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We present a vortex particle method coupled with a penalization technique to simulate single and multiple swimmers in an incompressible, viscous flow in two and three dimensions.
In [17], the existence of nontrivial solutions for a semilinear elliptic variational inequalities with gradient-dependent nonlinearity is discussed by using variational methods combined with a penalization technique and an iterative scheme.
The method is based on a penalization technique where the system is considered as a single flow, subject to the Navier Stokes equation with a penalization term that enforces continuity at the solid fluid interface and rigid motion inside the solid.
Krämer et al. [ 27] proposed a combination of the feature extraction technique PLS with a penalization framework.
For example, stepPLR combines the logistic regression criterion with a penalization of the L2-norm of the coefficients.
For example, stepPLR combines the LR criterion with a penalization of the L2-norm of the coefficients.
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We generalize their idea to the nFPL equation, with a different penalization operator, the Fokker Planck operator that can be inverted by the conjugate-gradient method.
In our experiments, we show that in most tests DPM outperforms both Pregel and Fork-Join in terms of recommendation time, with a minor penalization in network usage in some scenarios.
Copy number segmentation based on least squares principles and combined with a suitable penalization scheme is appealing, since the solution will be optimal in a least squares sense for a given number of breakpoints.
The proof of the main result is based on Schauder's fixed point theorem combined with adequate variational arguments and a penalization technique.
In [25], the author studied the existence of solutions to a variational inequality involving nonlocal elliptic operators and obtained the existence of solutions by using Schauder's fixed point theorem combined with adequate variational arguments and a penalization technique.
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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