The proposed control family includes a large class of saturated-type

hyperbolic function terms; the hyperbolic structure depends on k as a power function.

Caption: FIGURE 8: Prediction model for the settlement of driveway: (a)

hyperbolic function; (b) logarithmic function; (c) power function; (d) exponential function.

This is done as relatively rapid changes in indifference points are observed at relatively shorter delay values, whereas changes become less pronounced out at relatively longer delay values, which is characteristic of

hyperbolic functions.

By using the method, we have obtained new exact solutions in terms of the

hyperbolic functions, the trigonometric functions, the exponential functions, and the rational functions.

This idea comes from the vast applications of

hyperbolic functions to solve differential equations.

When [DELTA] > 0 and [lambda](v - 1) = 0 (or [mu](v - 1) = 0), the

hyperbolic function solutions of (28) are as follows:

Table 2--Estimates of the Linear

Hyperbolic Function' parameters for the different age classes and calving seasons.

Properties on

Hyperbolic Functions. Some properties on

hyperbolic functions will be used.

Much study has been conducted to prove that the

hyperbolic function can be applied to integral deformation behavior as well as to calculate the deformation activation energy Q of magnesium alloys.

From the limit forms of the elliptic function solutions, we obtain some trigonometric and

hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave.

A

hyperbolic function (1) was used to describe the amplitude-energy relationship at various fixed times.

Every element of the artificial neural network consists of the scalar vector of the input signal multiplied by the weight factor (which is argument of activation of

hyperbolic function).