The Bernstein expansion is an effective method for testing positivity or negativity of a multivariable polynomial over a box.
In the case of N stations, we have 3 N nonlinear equations, a system of multivariable polynomial to solve.
A multivariable fractional polynomial interaction (MFPI) model was used to detect an interaction between the effect of RT and Ki-67 LI on the risk of local recurrence (Royston and Sauerbrei, 2004).
We then ran a multivariable fractional polynomial (MFP) procedure designed for multiple imputed data to help guide the backwards selection of covariates, and identify appropriate transformation(s), to retain in the fully adjusted survival model [ 25, 26].
A multivariable fractional polynomial model was fitted to estimate the excess hazard of death in each deprivation category, adjusting for the confounding effects of age, stage, cancer site (colon, rectum) and sex, using generalised linear models.
The non-linear models include artificial neural networks (ANNs) and multivariable polynomial regression.
The study applied multivariable polynomial and normalized performance models, which were developed for the studied systems for both fault-free and faulty conditions based on measurements obtained in a laboratory under controlled conditions.
The theorems have been developed in terms of the product of ℵ-function and a general class of multivariable polynomials in a compact and elegant form with the help of Saigo-Maeda power function formulas.
A general class of multivariable polynomials is defined and studied by Srivastava and Garg [31]: S L h 1, …, h s = ∑ k 1, …, k s = 0 h 1 k 1 + ⋯ + h s k s ≤ L ( − L ) h 1 k 1 + ⋯ + h s k s A ( L ; k 1, …, k s ) x 1 k 1 k 1 !
