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
Hyperbolic models have also been used in geomechanics problems to model interfaces [17, 18], soil reinforcement pullout , and triaxial compression tests on soil , It should be noted that hyperbolic functions
have provided components of tensile load-strain models reported in the geosynthetics literature [1, 21-25].
Right and skew-right circulant matrices remains invariant on their type when evaluated on trigonometric and hyperbolic functions
that are used in this paper.
Later chapters cover continuity of functions, derivatives of functions, trigonometric limits, and exponential and logarithmic functions and their derivatives, in addition to implicit functions, parametric functions, Rolle's theorem, Taylor's formula, and hyperbolic functions
We applied deform hyperbolic functions
introduced for the first time by Arai in (ARAI, 1991)
There's also an advanced math library, including trigonometry and hyperbolic functions
Keywords: Pensions, Retirement, Hyperbolic Functions
, Consumption, Saving, Time Preference.
He included appendices on the D-operator methods and hyperbolic functions
The complement of processing commands for brightness and contrast includes stretching routines with linear, nonlinear, and hyperbolic functions
One disadvantage of the hyperbolic function
is that age-price functions estimated from a hyperbolic function
(or alternatively, hyperbolic functions
estimated from an age-price function) require an assumption to be made about a real discount rate.
To derive |Beta~l, A = cosh(|Gamma~l) in the ABCD matrix can be expanded using an identity for hyperbolic functions
Similarly, the development of the hyperbolic functions
follows from the unit equilateral hyperbola, [x.