomas). Cases were collected from the archives of the pathology d

The study area intendes for agricultural investment and establishment stations of water pumping for human use to the nearby areas, southwest of Samawah city. Twelve Two-Dimension (2-D) survey points were performed by using Wenner-Schlumberger array configuration to take the measurements. The inverse models of two survey point appear the effect of the saline groundwater that raises from Rus Formation, which caused a significant reduction in resistivity of the groundwater-bearing zone within middle Dammam Formation along the fault plane.  

    The present study aimed to investigate the effects of cages of fish farming of Mussayyib district,The fish farming have been selected at Euphrates river with in Mussayyib districtBabylon province the area of study extend 3 Km at the river and includes 541 cages in water with in 46 fish farming . Water samples were taken from 3 stations three times within one month for each two of them were taken from two water purification stations in mussayyib ,physical and chemical examination of water quality were taken ,The results for samples from the fish farming indicated that PH and salinity of water within acceptable levels, high proporation of dissolved oxygen and vital oxygen required were very high while the turbidity was more t

In this research, we sought to identify the nature of the relationship between the exchange rate of the Chinese yuan and the value of Chinese exports, through the formulation of a standard model based on the model of common integration, and based on the data of the study and using the test "Angel-Granger" It reflects the relationship between the two research variables, through which the relationship between the RMB exchange rate and the value of Chinese exports was estimated during the period 1978-2017.

It is an ideal area of research to examine related indicators to anticipate relative tectonic activities, where there is a broad range of geological formations with elements of different sedimentary rocks. This study includes assessing and evaluating the relative tectonic activities within the Sargalu area by using a morphometric approach, which involved the use of different indices that can explain and help understanding the geometry, development level, lithology, and structural disturbance on a sub-basinal level. The research was accomplished by using ArcGIS 10.5 hydrology tools to design the drainage system of each studied stream. The Advanced Spaceborne Thermal Emission Radiometer (ASTER) satellite imagery data and the Digital Elevat

Objective: to assessthe impact of psychological and social climacteric changes on quality of life among
middle age women in Baghdad city
Methodology: : A descriptive analytic study was conducted to study the quality of life among middle age
women due topsychological and social climacteric changes from February 2013- July 2013. A purposive
sampleconsisted of three hundred (300) womenaged (40-65) years who were attending health centers in two
sectors in Baghdad / AL- Russafa andAL- karhk . The data were collected through using interview technique ,
and questionnaire format , which comprises two parts, first part consist (socio-demographic characteristic , the
second part quality of life domains (psychological and socia

The paper studies the description of the colloquial and popular vocabulary  used by wholesales tradesmen in Varonech before the Bolshevik Revolution . The vocabulary were used in the personal letters written by the poet and sent to famous poets and critics like Belenisky, kryvesky and Malsheve. And some were sent to his father and his sister. Not only did these letter bear the personal taste, but they represented a literary product reflecting on the poet's impressions, views, ambitions, and opinion in arts, poetry, prose, and theatre. The researcher used about thirty instances of various levels of grammar, style and phonology, all representing colloquial vocabulary used commonly at the time of Alexi&nbsp