Universe bouncing its way to inflation

Cosmological models with inflation and those with bounce have their own strengths and weaknesses. Here we construct a model in which a phase of bounce is followed by a viable inflationary phase. This incorporates several advantages of both and hence, is a more viable model for cosmic evolution. We explore scenarios wherein the bouncing phase smoothly transits to an inflationary one, with the pivot scale leaving the Hubble horizon during the latter era, thereby maintaining consistency with observations. Staying within the ambit of Einstein-Hilbert gravity augmented by the inflaton, we ensure a pre-inflationary bounce by introducing a second scalar field that helps engineer the requisite violation of the null energy condition. Potential ghost instabilities can be mitigated by invoking a non-trivial coupling between the two scalar fields.Comment: 34 pages, 7 figures, Published in Int.J.Mod.Phys.

Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits

We give a criterion for a Dynkin diagram, equivalently a generalized Cartan matrix, to be symmetrizable. This criterion is easily checked on the Dynkin diagram. We obtain a simple proof that the maximal rank of a Dynkin diagram of compact hyperbolic type is 5, while the maximal rank of a symmetrizable Dynkin diagram of compact hyperbolic type is 4. Building on earlier classification results of Kac, Kobayashi-Morita, Li and Sa\c{c}lio\~{g}lu, we present the 238 hyperbolic Dynkin diagrams in ranks 3-10, 142 of which are symmetrizable. For each symmetrizable hyperbolic generalized Cartan matrix, we give a symmetrization and hence the distinct lengths of real roots in the corresponding root system. For each such hyperbolic root system we determine the disjoint orbits of the action of the Weyl group on real roots. It follows that the maximal number of disjoint Weyl group orbits on real roots in a hyperbolic root system is 4.Comment: J. Phys. A: Math. Theor (to appear

Local delivery systems of drugs/biologicals for the management of burn wounds

Severe burn injuries are one of the major challenging health issues and pertain to significant morbidity and mortality due to their extensive traumatic and physiological damage to the organs. For decades, crucial steps and procedures have been considered to comprehend burn management. Early debridement and graft application are common practices that have improved the conditions and outcomes of burn patients physically and cosmetically. However, many drawbacks are still arising while managing burn treatment. Delayed healing, scarring, infection, and pain are among the reasons. Moreover, it is necessary to overstep to bring up new techniques and medications for improved healing quality. In this present article, we review and discuss the latest treatment of burn wound management and treatment. This review aims to provide a comprehensive discussion of the use of antibiotics and metallic ions for local delivery at wound sites and also provides a thorough briefing of the mechanism of action of these therapeutic agents. Furthermore, this article also provides an overall scenario of burn wound management, different regulations, and the advancement of nanotherapeutics for burn wound management and novel strategies developed in the past decades. Overall, this review article primarily targets to provide the scientific community with some settler ideas and research advancements, that improve and uplift burn wound care with a focus on infections, scarring, drug deliveries, nanomaterial, growth factors, bioactive proteins, and tissue engineering