Resonance Raman scattering spectra were measured for a merocyanine dye, 4-(2-(4-hydroxyphenyl)ethenyl)-1 -methylpyridinium in a base form (M), in various solvents. M in protic solvents such as water and methanol takes on a trans conformation and a band mainly due to a central C=C stretching mode shifts to a lower frequency as the hydrogen bond donor acidity of the solvents is reduced, showing good parallelism with the bathochromic shift of for the dye. The measurement indicated also that M in aprotic solvents such as acetonitrile takes both trans and cis conformations; the trans/cis ratio increases with the dielectric constant of the solvents. The shift in the C=C stretching frequency was interpreted as due to the solvent-induced change in the relative contribution of resonance hybrids, i.e., the benzenoid and quinoid structures. These results were used to analyze the surface-enhanced resonance Raman scattering spectra of the dye adsorbed on silver colloids in acetonitrile as well as in water. The surface spectra proved that the adsorbates on the colloids in acetonitrile and in water take only the trans conformation. The C=C stretching frequency at 1573 cm"1 observed for the adsorbate on the colloid in acetonitrile is appreciably higher than the frequency at 1561 cm"1 3for the free dye in the same solvent, indicating that the relative contribution of the benzenoid structure increases on adsorption to the colloidal surface. On the other hand, the adsorbate on the silver colloid in water gives the C=C stretching frequency at 1570 cm"1, which is lower by 6 cm"1 than the corresponding frequency for the dye in water. Hence, contrary to the case of the colloid in acetonitrile the contribution of the benzenoid structure decreases on adsorption to the colloid.

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The prepotential in N = 2 SUSY Yang-Mills theories enjoys remarkable properties. One of the most interesting is its relation to the coordinate on the quantum moduli space u = Tr ϕ 2 that results into recursion equations for the coefficients of the prepotential due to instantons. In this work we show, with an explicit multi-instanton computation, that this relation holds true at arbitrary winding numbers. Even more interestingly we show that its validity extends to the case in which gravitational corrections are taken into account if the correlators are suitably modified. These results apply also to the cases in which matter in the fundamental and in the adjoint is included. We also check that the expressions we find satisfy the chiral ring relations for the gauge case and compute the first gravitational correction.

We propose a new computational algorithm for color constancy suitable to robot vision. A robot, or a computer, can exactly memorize image information observed in the past. Then it is natural to use more than one image to achieve color constancy. In our algorithm, we can recover the illumination color and the reflectance color only based on the RGB values of two objects identified on two images. It requires no specific assumption on the scene. Experiments show the validity of the proposed algorithm.

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