Herisanu, Application of Optimal Homotopy
Asymptotic method for solving nonlinear equations arising in heat transfer.
The analysis of several plausible nested alternative stock return generating processes suggests that stock returns with weak
asymptotic tail dependence will produce CoVaR and MES hypothesis test statistic distributions that significantly overlap the sampling distributions of test statistics calculated from Gaussian returns.
Although (10) and (11) only contain the leading order terms of the
asymptotics, and the
asymptotic decomposition is carried out by using the inverse powers of m, i.e., fractional powers of k[rho], they yield a rather accurate approximation for the field even when the frequency is not too high.
where [r.sub.mul] is the
asymptotic value of [[??].sub.mul] under [H.sub.1], [[??].sub.mul,0] is the estimation error vector resulted from [W.sub.i] (t) and [[??].sub.mul,1] is the estimation error vector resulted from both [w.sub.i] (t) and s(t), which are asymptotically distributed as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], respectively.
Surfaces with Common
Asymptotic Curve in [E.sup.3.sub.1]
Section 3 derives the exact and
asymptotic outage probability of partial relay selection system with feedback delay and CCI.
From the
asymptotic form of E[[??](x)] and V[[??](z)] and Theorem 1, we see that, for small [lambda], the bias of [??](x) is small and the variance becomes large.
By omitting members of the O ([[??].sup.3]) order and neglecting the sign (~), we receive the
asymptotic integration problem
Therefore, its
asymptotic expansion follows straightforwardly from formula (1.3) replacing a by U and setting b = [infinity].
Herisanu, "Determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy
asymptotic method," Journal of Sound and Vibration, vol.
Su and Zheng [22] developed two velocity-free controllers to deal with
asymptotic stabilization based on Rodrigues parameter and modified Rodrigues parameter, respectively.