Construction of exact solutions to eigenvalue problems by the asymptotic iteration method

We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue problems which includes Schroedinger problems with Coulomb, harmonic oscillator, or Poeschl-Teller potentials, as well as the special eigenproblems studied recently by Bender et al [J. Phys. A: Math. Gen. 34 9835 (2001)] and generalized in the present paper to higher dimensions.Comment: 10 page

The supersymmetric modified Poschl-Teller and delta-well potentials

New supersymmetric partners of the modified Poschl-Teller and the Dirac's delta well potentials are constructed in closed form. The resulting one-parametric potentials are shown to be interrelated by a limiting process. The range of values of the parameters for which these potentials are free of singularities is exactly determined. The construction of higher order supersymmetric partner potentials is also investigated.Comment: 20 pages, LaTeX file, 4 eps figure

Mechanisms, functions and ecology of colour vision in the honeybee.

notes: PMCID: PMC4035557types: Journal Article© The Author(s) 2014.This is an open access article that is freely available in ORE or from Springerlink.com. Please cite the published version available at: http://link.springer.com/article/10.1007%2Fs00359-014-0915-1Research in the honeybee has laid the foundations for our understanding of insect colour vision. The trichromatic colour vision of honeybees shares fundamental properties with primate and human colour perception, such as colour constancy, colour opponency, segregation of colour and brightness coding. Laborious efforts to reconstruct the colour vision pathway in the honeybee have provided detailed descriptions of neural connectivity and the properties of photoreceptors and interneurons in the optic lobes of the bee brain. The modelling of colour perception advanced with the establishment of colour discrimination models that were based on experimental data, the Colour-Opponent Coding and Receptor Noise-Limited models, which are important tools for the quantitative assessment of bee colour vision and colour-guided behaviours. Major insights into the visual ecology of bees have been gained combining behavioural experiments and quantitative modelling, and asking how bee vision has influenced the evolution of flower colours and patterns. Recently research has focussed on the discrimination and categorisation of coloured patterns, colourful scenes and various other groupings of coloured stimuli, highlighting the bees' behavioural flexibility. The identification of perceptual mechanisms remains of fundamental importance for the interpretation of their learning strategies and performance in diverse experimental tasks.Biotechnology and Biological Sciences Research Council (BBSRC