We establish pointwise characterizations of functions in the HardySobolev spaces H within the range p ∈ (n/(n + 1), 1]. In particular, a locally integrable function u belongs to H(R) if and only if u ∈ L(R) and it satisfies the Hajlasz type condition |u(x)− u(y)| ≤ |x − y|(h(x) + h(y)), x, y ∈ R \ E, where E is a set of measure zero and h ∈ L(R). We also investigate HardySobolev spaces on subdo...

We review lexical Association Measures (AMs) that have been employed by past work in extracting multiword expressions. Our work contributes to the understanding of these AMs by categorizing them into two groups and suggesting the use of rank equivalence to group AMs with the same ranking performance. We also examine how existing AMs can be adapted to better rank English verb particle constructi...

This paper is concerned with Kolmogorov's two-equation model for turbulence in R 3 $\mathbb {R}^3$ involving the mean velocity u, pressure p, an average frequency ω > 0 $\omega >0$ , and a turbulent kinetic energy k. We consider system space-periodic boundary conditions cube Ω = ( ] [ ) $\Omega =({]0,a[}){}^3$ which good choice studying decay of free motion sufficiently far away from boundaries...