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 research, an organobentonite (HDTMA-BT) was prepared by modifying a jordanian bentonite (BT) with hexadecyltrimethylammonium bromide. By means of in situ free radical polymerization in THF with AIBN as the initiator, this organobentonite is used to prepare the polymethylmethacrylate-bentonite (PMA-HDTMA-BT) nanocomposite. Scanning electron microscopy (SEM), x-ray diffraction (XRD), energy dispersive spectrometer (EDS) and Fourier transform infrared (FTIR) spectroscopy were used to characterize both HDTMA-BT and PMA-HDTMA-BT. Those adsorbents were used in a batch process to remove Pb(II), Cr(III) ions, and p-chlorophenol (PCP) from aqueous solution. Investigated factors included adsorbent dosage, initial pH solution, contact time, an

تقدم هذه الدراسة وصفا للطريقة المستخدمة في تحضير الكربون المنشط  (AC)من بقايا الشاي. تم دراسة الخواص الفيزيائية والكيميائية وكفاءة الامتزاز للكربون المنشط المحضر. تم إنتاج الكربون المنشط (AC) على مرحلتين: الاولى التنشيط باستخدام حامض الفوسفوريك (H3PO4) والثانية الكربنة عند درجة حرارة 450 درجة مئوية. استخدم الكربون المنشط لغرض امتصاص العقار الدوائي السيبروفلوكساسين(CIP) . تمت  دراسة عدة عوامل تشغيلية  بدرجة حرار

تقدم هذه الدراسة وصفا للطريقة المستخدمة في تحضير الكربون المنشط  (AC)من بقايا الشاي. تم دراسة الخواص الفيزيائية والكيميائية وكفاءة الامتزاز للكربون المنشط المحضر. تم إنتاج الكربون المنشط (AC) على مرحلتين: الاولى التنشيط باستخدام حامض الفوسفوريك (H3PO4) والثانية الكربنة عند درجة حرارة 450 درجة مئوية. استخدم الكربون المنشط لغرض امتصاص العقار الدوائي السيبروفلوكساسين(CIP) . تمت  دراسة عدة عوامل تشغيلية  بدرجة حرار

Different polymers were prepared by condensation polymerization of sebacic anhydride and adipic anhydride with ethylene glycol and poly(ethylene glycol). Their number average molecular weights were determined by end group analysis. Then, they were grafted on the prepared phthalocyaninatocopper(II) compounds with the general formula (NH2)4PcCu(II) having amino groups of 3,3',3'',3'''- or 4,4',4'',4'''- positions. All prepared polymers, compounds, and phthalocyaninatocopper(II)-grafted polymers were characterized by FTIR. The sizing measurements were carried out in 3,3',3'',3'''- (NH2)4PcCu(II) and 4,4',4'',4'''- (NH2)4PcCu(II) compounds with and without grafting polymers. The results showed that the grafting process led to decreasing in par

It is found that hypersensitive teeth have a larger number and wider patent tubules than those of non-sensitive teeth. Objective: The aim of this study is to compare between the effects of diode laser at different power densities, with and without sodium fluoride on the sealing of exposed dentinal tubules and dentin permeability. Materials and methods: 118 teeth were used. Samples were divided into three major groups. The first consisted of 100 teeth used for permeability test. The second consisted of 16 teeth for measuring external surface temperature elevation while irradiation. The third, in turn, consisted of one pair of teeth observed under SEM for dentine surface morphology analysis. Results: For dentin permeability measurement, th

The purpose of this work is to study the classification and construction of (k,3)-arcs in the projective plane PG(2,7). We found that there are two (5,3)-arcs, four (6,3)-arcs, six (7,3)arcs, six (8,3)-arcs, seven (9,3)-arcs, six (10,3)-arcs and six (11,3)-arcs. All of these arcs are incomplete. The number of distinct (12,3)-arcs are six, two of them are complete. There are four distinct (13,3)-arcs, two of them are complete and one (14,3)-arc which is incomplete. There exists one complete (15,3)-arc.

sanaa tareq, Baghdad Science Journal, - Cited by 1