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In order to reduce the average number of vectors in the approximation generator and still to obtain the minimal degradation, we combine a Ritz variational method for the actual minimization on a patch, and a complementary fractional variational principle.
The paper considers makespan minimization on a single machine subject to release dates in the relocation problem, originated from a resource-constrained redevelopment project in Boston.
The main idea of regularization by projection is to project the least squares minimization on a finite-dimensional subspace to obtain a well-conditioned problem and, consequently, a stabilization of the generalized inverse of the approximate operator.
Kacem, A. Ridha Mahjoub, Fully polynomial time approximation scheme for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers and Industrial Engineering 56 (2009) 1708 1712].
In this case of ordered growth, the areal density of the nucleated islands and their positioning are essentially driven by the elastic energy minimization on a textured surface, which predominate with respect to the local kinetics of diffusion of Si and Ge atoms.
Kacem, Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers & Industrial Engineering 54 (2008) 401 410], this paper is the first successful attempt to develop a constant ratio approximation algorithm for this problem.
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The cupping effect is almost removed, but the reconstructed slice is also noisy, which is a known effect of least squares minimization on an ill-posed problem when running too many iterations [13].
The method employs the weighted constrained-least-squares technique for the prototype filter design and is based on the minimization of a one-dimensional objective function.
For anisotropic mesh adaptation, a metric tensor (mathbb {M}_{text {aniso}}) is developed in [24] that is based on minimization of a bound on the H 1 semi-norm of linear interpolation error and is defined for any triangular element K as follows mathbb{M}_{text{aniso},K}=rho_{K} det left(I+frac{1}{alpha_{h}}|H_{K}|right)^{-frac{1}{2}} left[ I+frac{1}{alpha_{h}}|H_{K}|right], (8).
Some attempts in this field are focused on using classical analytical and numerical methods for parameter estimation based on minimization of a suitably chosen cost function [1, 5, 6, 7, 8, 9, 10].
The algorithm is based on the minimization of a functional depending on a least square error term combined with two penalties.
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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