We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a p-Laplacian system. We prove that any optimal matching measure for this problem is supported on the boundary of the target set when the two multiples that affect the Euclidean distances involved in the cost are different. Moreover, we present simple examples showing uniqueness or non-uniqueness of the optimal measure.
Investigations conceming the deactivation of radiant energy absorbed by the pigments of photosynthetic organisms, either through emitting the fluorescence and delayed luminescence or converting into heat in slow or fast processes, are described. These paths of deactivation can be established by measurements of the absorption, fluorescence excitation, delayed emission and photoacoustic spectra in the same sample. The slow paths of radiative and non-radiative deactivation are of a speciál interest. Even with complex photosynthetic samples it is possible to evaluate slow and fast components of the thermal deactivation from photoacoustic spectra taken at various frequencies of the radiation modulation. In all samples containing reaction centres, anteima complexes or their models, at least a part of delayed deexcitation is due to ionization and delayed recombination of pigments. This is confirmed by photopotential generation for the same samples located in a photoelectrochemical cell. The methods of investigating slow processes of radiative and radiationless deexcitation of the photosynthetic pigments in organisms, their fragments and model Systems are described. Also the results of spectral measurements from some experiments are shown as examples of the described proceduře. These measurements were carried out predominantly as an attempt at explaining the interactions between chlorophylls and carotenoids.