Classical Lie symmetries and reductions of a nonisospectral Lax pair

The classical Lie method is applied to a nonisospectral problem associated with a system of partial differential equations in 2+1 dimensions (Maccari A, J. Math. Phys. 39, (1998), 6547-6551). Identification of the classical Lie symmetries provides a set of reductions that give rise to different nontrivial spectral problems in 1+1 dimensions. The form in which the spectral parameter of the 1+1 Lax pair is introduced is carefully described.Comment: 11 pages (v2: A typo corrected in the authors' names

Coordinated regulation of chromatophore differentiation and melanogenesis during the ontogeny of skin pigmentation of Solea senegalensis (Kaup, 1858)

Abnormal pigmentation of Senegalese sole has been described as one problem facing the full exploitation of its commercial production. To improve our understanding of flatfish pigmentation of this commercially important species we have evaluated eleven genes related to two different processes of pigmentation: melanophore differentiation, and melanin production. The temporal distribution of gene expression peaks corresponds well with changes in pigmentation patterns and the intensity of skin melanization. Several gene ratios were also examined to put in perspective possible genetic markers for the different stages of normal pigmentation development. Further, the phenotypic changes that occur during morphogenesis correspond well with the main transitions in gene expression that occur. Given the dramatic phenotypic alterations which flatfish undergo, including the asymmetric coloration that occurs between the ocular and the blind side, and the synchrony of the two processes of morphogenesis and pigmentation ontogenesis, these species constitute an interesting model for the study of pigmentation. In this study we present a first approximation towards explaining the genetic mechanisms for regulating pigmentation ontogeny in Senegalese sole, Solea senegalensis.Ministry of Science and Innovation (MICIIN) of the Spanish Government [AGL2008-03897-C04-01/ACU]; European Community [FP7/2007-2013-222719-LIFECYCLE]; Spanish Governmentinfo:eu-repo/semantics/publishedVersio

Non-classical symmetries and the singular manifold method: A further two examples

This paper discusses two equations with the conditional Painleve property. The usefulness of the singular manifold method as a tool for determining the non-classical symmetries that reduce the equations to ordinary differential equations with the Painleve property is confirmed once moreComment: 9 pages (latex), to appear in Journal of Physics

Miura Transformation between two Non-Linear Equations in 2+1 dimensions

A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based upon the Painleve Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW Equation into the GLDW Equation. Through this Miura Transformation we shall also present the Lax pair of the 2LDW Equation as well as some interesting reductions to several already known integrable systems in 1+1 dimensions.Comment: 14 pages, latex. Journal of Mathematical Physics (to appear

Research activities on turbot industrial procedures in Spain

This technical report deals with the evolution during the last decade of the research activities of the governmental institutions working on the development of turbot (Scophthalmus maximus L.) culture. The Instituto Español de Oceanografía (Santander and Vigo), the CSIC (Vigo and Castellón), the Xunta de Galicia (Villajuán and Couso) and The University of Santiago are the institutions analyzed. A general review of the different projects on turbot farming is given, including those with grants from the institutions and from the CICYT (Comite Interministerial de Ciencia y Tecnología), C.D.T.I (Centro de Desarrollo Tecnologico e Industrial) and the EC (European Community). Finally, an analysis is given of the present situation and bottlenecks to development are highlighted. leading to priorities for future research.Versión del edito