Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian

In this paper, we settle in the affirmative the Jakobson-Levitin-Nadirashvili-Nigam-Polterovich conjecture, stating that a certain singular metric on the Bolza surface, with area normalized, should maximize the first eigenvalue of the Laplacian.Comment: 21 pages, 3 figure

Testing Colour-Appearance Models: Guidelines for Coordinated Research

These guidelines provide an overview of the many issues involved in generating visual data that can be used to evaluate the performance of colour-appearance models. the three main sections of these guidelines outline the parameters that must be evaluated and controlled in experimental setups for colour-appearance experiments, suggested psychophysical techniques for gathering the data, and some suggested techniques for data analysis. Experimental parameters addressed include models to be tested, illumination conditions, background and surround conditions, types of stimuli to be used, and issues relating to viewing technique. the psychophysical techniques of magnitude estimation, matching, and direct model testing (paired comparison) are described. Data analysis techniques for the evaluation of colour-appearance scales, corresponding-colours data, and model performance scales are suggested