Fluorescence: Mathematical methods and applications. Part One

The phenomenon of fluorescence is ubiquitous and as such has attracted Scientists' attention for centuries. The challenge is to describe fluorescence as observed in different materials under different conditions by mathematical models having some features in common. Section ``Fluorescence conversion models: Transform kernels or scaling constants ?'' addresses bulk properties of the fluorescent medium and is mainly \underline{literature-driven}: some Articles are quoted in order of appearance, the focus being on whether the fluorescent quantum efficiency turns out to depend or not on the wavelength of excitation. Section ``Approximate propagators in scalar optics'' is mainly \underline{model-driven} and summarises mathematical methods and models in wave propagation which are limited to scalar waves and are ordered by complexity. The relation of said models to radiative transfer theory need not be immediate and as such is a matter of ongoing investigation.