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 .

Complexes ofCo(ll),Cu(||),Ni(||),pt(|| ),and pd(||) with N3O-chelating Ligand Incorporating Azo and Shiff Base Moieties ;synthesis, spectroscopic ,Thermal Decomposition Theoretical

The present article discusses the synthesis of tetradentate Schiff base complexes formed by the condensation reaction of 2-hydroxy benzaldehyde and phthalohydrazide. The ligand (LH2) was detected using FT-IR spectra, 1H, 13C-NMR, UV-Vis spectroscopy, elemental microanalysis CHN, and mass spectrometry. The obtained solid complexes have been assessed using physicochemical and spectroscopic techniques, including UV-Vis, FT-IR, nuclear magnetic resonance (1H-NMR, 13C-NMR), mass spectrometry, thermal gravimetric analysis (TGA), and atomic absorption, in addition to complex conductivity and magnetic moment measurements. The infrared results demonstrated that ligands functioning as tetradentate ligands are chelated to metal ions via the ph

RKASFH Ghanim, Ibn Al -Haitham Journal for pure and applied science, 2017

Removing Congo red (CR) is critical in wastewater treatment. We introduce a combination of electrocoagulation (EC) and electro-oxidation (EO) to address the elimination of CR. We also discuss the deposition of triple oxides (Cu–Mn–Ni) simultaneously on both anodic and cathodic graphite electrodes at constant current density. These electrodes efficiently worked as anodes in the EC-EO system. The EC-CO combination eliminated around 98 % of the CR dye and about 95 % of the Chemical Oxygen demand (COD), and similar results were obtained with the absence of NaCl. Thus, EC-EO is a promising technique to remove CR in an environmentally friendly pathway.

The adsorption process of reactive blue 49 (RB49) dye and reactive red 195 (RR195) dye from an aqueous solutions was explored using a novel adsorbent produced from the sunflower husks encapsulated with copper oxide nanoparticle (CSFH). Primarily, the features of a CSFH, such as surface morphology, functional groups, and structure, were characterized. It was determined that coating the sunflower husks with copper oxide nanoparticles greatly improved the surface and structural properties related to the adsorption capacity. The adsorption process was successful, with a removal efficiency of 97% for RB49 and 98% for RR195 under optimal operating conditions, contact time of 180 min, pH of 7, agitation speed of 150 rpm, initial dye concentration

The designer must find the optimum match between the object's technical and economic needs and the performance and production requirements of the various material options when choosing material for an engineering application. This study proposes an integrated (hybrid) strategy for selecting the optimal material for an engineering design depending on design requirements. The primary objective is to determine the best candidate material for the drone wings based on Ashby's performance indices and then rank the result using a grey relational technique with the entropy weight method. Aluminum alloys, titanium alloys, composites, and wood have been suggested as suitable materials for manufacturing drone wings. The requirement