Exterior convexity and classical calculus of variations

We study the relation between various notions of exterior convexity introduced in Bandyopadhyay-Dacorogna-Sil \cite{BDS1} with the classical notions of rank one convexity, quasiconvexity and polyconvexity. To this end, we introduce a projection map, which generalizes the alternating projection for two-tensors in a new way and study the algebraic properties of this map. We conclude with a few simple consequences of this relation which yields new proofs for some of the results discussed in Bandyopadhyay-Dacorogna-Sil \cite{BDS1}.Comment: The original publication is available at www.esaim-cocv.org https://www.esaim-cocv.org/articles/cocv/abs/2016/02/cocv150007/cocv150007.htm

On Aspects of Holographic Thermal QCD at Finite Coupling

Some Physics (obtaining lattice-compatible deconfinement temperature, some transport coefficients and Einstein's relation) and Mathematics (torsion classes and supersymmetry) issues pertaining to the delocalized SYZ type IIA mirror of [1] and its M theory uplift in the MQGP limit of [2], are discussed.Comment: v3: 1+63 pages, LaTeX, title slightly modified, large amounts of explanatory material added and text rearranged though Results are unchanged, references added, to appear in NPB (the journal version also includes two figs excluded in the arxiv version due to size constraints). arXiv admin note: text overlap with arXiv:hep-th/0211102 by other author