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

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

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

Abstract: As human history is implicated in landscape or the natural history, it can be stated that the origins of the Caribbean writers' conflict, in general, are the colonial history of West India. That history which tells the story behind not only their fragmented identity, but also the problems connected to their language as well. Building on the arguments of the prominent Postcolonial ecoccritics such as Elizabeth DeLoughrey, George Handley, Helen Tiffin, and Graham Huggan, this research analyzes selected poems by Derek Walcott's which are bounded in his volume, Collected Poems. It shows how the Caribbean history has been erased due to the brutality of colonization offering landscape as a reliable source which has recorded that history

A simple and novel membraneless paper-based microfluidic fuel cell was presented in this study. The occurrence of laminar flow was employed to ensure no mixing of the fuel and oxidant fluids along the bath of reaction. The acidic wastewater was used as a fuel. It was an air-breathing cell, so air and tab water were used as oxidants. Both the fuel and tab water flowed continuously under gravity. Whatman filter paper was used for preparation of the fuel cell channel and two carbon fibre electrodes were used and firmed on the edges of the cell. The performance of the cell was examined over three consecutive days. The results indicated that the present cell has the potential to generate electric power, but an extensive study is required to harv

Endophytic fungi live inside plants or any part of them without creating any visible pathogenic signs. Endophytic fungi are found within medicinal plants and have shown strong biologic activity, such as anticancer and antioxidant activities, as well as producing extracellular enzymes. In this study, different fungal strains were isolated from the leaves of the medicinal plant Ziziphus spina, including Aspergillus flavus, Aspergillus fumigatus, Aspergillus niger, Cladosporium sp., Rhizopus sp., and Mucor sp. Extracellular enzymes have been quantified using agar plate-based methods in which fungi were grown in specified growth media to detect the enzymes produced. The results showed that A. niger has the highest ability to produce amy

Polyacrylonitrile nanofiber (PANFS), a well-known polymers, has been extensively employed in the manufacturing of carbon nanofibers (CNFS), which have recently gained substantial attention due to their excellent features, such as spinnability, environmental friendliness, and commercial feasibility. Because of their high carbon yield and versatility in tailoring the final CNFS structure, In addition to the simple formation of ladder structures through nitrile polymerization to yield stable products, CNFS and PAN have been the focus of extensive research as potential production precursors. For instance, the development of biomedical and high-performance composites has now become achievable. PAN homopolymer or PAN-based precursor copolymer can