Veldman proved that the contrapositive of countable binary choice is a theorem of full-fledged intuitionism, to which end he used a principle of continuous choice and the fan theorem. It has turned out that continuous choice is unnecessary in this context, and that a weak form of the fan theorem suffices which holds in the presence of countable choice. In particular, the contrapositive of count...

In this paper we present and analyse a simple two populations model with migrations among two different environments. The populations interact by competing for resources. Equilibria are investigated. A proof for the boundedness of the populations is provided. A kind of competitive exclusion principle for metapopulation systems is obtained. At the same time we show that the competitive exclusion...

Abstract In this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use compactness.

The main purpose of this work is to design a robust adaptive backstepping (RABS) control strategy for pediatric exoskeleton system during passive-assist gait rehabilitation. nonlinear dynamics the have ill-effects uncertain parameters and external interferences. In work, designed applied on assist children 08–12 years, 25–40 kg weight, 115–125 cm height. dynamic model coupled human-exoskeleton ...

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that V̇ ≤ 0. As a consequence, the uniform invariance principle can deal with a larger ...