We prove sparse bounds for the spherical maximal operator of Magyar, Stein and Wainger. The bounds are conjecturally sharp, and contain an endpoint estimate. The new method of proof is inspired by ones by Bourgain and ...

Consider the discrete quadratic phase Hilbert Transform acting on $\ell^{2}(\mathbb{Z})$ finitely supported functions $$ H^{\alpha} f(n) : = \sum_{m \neq 0} \frac{e^{i\alpha m^2} f(n - m)}{m}. $$ We prove that, ...

Dengue is a public health problem on the rise in many tropical regions and affects approximately 100 million people every year worldwide. In this paper, the authors retrospectively assess the association between five ...

A new extension operator for a virtual coarse space is presented which can be used in domain decomposition methods for nodal elliptic problems in two dimensions. In particular, a two-level overlapping Schwarz algorithm is ...

There has recently been a considerable activity in developing adaptive methods for the selection of primal constraints for BDDC algorithms and, in particular, for BDDC deluxe variants. The primal constraints of a BDDC or ...

The Bochner–Riesz multipliers are shown to satisfy a range of sparse bounds. The range of sparse bounds increases to the optimal range, as δ increases to the critical value, even assuming only partial information on the ...

A bound is obtained for the condition number of a BDDC algorithm for problems posed in H(curl) in two dimensions, where the subdomains are only assumed to be uniform in the sense of Peter Jones. For the primal variable ...

For decades, dengue virus has caused major problems for public health officials in tropical and subtropical countries around the world. We construct a compartmental model that includes the role of hospitalized individuals ...

We formulate an age-structured three-staged nonlinear partial differential equation model that features nonlinear recidivism to the infected (infectious) class from the temporarily recovered class. Equilibria are computed, ...