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 .

Volumetric chemical adsorption was done in a volumetric apparatus using hydrogen gas at room temperature on eleven platinum catalyst, commercial catalysts (RG-412,RG-402 ,RG-432, RG-451, RG-482, and PS-10) and prepared platinum catalysts with 0.1, 0.2 , 0.45 , and 0.55% by weight of Pt supported with Y-alumina. The results show that the metal crystallite area increases with increasing platinum content. The dispersion and particle size of metal crystallite located between 48.2-96.1% and 3.85-12.72 nm, respectively. For bimetallic catalysts, the hydrogen intake decrease in the following order : Re < Sn < Ir.

يهدف البحث الحالي إلى الاستفادة من القهوة المستهلكة , كمادة وسيطة حيث تعد القهوة المستهلكة من المخلفات المضرة للبيئة الاستخراج الكافيين الطبيعي والذي يعد مادة ذات نشاط حيوي واهمية, وتحديد العوامل الفعالة في كفاءة عملية الاستخلاص من حيث تركيز الكافيين. تضمنت المتغيرات الرئيسية المدروسة وقت الاستخلاص  0-150 دقيقة  ، ودرجة الحرارة  25-55 درجة مئوية  ، وسرعة الخلط  180-450 دورة في الدقيقة  ،   ودرجة الحموضة العالق

Nanoparticles are defined as an organic or non-organic structure of matter in at least one of its dimensions less than 100 nm. Nanoparticles proved their effectiveness in different fields because of their unique physicochemical properties. Using nanoparticles in the power field contributes to cleaning and decreasing environmental pollution, which means it is an environmentally friendly material. It could be used in many different parts of batteries, including an anode, cathode, and electrolyte. This study reviews different types of nanoparticles used in Lithium-ion batteries by collecting the advanced techniques for applying nanotechnology in batteries. In addition, this review presents an idea about the advantages and d

Chromium tanned leather wastes (CTLW) and vegetable tanned leather wastes (VTLW) were used as adsorbent materials to remove the Biebrich scarlet dye (BS), as an anionic dye from wastewater, using an adsorption method. The effects of various factors, such as weight of leather waste, time of shaking, and the starting concentration of Biebrich scarlet dye, temperature and pH were studied. It described the adsorption process using Langmuir and Freundlich isotherm models. The obtained results agreed well with the Langmuir model, and the maximum adsorption capacities of CTLW and VTLW were 73.5294 and 78.1250 mg.g⁻¹, respectively, suggesting a monolayer adsorption process. The adsorption kinetic was found to follow a pseudo-second-order kinetic

Antibacterial Activity of Bioactive Glass 45S5 and Chitosan Incorporated as Fillers into Gutta Percha, Ahmed I AL-Jobory*, Raghad AL-Hashimi

The adsorption process of 5-Fluorouracil (5FU) drugs on Aluminum nitride nanotubes surface (AlNNTs) have been evaluated through density functional theory (DFT). The DFT results show that the interaction of AlNNTs with the F atoms of 5FU drugs is strong due to the fact that the amount of adsorption energy was about − 29.65 kcal.mol−1. Conversely, the interaction of the 5FU through O atoms with the AlNNTs was weaker due to the lower value of adsorption energy. Also, based on the values of Gibbs free energy, the 5FU adsorption on the surfaces of AlNNTs was spontaneous. In addition, based on natural bond orbital (NBO) analysis, the direction of charge transfer was from fluorine’s σ orbitals of the drug to nitrogen’s and aluminum’s n*