In Section 3, we use the time scales Taylor formula, see [11, Theorem 1.113], i.e.,
and, by the time scales Taylor formula, more precisely, (2.1),
Taylor presented a semiempirical formula (Taylor formula
) for the long cylindrical shell, and the projection angle of fragments can be obtained by using the Taylor formula
In particular, we have also the following Taylor formula of order m for a function f in B[C.sup.m] (see [10,25]),
In  the following estimate of the remainder [R.sub.m](f; s, t) := [h.sub.s](t) [log.sup.m] t in the Taylor formula of order m is proved, which extends a result proved in  for the classical Taylor formula in a slightly different setting.
Moreover, in the past years, central bank has used McCallum and the Taylor formula
based on quarter data as assistance by decision taking.
Analogously to [[summation].sub.2,1], here we can again use the Taylor formula
Using the modified Taylor formula
we Get [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Formula (9.17) is the second Taylor formula
of Theorem 9.2.
Hence, it is likely that after 2000 the Taylor formula does not accurately reflect the information used by the FOMC as input to its deliberations.
Note that the target funds rate predicted by the Taylor formula generally tracks the actual funds rate through 2000, though there are sizable and persistent deviations of the funds rate from the values predicted by the formula.
By Taylor formula
in the local basis ([sigma][beta]) we get [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] and a similar formula for [P.sup.t.sub.[alpha]][[sigma].sup.2].