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 applications of herbal medicine have recently acquired growing interest in range of the prophylaxis and treatment of diseases. Olibanum has been used since ancient eras and several reports studied the pharmacological characteristics of boswellic acid, particularly their effect on the inflammatory response, analgesic properties, and anti-arthritic activity mostly in cell lines, but new approaches include animal models to assess these natural derivatives effects taking into consideration of being safer than synthetic preparations.  The impact of olibanum oil on several parameters was studied in rats during this study. These included white blood cell (WBC) count, lactate dehydrogenase (LDH), and C reactive protein (CRP), as well a

In Indonesia, cattle feces (CF) and water hyacinth (WH) plants are abundant but have not been widely revealed. The use of microorganisms as decomposers in the fermentation process has not been widely applied, so researchers are interested in studying further. This study was to evaluate the effect of the combination of CF with WH on composting by applying white-rot fungal (WRF) (Ganoderma sp) microorganism as a decomposer. A number of six types of treatment compared to R₁(ratio of CF:WH)(25%:75%)+WRF; R₂(ratio of CF:WH)(50%:50%)+WRF; R₃(ratio of CF:WH)(75%:25%)+WRF; R₄(ratio of CF:WH)(25%:75%) without WRF; R₅(ratio of CF:WH)(50%:50%) without WRF; R₆(ratio of CF:WH)

Biodiesel production from microalgae depends on the biomass and lipid production. Both biomass and lipid accumulation is controlled by several factors. The effect of various culture media (BG11, BBM, and Urea), nutrients stress [nitrogen (N), phosphorous (P), magnesium (Mg) and carbonate (CO₃)] and gamma (γ) radiation on the growth and lipid accumulation of   Dictyochloropsis splendida were investigated. The highest biomass and lipid yield of D. splendida were achieved on BG11 medium. Cultivation of D. splendida in a medium containing 3000 mg L⁻¹ N, or 160 mg L⁻¹ P, or 113 mg L⁻¹ Mg, or 20 mg L^-1 CO_3, led to enhanced growth rate. While u

Background: Difficulties arise when attempting to imagine the interpupillary line and comparing it with the Fox plane guide and not more difficult than holding any instrument over the movable pupils just to demonstrate the interpupillary line. The aim of this study was to introduce ear lobes as alternative landmarks for the interpupillary line during orientation of the occlusal plane. Also, the other aim was to compare the ear lobes with the pupils of the eyes to verify that they were indifferent as anatomical landmarks. Materials & methods: The alternative landmarks, ear lobes, were presented and the method for orienting the occlusal plane with these landmarks was introduced. Digital pictures of 30 subjects, who participated in the study,

Excerption and inclusion are two terms in Arabic rhetoric. The excerption is defined as a taking a part of text from Holly Quran or Hadith and put it in a poem, verse line, or put it in a prose text. But the linguistics expand the concept of this term to include taking from another sciences and knowledge, like Grammar, Philology, and Prosody.
Inclusion is defined as taking a verse line or part of verse line from another poet to put it in a new poem, it is necessary that the poet who take the text should declare it, and if he hides it, it will be plagiarism.
This search is use these two terms in architecture, we have now new two terms in architecture, first one; architectural excerption, it means the designer takes a part of religio

Islamic shrines architecture is one of the Islamic Architectural building types. It is called (Thresholds); (Atabat) in Arabic. Thoroughbred throughout the Islamic world from the east to west. In addition, it carries the style features and peculiarities of uniqueness from the rest of the types of Islamic architecture. By virtue of the particularity of its function as tomb for important person in Islamic history. Islamic shrines architecture has grown and evolved in started from the small shrines, and then taken to widen with the evolution of time in line with the value of the event and the rituals associated with it. Some of them to became centers of large cities of the largest in many parts of the Islamic world.

This study proposes a mathematical approach and numerical experiment for a simple solution of cardiac blood flow to the heart's blood vessels. A mathematical model of human blood flow through arterial branches was studied and calculated using the Navier-Stokes partial differential equation with finite element analysis (FEA) approach. Furthermore, FEA is applied to the steady flow of two-dimensional viscous liquids through different geometries. The validity of the computational method is determined by comparing numerical experiments with the results of the analysis of different functions. Numerical analysis showed that the highest blood flow velocity of 1.22 cm/s occurred in the center of the vessel which tends to be laminar and is influe