Suppose a feedback control law has been designed such that the nominal closed-loop system is exponentially stable for a certain switching signal, and suppose further that a corresponding Lyapunov function for the nominal closed-loop system is available.
Suppose further that a friendly neuroscientist is able to trace the causal history of neural firings in the child's brain.
Suppose, further, that a ′ ( t ) > 0. Then every solution x ( t ) of Eq. (1) is either oscillatory or converges to zero.
Suppose, further, that a domain, such as perhaps ethics or aesthetics, are "response dependent," constituted by our conceptual responses; suppose, that is, that what determines the nature of, say, the good, the funny, or the beautiful are simply the principles underlying people's competence with their concepts of them.
Suppose further that a beneficial allele appears at one of the E loci in one individual of the population.
By the end of June a Greek government is supposed to specify a further package of reforms and spending cuts, worth 5.5% of GDP; these are to be carried out in two instalments, the first in 2013, the second in 2014.
Commentators and experts have been writing obituaries for the Congress party and predicting its terminal decline since the 1990s, and this election was supposed to confirm a further fragmentation of the Indian political party scene with the big two, the centre-left Congress and the rightwing BJP, having to depend even more on a plethora of outfits with region-specific support-base.
It is constructed around seven basic propositions, numbered by the natural numbers 1-7, with all other paragraphs in the text numbered by decimal expansions so that, e.g., paragraph 1.1 is (supposed to be) a further elaboration on proposition 1, 1.22 is an elaboration of 1.2, and so on.
Though Plan 9 was supposed to be a further development of Unix concepts, compatibility with preexisting Unix software was never the goal for the project.
(a) for all and suppose further that there exist a compact homotopy and an such that.
