In addition, the continuity, such as ((eta, u,q in C^{0}([0,T],H^{7}times H^{6}timathcal{})), (mathcal{G}(t)) and so on, can be verified by using the regularity of ((eta,u,q)), the transformed MHD equations and a standard regularized method.
The results presented in this paper improve and extend the main results of Tian and Zhang (J. Inequal. Appl. 2017 Article ID 13, 2017), and Tang et al. (Acta Math. Sci. 36B(201602–613, 2016) (in a single-step regularized method) with a new step size, and many others.
In the third stage, a non-local regularized method combining the transmission is proposed to recover the underlying image.
In the third stage, a non-local regularized method combining the transmission is proposed to recover the underlying image with the known atmospheric light and transmission.
Motivated by Byrne's CQ algorithm, Xu [6] suggested a single step regularized method x n + 1 = P C ( ( 1 − α n γ n ) x n − γ n A ∗ ( I − P Q ) A x n ), n ∈ N. (1.2).
The Lasso variable selection method [38] is a regularized estimation method for regression models including the Cox PH model.
Similarly, many methods have been investigated to solve the Cauchy problem for a linear homogeneous elliptic equation such as the method of successive iterations [8, 9], the optimization method [10, 11], the quasi-reversibility method [12 14], fourth-order modified method [15, 16], Fourier truncation regularized (or spectral regularized method) [17 19], etc.
A version of the regularized method which can account for viscous diffusion is developed using a scheme that redistributes the particle strength vectors.
For the regularized method, a new algebraic smoothing is presented with convergence properties equal to those of Gaussian smoothing.
