In the search for evidence for the long memory property in the markets, we modelled the time series using a formulation of fBm to obtain Hurst exponents
H estimated by the M-R/S technique and the DFA technique, with different window sizes.
However, the Hurst exponent
is only suitable for distinguishing the types of long-run dependence in time series.
From Figures 3 and 4, it can be seen that the Lyapunov exponents
of the corresponding roll angle and yaw angle are almost the same while the Lyapunov exponents
of the corresponding pitch angle and manipulator joint angle differ.
Generally, the scaling exponents
in IMR are smaller than those of TP, which indicates stronger long-term memory characteristic for TP.
In Figures 6(a)-6(d), we plot the top Lyapunov exponents
, the time history, the phase portrait, and Poincare map of nonlinear system.
After the Pareto exponents
are estimated, we can estimate the allometric scaling exponent
based on maximum-likelihood fitting.
Recently, Tan and Liu  gave some boundedness of [T.sub.[OMEGA],[sigma]] on function spaces with variable exponent
. For the applications of fractional integral operator in fractional order system, we choose to refer to .
Such numbers are so-called the Lyapunov exponents
Data for MA and MB were log10-transformed and Model Type II (reduced major axis, RMA) regression analysis was used to determine the scaling exponents
(aRMA) and allometric constants (log bRMA) (Niklas, 1994, 2005, 2006; Falster et al., 2006; Warton et al., 2006).
In general, the participants of TransRussia give positive assessment to the exhibition, they point out activity of exponents
, interesting meetings with prospect clients and development of new directions and types of services.