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Such a conception of liberalism and democracy, however, will not only reveal its inability to offer wise representation to citizens.
For linear operators, the required source inequality follows from a source wise representation of a subgradient of R at x†.
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Step-wise representation of methodology applied to construct BRN and subsequent state graph analysis using Graphviz tool.
A primary objective is to benchmark two different models of the MSFR primary circuit, both of them including a detailed and fully-coupled (node-wise) representation of turbulent fuel-salt flow, neutron diffusion, and delayed-neutron precursor diffusion and convection.
To solve this problem the programs use a different representation for each term: normalized associated Legendre polynomials PKj x) as a functional basis for the angular kinetic term and an evenly spaced grid for the radial kinetic term yielding a fully point-wise representation of the wave functions.
Because the recursive algorithm in (30) can be observed as a one-to-one translation of a frequency-domain (bin-wise) representation of adaptive PCA [54], it provides approximately a bin-wise unit norm, i.e., ( left |{widehat {H}_{l}}right |^{2} + left |{widehat {H}_{r}}right |^{2} approx 1) when the convergence toward the principle components is achieved.
Additional file 8. Cytoband-wise representation of CNVs found in all 48 samples along with clinical parameters and patient epidemiology.
At last, the reconstruction layer aggregates the patch-wise representations to generate the final output.
Frame wise cepstral representation is provided in the input layer of the deep-structured model.
For the popular background subtraction approach called the Gaussian background model, Stauffer and Grimson [4] presented a pixel-wise background representation scheme using the mixture of Gaussians (MoG) and pixel-wise background updating to update the intensity mean and variance of each pixel in real-time.
Aggarwal et al. [36] adopted a part-wise sparse representation approach for matching plastic surgery-altered faces.
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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