We apply the (C, F )-construction from [Da] to produce a number of funny rank one infinite measure preserving actions of Abelian groups G with “unusual” multiple recurrence properties. In particular, we construct the following for each p ∈ N ∪ {∞}: (i) a p-recurrent action T = (Tg)g∈G such that (if p 6=∞) no one transformation Tg is (p + 1)-recurrent for every element g of infinite order, (ii) ...

Preserving the privacy of individuals when data are shared for clustering is a complex problem. The challenge is how to protect the underlying data values subjected to clustering without jeopardizing the similarity between objects under analysis. In this short paper, we revisit a family of geometric data transformation methods (GDTMs) that distort numerical attributes by translations, scalings,...

In our previous studies (Li and Zhong, 2021a; Li 2021b), the commonly reported issue that most of existing mapped WENO schemes suffer from either losing high resolutions or generating spurious oscillations in long-run simulations hyperbolic problems has been successfully addressed, by devising improved schemes, namely MOP-WENO-X, where “X” stands for version scheme. However, all MOP-WENO-X brin...

We show that a certain type of conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also consider distribution asymptotics of information; e.g. for Boole’s transformation, information is asymptotically mod-normal, a property shared by certain ergodic, probability preserving transformations with zero entropy. §0 Intr...

For the initial value problem of scalar conservation laws, a bound-preserving property is desired for numerical schemes in many applications. Traditional methods to enforce a discrete maximum principle by defining the extrema as those of grid point values in finite difference schemes or cell averages in finite volume schemes usually result in an accuracy degeneracy to second order around smooth...

Positivity-preserving discontinuous Galerkin (DG) methods for solving hyperbolic 5 conservation laws have been extensively studied in the last several years. But nearly all the devel6 oped schemes are coupled with explicit time discretizations. Explicit discretizations suffer from the 7 constraint for the Courant-Friedrichs-Levis (CFL) number. This makes explicit methods impractical 8 for probl...