The median PSA evolution over time can be modeled by a
cubic equation in time (-49.9277+2.7750 t- 0.0469 [t.sup.2] +0.0003 [t.sup.3]), where t is given in years, and PSA in ng/mL.
The boundary between these two cases is determined by the vanishing discriminant of the thirddegree equation (14), which can be received, for example, from the Cardano's formula for solving the
cubic equation:
Descriptions for each of the equations used to fit the J and H brightness data Equation Description Number 1 The solar phase angle is negative for waxing phases and positive for waning phases and data are fit to a
cubic equation. 2 Same as equation 1 except that data are fit to a quadratic equation.
In this study, analytical expressions of sin(n[pi]/7), where n is a positive integer, are found by expanding the function as a polynomial, solving a
cubic equation and extracting the square root of that equation.
For notational convenience, we let the difference operators [CE.sub.f] of
cubic equation (6) and [CD.sub.f] of cubic derivation be as follows:
(i) boundary equilibrium [E.sub.1] = ([x.sup.*.sub.1], g[x.sup.*.sub.1]([x.sup.*.sub.1] - 1),0), which is corresponding to extinction of the predator, where [x.sup.*.sub.1] > 1 is a real positive root of the
cubic equationIf bending moment sign is taken to be positive, the only positive root of the
cubic Equation (7) defines true maximum strain of the cross-section [[epsilon].sub.max].
[29] developed a new
cubic equation of state for carbon dioxide for the purpose of modeling carbon capture and sequestration.
Because the reduction in power is related to the airflow by a
cubic equation (O'Neal et al.
The corresponding
cubic equation with one unknown to the above inequality has three solutions:
Shengjin, "A new extracting formula and a new distinguishing means on the one variable
cubic equation," Natural Science Journal of Hainan Teacheres College, vol.