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A class of semiparametrically structured models is proposed in which the predictor decomposes into components that may be given by a parametric term, an additive form of unspecified smooth functions of covariates, varying-coefficient terms or terms which vary smoothly (or not) across the repetitions in a repeated measurement design.
Each GAM model included two predictor variables, including log-transformed length of upstream sequence scanned for a given gene (x1; non-parametric term with cubic spline smoothing) and the number of motif sites detected within the upstream sequence (x2; parametric term without smoothing) [ 77].
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In particular, the case in which the parametric terms share close frequencies is examined.
It is shown that the presence of parametric terms gives rise to additional conditions for resonance in the support motion.
Quartic non-linearities in oscillators have beendiscussed in [7, 8];parametric terms in the nano-electromechanical context have been discussed in[9 11].
Superharmonic components of the ordern, supported by the parametric terms of the excitation and the non-linear coupling terms, are registered in the response for circular frequency ω≃ω1/n.
Approximate solutions are obtained for the fundamental and half subharmonic steady state responses and the effect of the non-linear and parametric terms examined.
With the GAM, three variables were estimated with a smoothing parameter of 1 (NBR, CTI, bulk density); therefore we fit the model with these variables as parametric terms, as recommended by Wood (2006).
A theoretical analysis with retention of both the parametric terms and up to the quadratic inertial non-linearities reveals the conditions required for resonant behaviour, and in the vicinity of each yields an approximate solution.
Due to the geometric asymmetry of the rotor and to the rotational motions of the support, the equations of motion include time-varying parametric terms which can lead to lateral dynamic instability.
The secondary forces are applied with the aim of enhancing the energy harvested from the base motion, and they may constitute direct excitation, or they may produce parametric terms in the equations of motion.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com