The solution operator − 1 : L r → W 0 1, 2 ∩ W 2, r , h ↦ w, associated to the problem − Δ w = h in Ω, w = 0 on ∂ Ω, is well defined, obviously linear, continuous, and compact.
But Britain's big daily newspapers have long done battle on a national stage, slicing and dicing markets defined most obviously by the class divide of blue-collar tabloids and white-collar broadsheets, but also by political persuasion — liberal for The Guardian, for instance, conservative for The Daily Telegraph.
where is well defined since obviously.
Moreover, by a similar reasoning to Algorithm 3.1, Algorithm 3.2 is well defined and obviously the solution set S of the FPSCSEP is convex and closed.
The processes of transcription and DNA repair are intimately linked, as defined most obviously for the basal transcription factor TFIIH, which is essential for transcription initiation by RNA polymerase II (PolII), but is also required for the transcription-coupled nucleotide excision repair (Compe and Egly, 2012; Kamileri et al., 2012).
What most obviously define this collection, though, are Jungr's husky alto – gentle but rich, pure yet at times beautifully cracked – and the spare, jazz-inflected arrangements by the singer and her long-time collaborator, the pianist Simon Wallace.
We could obviously define infinitely many grue-like predicates that would all lead to new, similarly incompatible predictions.
