Given the relatively low sample size, only univariate survival analysis was performed, and the Cox proportional hazard regression model was used, assuming a linear functional form of the covariates being assumed.
Together, Eqns (1)–(7) allow for a very large possible number of models, with a wide variety of numbers of parameters, depending on which predictor variables are included, and depending on whether each variable is included using a linear or non-linear (quadratic) functional form.
Individual structural T1-weighted images were coregistered to the mean motion-corrected functional images using a linear transformation.
I approximate the functional form in (7) using a linear model in the estimation.
Next, using Lemma 4.3, we can define a linear functional determined by (422).
The majority of techniques that incorporate shape priors use a linear combination of two functionals with one as a common segmentation functional (as discussed in Equation 9) and the other a shape difference [14].
an MOPS with respect to a linear functional.
We will show using purely linear functional analytic methods that each exact complex0→F→(C∞s00(C∞s11(C∞s22…,wherepiare matrices of convolution operators (in particular, linear differential operators with constant coefficients), splits fromp1on (in the category of topological vector spaces).
By using linear functional analysis theory, we can prove X, (X^{1}) are Banach spaces.
The result obtained by Kirk is, in some sense, surprising because it uses geometric properties of Banach spaces (commonly used in Linear Functional Analysis, but rarely considered in Nonlinear Analysis until then).
