Dominators for Multiple-objective Quasiconvex Maximization Problems

In this paper we address the problem of finding a dominator for a multiple-objective maximization problem with quasiconvex functions. The one-dimensional case is discussed in some detail, showing how a Branch-and-Bound procedure leads to a dominator with certain minimality properties. Then, the well-known result stating that the set of vertices of a polytope S contains an optimal solution for single-objective quasiconvex maximization problems is extended to multiple-objective problems, showing that, under upper-semicontinuity assumptions, the set of (k 21)-dimensional faces is a dominator for k-objective problems. In particular, for biobjective quasiconvex problems on a polytope S, the edges of S constitute a dominator, from which a dominator with minimality properties can be extracted by Branch-and Bound methods.     

Electrons in dry DNA from density functional calculations

The electronic structure of an infinite polyguanine-polycytosine DNA molecule in its dry A-helix structure is studied by means of density functional calculations. An extensive study of 30 nucleic base pairs is performed to validate the method. The electronic energy bands of DNA close to the Fermi level are then analysed in order to clarify the electron transport properties in this particularly simple DNA realization, probably the best suited candidate for conduction. The energy scale found for the relevant band widths, as compared with the energy fluctuations of vibrational or genetic-sequence origin, makes highly implausible the coherent transport of electrons in this system. The possibility of diffusive transport with subnanometre mean free paths is, however, still open. Information for model Hamiltonians for conduction is provided.     

Simple parameter-dependent relations for the maximum value of the optical activity of push—pull molecules in solution

Based on the valence bond-charge transfer model for push-pull polyenes and reaction field theory, several parameter-dependent relations for selecting the molecule-solvent pair that produces a maximum value of the nonlinear optical response have been established. From these relations, we have determined a limit to the value of the dielectric constant of the solvent (above ε = 9) and effectiveness of the donor-acceptor pairs (between 5 and 6eV) beyond which the (hyper)polarizabilities of push-pull molecules in solution do not exhibit any significant change in magnitude.