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 paper, the ability of using corn leaves as low-cost natural biowaste adsorbent material for the removal of Indigo Carmen (IC) dye was studied. Batch mode system was used to study several parameters such as, contact time (4 days), concentration of dye (10-50) ppm, adsorbent dosage (0.05-0.25) gram, pH (2-12) and temperature (30-60) ^oC. The corn leaf was characterized by Fourier-transform infrared spectroscopy device before and after the adsorption process of the IC dye and scanning electron microscope device was used to find the morphology of the adsorbent material. The experimental data was imputing with several isotherms where it fits with Freundlich (R² = 0.9

Skin drug administration is the method used to provide drugs for local or systemic therapy, which is recognized for clinical usage. It is the third-largest method of medication delivery, after only intravenous administration and oral administration. Using a transdermal delivery method makes the administration easy, and blood concentration and adverse effects can be reduced. A microneedle is a micron-sized needle with a short height of no more than 500 micrometers and a width of no more than 50 micrometers. The needle comes into contact with the epidermal layer of the skin before it gets to the dermal layer, where there is no discomfort. Several materials, such as metals, inorganic, and polymer materials, are used to create microneed

This study concerns the removal of a trihydrate antibiotic (Amoxicillin) from synthetically contaminated water by adsorption on modified bentonite. The bentonite was modified using hexadecyl trimethyl ammonium bromide (HTAB), which turned it from a hydrophilic to a hydrophobic material. The effects of different parameters were studied in batch experiments. These parameters were contact time, solution pH, agitation speed, initial concentration (C0) of the contaminant, and adsorbent dosage. Maximum removal of amoxicillin (93 %) was achieved at contact time = 240 min, pH = 10, agitation speed = 200 rpm, initial concentration = 30 ppm, and adsorbent dosage = 3 g bentonite per 1L of pollutant solution. The characterization of the adsorbent, modi

Understanding, promoting, and teaching media literacy is an important societal challenge. STEM educators are increasingly looking to incorporate 21st century skills such as media literacy into core subject education. In this paper we investigate how undergraduate Computer Science (CS) students can learn media literacy as a by-product of collaborative video tutorial production. The paper presents a study of 34 third-year CS undergraduates who, as part of their learning, were each asked to produce three video tutorials on Raspberry Pi programming, using a collaborative video production tool for mobile phones (Bootlegger). We provide results of both quantitative and qualitative analysis of the production process and resulting video tutorials,

This paper presents the ability to use cheap adsorbent (corn leaf) for the removal of Malachite Green (MG) dye from its aqueous solution. A batch mode was used to study several factors, dye concentration (50-150) ppm, adsorbent dosage (0.5-2.5) g/L, contact time (1-4) day, pH (2-10), and temperature (30-60)   The results indicated that the removal efficiency increases with the increase of adsorbent dosage and contact time, while inversely proportional to the increase in pH and temperature. An SEM device characterized the adsorbent corn leaves. The adsorption's resulting data were in agreement with Freundlich isotherm according to the regression analysis, and the kinetics data followed pseudo-first-order kinetic with a correlation

Somerset Maugham is known mainly as a novelist . This paper presents Maugham the dramatist . Many critics have found him a promising dramatist . He has written 30 plays , then he turns his back upon the theater and writes his autobiographical and most successful novel Of Human Bondage ( 1915) .

        Maugham's writing is clear , precise , and simple . He is described as a realist who is keenly aware of human nature , its concentration and frustration . His only tragedy A Man of Honour is a play in 4 acts . This paper concentrates mainly on this play to show Maugham as a dramatist and to show his concept of " honour " .

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     The Beggar (1965) is a story of isolation and depression which is written by the Egyptian novelist Naguib Mahfouz who is considered the father of Arabic Literature in the modern era. Specifically, he refers in his great novel called The Beggar that the man unable to achieve psychological revival after Nasser’s revolution, the man sacrificed his own job and his family for a desire that increases his feelings of alienation and depression which leads him to an emotional outcry against the indifferent. The main aim of the study highlights the concept of existential dilemma as a philosophical problem and personality crisis by the protagonist of The Beggar novel, Omer Al-Hamzawi who had acc

Breast cancer constitutes about one fourth of the registered cancer cases among the Iraqi population (1)
and it is the leading cause of death among Iraqi women (2)
. Each year more women are exposed to the vicious
ramifications of this disease which include death if left unmanaged or the negative sequels that they would
experience, cosmetically and psychologically, after exposure to radical mastectomy.
The World Health Organization (WHO) documented that early detection and screening, when coped
with adequate therapy, could offer a reduction in breast cancer mortality; displaying that the low survival rates
in less developed countries, including Iraq, is mainly attributed to the lack of early detection programs couple

The human intellect and his ability to complex thinking is a characteristic that Allah has given him above all his creatures. Islam came to encourage the utilization of the mind by thought, contemplation and consideration of the kingdom of Allah, His signs and religion, and He gave us a set of legislation that preserves the mind and protects it from falling into error or deviation.

This research deals with one of the most important components of civilizations in general and Islamic civilization in particular, which is thinking and what is related to it. It is an essential and influential component in man's dealing with life around him and the for