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Then the growth of ∥ v ∥ is sublinear in view of estimate (9).
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We present two algorithms whose regret is sublinear in the number of trials and polynomial in the size of the network.
Moreover, system (1) can be additively perturbed, for the same goal, by another Carathéodory function which is sublinear in both states variables x and y.
As shown in Beckstette et al. (2006), the expected runtime of ESAsearch is sublinear in the text length, whereas its worst case runtime is 𝒪(n + m) under the special condition that n≥|𝒜| m + m − 1 holds, independent of the chosen threshold θ.
Unfortunately, they cannot assert that the minimal members of convex expectations must be sublinear in that lemma (see line 13 of p.48).
Up to now, there have been few works concerning the case that V ( x ) is nonradial potential and f ( x, u ) is sublinear at infinity in u.
In this subsection, we will consider the case where is sublinear.
Notice that is sublinear.
It is clear that f is sublinear.
Since is superlinear and is sublinear,.
Theorem 3.4 Suppose that f is sublinear and the impulsive functions I j have sublinear growth.
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CEO of Professional Science Editing for Scientists @ prosciediting.com