Chemin et al. [M2AN Math. Model. Numer. Anal., 34 (2000), pp. 315–335.] considered the three-dimensional Navier–Stokes equations with vanishing vertical viscosity. Assuming that the initial velocity is square-integrable in the horizontal direction and Hs in the vertical direction, they prove existence of solutions for s > 1/2 and uniqueness of solutions for s > 3/2. Here, we close the gap betwe...

Regarding our article on the association of androgen deprivation therapy (ADT) with increased Alzheimer’s disease risk, Bowen et al, Froehner and Wirth, Leow et al, and Brady et al highlight a number of significant considerations that will prove important in the design of future studies that investigate the association of ADT and Alzheimer’s disease. We agree with Bowen et al and Leow et al tha...

The purpose of the paper is to study the uniqueness problems of difference polynomials of meromorphic functions sharing a small function. The results of the paper improve and generalize the recent results due to Liu, et al. [11] and Liu, et al. [12].

Much effort has gone into the understanding of regularization in ill-posed problems in computer vision. Yuille and Grzywacz were among the first to propose use of the Gaussian Tikhonov regularizer for image registration, illustrating the ideal properties of this regularizer for preserving motion coherence. Nielsen et al. later described the intricate connection between the Gaussian Tikhonov reg...

To recover a sharp image from its blurry observation is the problem known as image deblurring. It frequently arises in imaging sciences and technologies, including optical, medical, and astronomical applications, and is crucial for allowing to detect important features and patterns such as those of a distant planet or some microscopic tissue. Mathematically, image deblurring is intimately conne...

The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution arising from the Poisson model with a Gaussian prior. This is achieved by seeking an optimal Gaussian distribution minimizing the Kullback...

A novel variant of the level set method is introduced for dynamic two-dimensional X-ray tomography. The target is allowed to change in time while being imaged by one or several source-detector pairs at a relatively high frame-rate. The algorithmic approach is motivated by the results in [Kolehmainen et al., SIAM J. Sci. Comput. 30(3)], showing that the modified level set method can tolerate hig...