The factor ε 1≪1 ensures that the exponential term remains small whenever p LV −p e >0 but it increases rapidly when p LV −p e <0.
Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy.
By examining the arguments of the previous lemma it is possible to see that the constant c 1 appearing in (76) shows the following natural asymptotic for q → p m : c 1 = c ( n, p, ν ) 1 p m - q q / ( p - 1 ), (80 where c is a constant that remains bounded whenever p varies in a compact subset of ( 1, ∞ ) ; see (79) and the constant appearing in Sobolev Morrey embedding theorem.
While the political future of basic federal transportation projects remains unclear, whenever House Republicans can find something to agree on, it's a safe bet that an ACORN funding ban will make the cut.
Our results support previous findings of temporal changes in museum collections [22] and we conclude that it remains important, whenever possible, to compare clutches of similar age to control for any inflation of colour variance among specimens.
Reproduction remains clonal whenever nutrients are present [ 66] and even under conditions inducing sexual reproduction (such as starvation), conjugation is impossible between clone mates because they carry the same mating type ([ 67], reviewed by [ 68]).
City policy at archaeological sites is to leave remains in place, whenever possible, out of respect for the dead.
Bendtner admits it has been "difficult" watching from the bench as Arsenal stormed to the top of the Premier League, but remains ready for whenever his next chance comes along.
Then again, Chris Bosh remains injured, and whenever Miami loses and James fails to play to the ridiculously dominant standard he set for himself Sunday, it is time to panic, lose all perspective.
Although, unlike Pratchett's, his golems have no personality, independence or speech, Low pours his own strength into them, suffering through them when they meet destruction, so the reader remains on tenterhooks whenever they fight.
