De Moraes, "Limit cycles for a class of continuous and discontinuous cubic polynomial
differential systems," Qualitative Theory of Dynamical Systems, vol.
The eigenfunction expansion method is a suitable choice of discretization method for finding multiple solutions of fourth-order ODEs with cubic polynomial
McNally  used a cubic polynomial
to blend a target lane-change curve.
If you appreciate that pattern, it is straightforward to extend Lagrange's formula to find a cubic polynomial
passing through four given points, or any higher order scenario you require.
The Hermite interpolation function is actually the basic cubic two-point interpolation function, the simplest case of a cubic polynomial
with boundary conditions settled (C0 and C1 continuity) as stated by Lehmann et al.
The fixed curve was estimated by race using the cubic polynomial
It was found that the DSG is effective to eliminate shear locking for a Kriging-based element with cubic polynomial
basis, but not effective for those with quadratic and linear bases.
Meanwhile for Figure 1(b) the values for shape parameter are [[alpha].sub.i] = 0 (black), cubic polynomial
Ball, that is, from (8), and [[alpha].sub.i] = 1000 (dashed).
From Figure 6 and Table 2, it can be seen that the RMSE about the cubic polynomial
function is lowest.
According to a full cubic polynomial
approach 35 measurements are mandatory for estimating the 35 coefficients in the model equation.
Second lane prediction method uses vehicle lateral motion model and the clothoidal cubic polynomial
curve road model.
Odds ratios were estimated from a conditional logistic regression model with stratification by ZIP code, year, and month and with parametric control for lag 0 mean temperature, lag 0 mean humidity, and day of year using cubic polynomials
; indicators for day of week, warm season, holiday, and lag holiday; and product terms between the warm season indicator and the temperature cubic polynomial
, humidity cubic polynomial
, day of week indicators, holiday indicators, and lag holiday indicators.