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Notes: Each point represents beta coefficient from the corresponding partial model.
Toward this end, we relax the coupled constraints and obtain the corresponding partial Lagrangian function given by (21).
The following lemma assures that if an eigenfunction u is smooth enough, then u solves the corresponding partial differential equation.
Each point in the plot represents an estimate of the beta coefficient from the corresponding partial model.
Let be a solid cone in and let be the corresponding partial ordering on with respect to.
In the spatially inhomogeneous case, it is an indication of the richness of the corresponding partial differential equational dynamics.
The top-down algorithm selects a variable by detecting if the corresponding partial derivative is zero or not at the point of interest.
The distortion is averaged over realizations of the source and the corresponding partial observations, the observation and receiver noises, and the channel gains.
The results are obtained through researching a system of corresponding partial differential equations which approximates the perturbed coupled KdV equations and the symmetry method.
In the case k = 0, for all α ∈ R +, the T j, j = 1, 2, …, d, reduce to the corresponding partial derivatives.
Lattice differential equations can be considered as a spatial or temporal discrete analogue of corresponding partial differential equations on unbounded domains.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com