Davies’ version of the Hardy inequality gives a lower bound for Dirichlet integral function vanishing on boundary domain in terms squared with weight containing averaged distance to boundary. This is applied easily derive two classical results spectral theory, E. Lieb’s first eigenvalue Laplacian and G. Rozenblum’s estimate counting an unbounded number disjoint balls preset size whose intersect...

At CRYPTO 2016, Cogliati and Seurin introduced the Encrypted Davies-Meyer construction, p2(p1(x) ⊕ x) for two n-bit permutations p1, p2, and proved security up to 2 . We present an improved security analysis up to 2/(67n). Additionally, we introduce the dual of the Encrypted Davies-Meyer construction, p2(p1(x)) ⊕ p1(x), and prove even tighter security for this construction: 2/67. We finally dem...

Davies et al. (1988) concluded that body size did not directly influence annual fecundity in Lesser Snow Geese (Chen c. caerulescens, hereafter called Snow Geese). This disagrees with Ankney and Macinnes (1978) who showed that there was a positive correlation between culmen length and body mass in prelaying female Snow Geese, and that heavier females laid more eggs than did lighter females. A r...