Abstract In this paper, we collect the basic theory and most important applications of a novel technique that has shown to be suitable for scattered data interpolation, quadrature, bio-imaging reconstruction. The method relies on polynomial mapped bases allowing, instance, incorporate or function discontinuities in mapping function. new substantially mitigates Runge’s Gibbs effects.

A bst ract. A one-dimensional cellular automaton rule with specified boundary conditions can be considered as acting simultaneously on all finite lattices, which gives a mapping between formal languages. Regular lang uages are always mapped to regular langu ages, contex t-free to context-free, context-sensitive to context-sensitive, and recursive sets to recursive sets . In particular, the fini...

Binary Constraint Problems have traditionally been considered as Network Satisfaction Problems over some relation algebra. A constraint network is satisfiable if its nodes can be mapped into some representation of the relation algebra in such a way that the constraints are preserved. A qualitative representation φ is like an ordinary representation, but instead of requiring (a ; b) = a | b, as ...

We investigate structures recognizable by finite state automata with an input tape of length a limit ordinal. At limits, the set of states which appear unboundedly often before the limit are mapped to a limit state. We describe a method for proving nonautomaticity and determine the optimal bounds for ranks of linear orders recognized by such automata.