In the framework of Bishop’s constructive mathematics we introduce co-convexity as a property of subsets B of ${\left\{ {0,1} \right\}^{\rm{*}}}$, the set of finite binary sequences, and prove that co-convex bars are uniform. Moreover, we establish a canonical correspondence between detachable subsets B of ${\left\{ {0,1} \right\}^{\rm{*}}}$ and uniformly continuous functions f defined on the unit interval such that B is a bar if and only if the corresponding function f is positive-valued, B is a uniform bar if and only if f has positive infimum, and B is co-convex if and only if f satisfies a weak convexity condition.

Among the different recombination mechanisms in organic solar cells the photoluminescence (PL) of charge transfer excitons (CTEs) has been identified has one of the most important, impacting both the open circuit voltage and the short circuit current. Here, we study their recombination dynamics, monitoring the decay of the PL on a time scale spanning three orders of magnitude from nanoseconds to microseconds. As a model system we investigate blends of the conjugated polymer poly(2-methoxy-5-(3′,7′-dimethyloctyloxy)-1,4-phenylene-vinylene) (MDMO-PPV) and the fullerene derivative [6,6]-phenyl C61-butyric acid methyl ester (PCBM). We observe that the dynamics of recombination follows a power-law, which is independent of sample morphology. Upon application of a transient electric field, which is capable of separating the bound charge pairs, we observe different dynamics of recombination only for the separated pairs. Those also follow a power-law and show a strong dependence on the film morphology.

We prove constructively that the weak König lemma and quantifier-free number–number choice imply that every pointwise continuous function from Cantor space into Baire space has a modulus of uniform continuity.

The existence and uniqueness of a maximum point for a continuous real–valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.