We formulate a theory of shape valid for objects arbitrary dimension whose contours are path connected. apply this to the design and modeling viable trajectories complex dynamical systems. Infinite families qualitatively similar shapes constructed giving as input finite ordered set characteristic points (landmarks) value continuous parameter κ∈(0,∞). prove that all belonging same family located...

Specker sequences are constructive, increasing, bounded sequences of rationals that do not converge to any constructive real. A sequence is said to be a strong Specker sequence if it is Specker and eventually bounded away from every constructive real. Within Bishop’s constructive mathematics we investigate non-decreasing, bounded sequences of rationals that eventually avoid sets that are unions...

We introduce an operational set theory in the style of [5] and [17]. The theory we develop here is a theory of constructive sets and operations. One motivation behind constructive operational set theory is to merge a constructive notion of set ([1], [2]) with some aspects which are typical of explicit mathematics [14]. In particular, one has non-extensional operations (or rules) alongside exten...