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 .

Increasing requests for modified and personalized pharmaceutics and medical materials makes the implementation of additive manufacturing increased rapidly in recent years. 3D printing has been involved numerous advantages in case of reduction in waste, flexibility in the design, and minimizing the high cost of intended products for bulk production of. Several of 3D printing technologies have been developed to fabricate novel solid dosage forms, including selective laser sintering, binder deposition, stereolithography, inkjet printing, extrusion-based printing, and fused deposition modeling. The selection of 3D printing techniques depends on their compatibility with the printed drug products. This review intent to provide a perspecti

In present days, drug resistance is a major emerging problem in the healthcare sector. Novel antibiotics are in considerable need because present effective treatments have repeatedly failed. Antimicrobial peptides are the biologically active secondary metabolites produced by a variety of microorganisms like bacteria, fungi, and algae, which possess surface activity reduction activity along with this they are having antimicrobial, antifungal, and antioxidant antibiofilm activity. Antimicrobial peptides include a wide variety of bioactive compounds such as Bacteriocins, glycolipids, lipopeptides, polysaccharide-protein complexes, phospholipids, fatty acids, and neutral lipids. Bioactive peptides derived from various natural sources like bacte

Cephalexin and its derivatives are commonly utilized in the pharmaceutical and medicinal industry due to their biological and pharmaceutical activities, including anti-microbial, anti-cancer, anti-bacterial, and herbicidal activities as well as possessing high palatability and being useful for skin and joint infections. Interestingly, some organic drugs, including cephalexin, which exhibit toxicological and pharmacological properties, can be administered in forms of metal complexes. Many researchers have synthesized organic ligands derived from cephalexin in forms of Schiff bases and azo compounds which exhibited higher biological and medicinal properties when compared to cephalexin alone. One of the important features that make Schiff base

Today’s modern medical imaging research faces the challenge of detecting brain tumor through Magnetic Resonance Images (MRI). Normally, to produce images of soft tissue of human body, MRI images are used by experts. It is used for analysis of human organs to replace surgery. For brain tumor detection, image segmentation is required. For this purpose, the brain is partitioned into two distinct regions. This is considered to be one of the most important but difficult part of the process of detecting brain tumor. Hence, it is highly necessary that segmentation of the MRI images must be done accurately before asking the computer to do the exact diagnosis. Earlier, a variety of algorithms were developed for segmentation of MRI images by usin

Cerium (III), Neodymium (III) and Samarium (III) Complexes existent a wide range of implementation that stretch from their play in the medicinal and pharmaceutical area because of their major significant pharmacological characteristic such as antifungal, anti-cancer, anti-bacterial ,anti-human immunodeficiency virus ,antineoplastic, anti-inflammation,inhibition corrosion,in some industrial (polymers, Azo dye).It is likely to open avenuesto research among various disciplines such as physics, electronics, chemistry and materials science by these complexes that contain exquisitely designed organic molecules.This paper reviews the definition, importance and various applications of Cerium (III), Neodymium (III) and Samarium (III) Complexes anddi