Grothendieck constant is norm of Strassen matrix multiplication tensor
Sign Up to like & getrecommendations! Published in 2019 at "Numerische Mathematik"
DOI: 10.1007/s00211-019-01070-6
Abstract: We show that two important quantities from two disparate areas of complexity theory --- Strassen's exponent of matrix multiplication $\omega$ and Grothendieck's constant $K_G$ --- are intimately related. They are different measures of size for… read more here.
Keywords: grothendieck constant; tensor; grothendieck; matrix multiplication ... See more keywords
Expanding phenomena over matrix rings
Sign Up to like & getrecommendations! Published in 2018 at "Forum Mathematicum"
DOI: 10.1515/forum-2019-0032
Abstract: Abstract In this paper, we study expanding phenomena in the setting of matrix rings. More precisely, we will prove that • if A is a set of M 2 ( ???? q ) {M_{2}(\mathbb{F}_{q})}… read more here.
Keywords: expanding phenomena; rvert lvert; lvert rvert; rvert ... See more keywords
A note on Hopf’s lemma and strong minimum principle for nonlocal equations with non-standard growth
Sign Up to like & getrecommendations! Published in 2022 at "Forum Mathematicum"
DOI: 10.1515/forum-2022-0331
Abstract: Abstract Let Ω ⊂ R n \Omega\subset\mathbb{R}^{n} be any open set and 𝑢 a weak supersolution of L u = c ( x ) g ( | u | ) … read more here.
Keywords: lvert; strong minimum; lvert rvert; lemma strong ... See more keywords