– The Brunn-Minkowski theory is a central part of convex geometry. At its foundation lies the Minkowski addition of convex bodies which led to the definition of mixed volume of convex bodies and to various notions and inequalities in convex geometry. Its origins were in Minkowski’s joining his notion of mixed volumes with the Brunn-Minkowski inequality, which dated back to 1887. Since then it h...

We show that for any 1 ≤ t ≤ c̃n log−5/2 n, the set of unconditional convex bodies in R contains a t-separated subset of cardinality at least exp ( exp ( c t2 log(1 + t) n )) . This implies the existence of an unconditional convex body in R which cannot be approximated within the distance d by a projection of a polytope with N faces unless N ≥ exp(c(d)n). We also show that for t ≥ 2, the cardina...

In this paper, we introduce and investigate two new generalized mixed equilibrium problems and explore the relationship between them and the properties of their solutions in Banach spaces. Based on the generalized f -projection, we construct hybrid algorithms to find common fixed points of a countable family of quasi-φnonexpansive mappings in Banach spaces, a common element of the set of soluti...

This paper presents a novel mixed source localization algorithm based on high-order cumulant (HOC) and oblique projection techniques. To address the issue of lower accuracy in near-field (NFS) compared to far-field (FFS) localization, presented further enhances NFS localization. First, FFS’s direction-of-arrival (DOA) estimate is acquired utilizing multiple signal classification (MUSIC) spectra...

Abstract Terrestrial ecosystems respond to climate change in various ways, making it crucial improve our understanding of these dynamics and uncertainty projections. Here, we investigate how the species composition a temperate-subtropical mixed forest on Jeju Island, South Korea, would by 2099 analysed resultant effects phenological timings carbon flux using an individual cohort-based model—the...