The continuous variables are estimated non-parametrically by applying second order Gaussian random walk prior, which permits enough flexibility while avoiding over-fitting the data [ 18].
First, we develop a linear modeling by applying first-order Taylor series expansion about the initial values of the controller.
The composite laminated doubly-curved shells of revolution are divided into their segments in the axial direction, and the theoretical model for vibration analysis is formulated by applying first-order shear deformation theory.
The transverse beam envelope analyses, such as error sensitivity, chromatic aberration, and emittance growth, are presented by applying second-order perturbation treatment to a formulated matrix describing a quasi-periodic lattice in the linear accelerator system.
When a correction was applied, second order aberrations (excluding defocus) up to and including the sixth radial order were corrected.
To circumvent this problem, we applied second-order autoregressive time series analyses to data generated by a realistic agent-based computer model.
The dynamics of Cd2+ adsorption by bacterial cells were evaluated by applying pseudo first order and pseudo second order models.
Moreover, at the optimal operational conditions (pH 3.5 and room temperature) kinetic studies were carried out by applying pseudo-first order, pseudo-second order, Chien Clayton and intraparticle diffusion models, observing a good agreement between theoretical and experimental results.
The C stock of each HWP category, in each year, is estimated by applying a first order decay function taking into account the C outflow and inflow from and to each category, as reported in the Methods (see the subsection on First Order decay functions).
We extend this concept for the vectored CM-DM processing in the upstream transmissions by applying a first order approximation of inverse of the combined CM-DM channel as H ( c d ) - 1 = H diag ( c d ) ( I + C ( c d ) ) - 1 ≈ ( I - C ( c d ) ) H diag ( c d ) - 1, (38).
