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ii) Use the standard matrix-form representation (see Section 2.2) to represent all second-order kernels that compose the kernel of interest.
Exploit the strategy described in Section 3.1 (see Fig. 3) to obtain an implementation of the pth-order kernel of interest in the form of a parallel structure composed of second-order kernels.
In this context, the proposed approach can be summarized as follows: i) Exploit the strategy described in Section 3.1 (see Fig. 3) to obtain an implementation of the pth-order kernel of interest in the form of a parallel structure composed of second-order kernels.
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The objective of this study is to design a seed trap configuration surrounding a parent plant when the long distance component of the seed dispersal kernel is of interest.
A fine resolution (small Δ r) has to be chosen if the precise shape of the kernel is of interest.
The necessary density condition in C known for sampling and interpolation in the Lp space of entire functions with a subharmonic weight is extended to the case of a 2-homogeneous, plurisubharmonic weight function in C. The method is by estimating the eigenvalues of a certain Toeplitz concentration operator, using asymptotic estimates for the Bergman kernel of independent interest.
The position of a given mean is calculated using Equation 2 on the elements residing in the kernel's region of interest (ROI).
The CT reconstruction was performed using two different kernels: smoother kernel (B08s) for attenuation correction and scatter correction and sharper kernel (B35) for volume of interest (VOI) delineation.
Based on the reproducing kernel approximation, the domain of interest is discretized by a set of particles without the employment of a structured mesh, which constitutes an advantage over the finite element method.
This method not only suppresses noise (via an appropriate Gaussian kernel) but also sharpens the object of interest (by adjusting the size of the boxcar kernel).
Therefore, when we later verify parameter estimates we will not check each individual estimate, but only plot the estimated shape of the kernel function, which is the quantity of interest.
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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