An Application of the supremum cosine angle between multiplication invariant spaces in L^2(X; \mc H)

In this article, we describe the supremum cosine angle between two multiplication invariant (MI) spaces and its connection with the closedness of the sum of those spaces. The results obtained for MI spaces are preserved by the corresponding fiber spaces almost everywhere. Employing the Zak transform, we obtain the results for translation invariant spaces on locally compact groups by action of its closed abelian subgroup. Additionally, we provide the application of our results to sampling theory

An Appraisal of the Current Scenario in Vaccine Research for COVID-19

The recent coronavirus disease 2019 (COVID-19) outbreak has drawn global attention, affecting millions, disrupting economies and healthcare modalities. With its high infection rate, COVID-19 has caused a colossal health crisis worldwide. While information on the comprehensive nature of this infectious agent, SARS-CoV-2, still remains obscure, ongoing genomic studies have been successful in identifying its genomic sequence and the presenting antigen. These may serve as promising, potential therapeutic targets in the effective management of COVID-19. In an attempt to establish herd immunity, massive efforts have been directed and driven toward developing vaccines against the SARS-CoV-2 pathogen. This review, in this direction, is aimed at providing the current scenario and future perspectives in the development of vaccines against SARS-CoV-2

An overview of vaccine development for COVID-19

The COVID-19 pandemic continues to endanger world health and the economy. The causative SARS-CoV-2 coronavirus has a unique replication system. The end point of the COVID-19 pandemic is either herd immunity or widespread availability of an effective vaccine. Multiple candidate vaccines - peptide, virus-like particle, viral vectors (replicating and nonreplicating), nucleic acids (DNA or RNA), live attenuated virus, recombinant designed proteins and inactivated virus - are presently under various stages of expansion, and a small number of vaccine candidates have progressed into clinical phases. At the time of writing, three major pharmaceutical companies, namely Pfizer and Moderna, have their vaccines under mass production and administered to the public. This review aims to investigate the most critical vaccines developed for COVID-19 to date

Subspace Dual and orthogonal frames\\ by action of an abelian group

In this article, we discuss subspace duals of a frame of translates by an action of a closed abelian subgroup $\Gamma$ of a locally compact group $\mathscr G.$ These subspace duals are not required to lie in the space generated by the frame. We characterise translation-generated subspace duals of a frame/Riesz basis involving the Zak transform for the pair $(\mathscr G, \Gamma) .$ We continue our discussion on the orthogonality of two translation-generated Bessel pairs using the Zak transform, which allows us to explore the dual of super-frames. As an example, we extend our findings to splines, Gabor systems, $p$-adic fields $\mathbb Q p,$ locally compact abelian groups using the fiberization map.Comment: 21 page