The phrase "and regularized by the" is correct and usable in written English.
It can be used in contexts where you are discussing processes, methods, or systems that have been standardized or made consistent.
Example: "The data was collected and regularized by the research team to ensure accuracy and reliability."
Alternatives: "and standardized by the" or "and normalized by the".
This leads to a specific scaling of an approximating elastic adhesive contact problem, discretized by a semi-implicit scheme and regularized by a BV-type gradient term.
Such stops involve only a modest intrusion, are not likely to be frightening or significantly annoying, are regularized by the fixed situs, and effectively serve the important national interest in controlling illegal entry.
The mathematical formulation is described by an ill-conditioned system of non-linear equations, which is regularized by the TSVD method.
The solution of a Fredholm integral equation of the first kind which is, in general, an ill-posed problem, can be regularized by the maximum entropy method (MEM ).
Further, the TSSG tracker is novel in exploiting the sparsity present in the grid-based state vector, which allows one to leverage efficient solvers of (weighted) least-squares (LS) minimization problems regularized by the ℓ1-norm of the desired state estimate.
The resulting system of linear algebraic equations is ill-conditioned and therefore its solution is regularized by employing the zeroth-order Tikhonov functional, while the choice of the regularization parameter is based on the L-curve method.
The expression values were regularized by adding the noise to the expression of each gene before the ratios were calculated.
Noise data solutions are regularized by stopping the iterations with the discrepancy principle of Alifanov, before the high frequency components of the random noises are reproduced.
The magnetic field inverse problem was implicitly regularized by setting the maximum SH degree, selecting the quadratic time basis functions, and ensuring that the chosen time window and the data distribution were compatible with these settings.
An entropy-bounded Discontinuous Galerkin (EBDG) scheme is proposed in which the solution is regularized by constraining the entropy.
