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Braid Groups
Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces. In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups.
Bigel : An innovative drug delivery system
Bigel is a promising drug delivery system that modifies the pharmacotherapeutic characteristics of knowing active pharmaceutical ingredient (API).It is a mix between hydrogel and organogel (oleogel). The objective of the present work demonstrates the ability of bigel to overcome the disadvan- tages of both types of gels, including the limited ability to cross lipophilic barriers of the skin for hydrogels and the low patient compliance for organogels due to their stickiness and oily residues. Materials andmethods : Carbomer934, PolyvinylpyrrolidoneK 90 and Castor oil where mixed in a high shear mixer using diferent weight percentages of each. Hence,13 for mulations (BG1 to BG13) prepared by simplex mixture design modelis used to study the inuenceofafore- mentioned ingredients on appearance, dynamicviscosity, pH, stability, microscopicstructure of bigel and to understand the chemical interactions between bigel components, Fouriertrans- form infrared (FTIR) analysis will bereported.
