The
logarithmic function restricts a value interval when applied while the exponential one is expanding that interval.
The approximation error is evaluated by the
logarithmic functionCaption: FIGURE 7: Prediction model for the settlement of the road shoulder: (a) hyperbolic function; (b)
logarithmic function; (c) power function; (d) exponential function.
Using the
logarithmic function NB model, Xiang Liu [24] and Rong Li (2013) established the frequency forecast model of the highway traffic crash in Ontario, Canada.
It adopts the Schroeder phases as the initial phases and uses variable clipping level based on
logarithmic function in the iteration procedure.
The three data points [C.sup.o] connected with a smooth curve presents a
logarithmic function (Figure 6).
Based on the quadratic function and Taylor series, a
logarithmic function is constructed and as Lyapunov function, which is applicable to not only Rotary Inverted Pendulum but also the physical systems with the linear or nonlinear models.
Gent and Thomas [16] proposed an empirical model similar to that of Mooney and Rivlin but containing a
logarithmic function of the second invariant.