For example, if k < 2p(p − 1) − 2 for a prime p then the p-primary component of the stable homotopy group πkS vanishes unless k + 1 is divisible by 2(p − 1), in which case it is cyclic of order p. An important subgroup of πn+k(Sn), for k ≥ 2, is the image of the J-homomorphism J: πk SO(n)) → πn+k(Sn), where SO(n) denotes the special orthogonal group.
Their exhalations, oxygen, did for both methanogens and methane and created an atmosphere similar to the one that exists now.The main upshot is that although oxygen is unquestionably a biomarker (it is so reactive that it would vanish from any atmosphere unless constantly replenished) methane may be one, too.
But unless art schools vanish or artists decide they really like their day jobs, novelty won't be a problem for the Armory Show, ever.
Soon it would be just a ripple in the water, then a shadow, and then it would vanish entirely, easy to forget unless someone was around to remember it.
In particular, Eq. (17) implies that, in such state, the interference terms vanish and, therefore, the two bands are decoupled (unless additional coupling mechanisms are considered [6, 10, 14]).
Potato chips aren't going to vanish off the planet - and unless they do - making them more healthy, and their packaging bio-degradable seems like a good thing.
I'm an 18-year-old Afghan living in Kabul and unless these war-stricken Afghans vanish I'm pessimistic about the future of this war-torn country.
At the moment, unless you're willing to watch consumer spending vanish (even more than it already has), I don't think it is.
