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If f satisfies the only condition (51), we need to modify the representation of the solution by adding some extra terms (see Theorem 6.4 below).
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A simple reduced-order observer scheme is proposed by including extra terms.
The extra terms related to axisymmetry in the macroscopic equations are recovered by adding source terms into the LB equation, which are simple and involve no gradients.
A multi-level augmented error is designed to account for the extra terms appearing due to the use of PID and saturation.
In contrast to traditional layered isopycnal models, in which along-layer density gradients vanish, general coordinate approaches must deal with extra terms.
By utilizing the properties of internal forces, extra terms are also added to the control signals to consider the force tracking problem.
Continuously altering macroscopic material properties can therefore be easily captured by selecting a proper order of these B-spline functions without any extra terms.
To allow for opening and sliding at crack kinking and branching the dipole density representation contains conditional extra terms which fulfills the asymptotic behaviour at each endpoint.
Device shows bipolar switching characteristics owing to the extra terms added in the model equations.
The rationale behind the "extra" terms in Eq. 4 is straightforward.
To represent such an open system, two extra terms get introduced in the Schrodinger equation.
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CEO of Professional Science Editing for Scientists @ prosciediting.com