Maximal Function Pooling with Applications

Posets with maximal Möbius function

The absolute value of the Möbius function of a bounded poset P with n + 2 elements satisfies |μ(P )| ≤ max r≥0 max p1+...+pr=n pi≥1 r ∏

Maximal elements of sub-topical functions with applications to global optimization

We study the support sets of sub-topical functions‎ ‎and investigate their maximal elements in order to establish a necessary and sufficient condition‎ ‎for the global minimum of the difference of two sub-topical functions‎.

Mixed integer bilinear programming with applications to the pooling problem

DNA Hash Pooling and its Applications

Biologists often examine large and diverse populations of organisms (for example, molecules, microbes or plants). This is particularly the case in fields such as microbial ecology, which studies the interactions between living microorganisms (such as algae, or bacteria) and their environment. One of the most significant and challenging problems in these areas of biology is to compare the specie...

A pointwise estimate for the local sharp maximal function with applications to singular integrals

Following the ideas of Carleson, Garnett–Jones and Fujii, we obtain a decomposition of an arbitrary measurable function f in terms of local mean oscillations. As a main application, in the case p > n we prove a conjecture by Cruz-Uribe and Pérez about two-weight norm inequalities for singular integrals. Also we extend an inequality, due to the author, relating f and the local sharp maximal func...