A ll transition metals are highly toxic to life at low levels, but at the same time some, such as manganese, iron, cobalt, nickel, copper, zinc and molybdenum, are essential micronutrients needed to catalyse key enzymatic reactions. To survive, living organisms have had to evolve mechanisms that either remove such metals from their bodies or detoxify and make use of them metabolically. Many of ...

In this paper we extend the notion of a Lebesgue-null set to a notion which is valid in any completely metrizable Abelian topological group. We then use this deenition to introduce and study the class of essentially smooth functions. These are, roughly speaking, those Lipschitz functions which are smooth (in each direction) almost everywhere.

It is impossible to securely carry out general multi-party computation in arbitrary network contexts like the Internet, unless protocols have access to some trusted setup. In this work we classify the power of such trusted (2-party) setup functionalities. We show that nearly every setup is either useless (ideal access to the setup is equivalent to having no setup at all) or else complete (compo...

David Guaspari [G] conjectured that a modal formula is essentially Σ1 (i.e., is is Σ1 under any arithmetical interpretation), if and only if it is provably equivalent to a disjunction of formulas of the form 2B. This conjecture was proved first by A. Visser. Then, in [DJP], the authors characterized essentially Σ1 formulas of languages with witness comparisons using the interpretability logic I...

Let ẋ = f(x) be a C autonomous differential system with k ∈ N ∪ {∞, ω} defined in an open subset Ω of R. Assume that the system ẋ = f(x) is C completely integrable, i.e. there exist n−1 functionally independent first integrals of class C with 2 ≤ r ≤ k. If the divergence of system ẋ = f(x) is non–identically zero, then any Jacobian multiplier is functionally independent of the n − 1 first integ...