If one is only interested in upper O-estimates on N, the next theorem gives such bounds under much weaker assumptions on the symbol.
In [[2], Lemma 5.3], under much weaker assumptions on p ( t ), v ( t ) and q i ( t ), the initial value problem (2) is equivalent to the Volterra fractional integral equation x ( t ) = a 1 ( t − a ) q − 1 Γ ( q ) + 1 Γ ( q ) ∫ a t ( t − s ) q − 1 [ v ( s ) + p ( s ) x ( s ) − ∑ i = 1 m q i ( s ) | x ( s ) | λ i − 1 x ( s ) ] d s. (5).
The assumption on the reference signal is much more relaxed than those given in the previous papers.
They rely too much on the assumption that we, the reader, have nothing better to do but trawl through the jigsaw puzzle.
I've worked on clean-energy policy for twenty-five yeand, and I have observed that there are three major problems with a carbon tax: First, it relies too much on the assumption that any small tax will somehow alter markets.
Exxon posts its assumption on its website.
Of course, research into the adequacy of savings is often not conclusive, because so much depends on assumptions about investment returns and other factors like inflation and expanding life spans.
A recent report by Britain's Pension Commission argued that, given downward trends in the occupational pensions provided by employers and the erosion of state pensions, 60% of workers over 35 are not saving enough.A return to saving?In all of these analyses much depends on assumptions about the rate of return on savings.
In these cases, power calculations may more accurately reflect reality when based on simulations that do not rely as much on distributional assumptions.
As we discussed in the Explanation Generation section, the explanation generated by current ITS (Conati and VanLehn 1996; VanLehn et al. 2005; VanLehn and van de Sande 2009) does not focus much on modeling assumptions, or does so at most in an indirect/ad hoc way.
