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This work is focused on the design and evaluation of an explicit parametric controller for a batch polymerization process.
The paper presents an explicit parametric description of the band structure governing the free propagation of elastic waves.
These lead to an elegant process from which an explicit parametric representation of the general offset curves is derived.
Moreover, the veering amplitude between any two of the three frequency loci can be expressed as an explicit parametric function.
In this work we aim at exploiting the properties of explicit parametric controllers and demonstrate the potential benefits of this control method in batch polymerization processes.
For laminated plates, an explicit parametric representation of the yield surface ∂Ghomp is given thanks to the π-function (the plastic dissipation power density function) that describes the local strength domain at each point of the plate.
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In contrast with parametric methods, such as snakes [ 17] that provide an explicit parametrization of the interface, level sets [ 18] embed the interface implicitly, which has some computational advantages (i.e., regarding propagation and topology of the interface).
This approach consists of five steps: (1) sampling data points; (2) regressing the sampled points into an explicit non-parametric equation; (3) filtering the unwanted points with pre-determined tolerance; (4) regressing the residual points; and (5) regenerating data points from the second-time regressed equation.
On the basis of this, explicit expressions of parametric sensitivities are given.
Explicit and complete parametric solutions to these equations are derived without any constraints on the coefficient matrices.
In order to obtain the explicit function form, multivariate parametric regression is applied.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com