Ume-jolasak : kontzertu didaktikoa pianoarentzat lau eskuez jotzekoa eta narrazioa. 'Juegos de niños : concierto didáctico para piano a cuatro manos y narración'.

Resumen tomado de la publicación

Cartas a Clara : concierto didáctico para alumnos de educación secundaria : espectáculo musical para orquesta, piano y narrador.

Resumen tomado de la publicación

Klarari Gutunak : bigarren hezkuntzako ikasleentzako kontzertu didaktikoa : musika ikuskizuna orkestra, piano eta narratzailerako. 'Cartas a Clara : concierto didáctico para alumnos de educación secundaria : espectáculo musical para orquesta, piano y narrador'.

Resumen tomado de la publicación

Concepciones de profesores de piano sobre la evaluación.

Resumen basado en el de la publicación

Programación de la música contemporánea en los estudios de piano.

Se adjunta a la memoria el trabajo de investigación propiamente dicho que es el que figura en el enlace.

Piano complementario en el Grado Superior.

Resumen tomado de la publicación. La publicación recoge resumen en inglés

Optimal linearization trajectories for tangent linear models

We examine differential equations where nonlinearity is a result of the advection part of the total derivative or the use of quadratic algebraic constraints between state variables (such as the ideal gas law). We show that these types of nonlinearity can be accounted for in the tangent linear model by a suitable choice of the linearization trajectory. Using this optimal linearization trajectory, we show that the tangent linear model can be used to reproduce the exact nonlinear error growth of perturbations for more than 200 days in a quasi-geostrophic model and more than (the equivalent of) 150 days in the Lorenz 96 model. We introduce an iterative method, purely based on tangent linear integrations, that converges to this optimal linearization trajectory. The main conclusion from this article is that this iterative method can be used to account for nonlinearity in estimation problems without using the nonlinear model. We demonstrate this by performing forecast sensitivity experiments in the Lorenz 96 model and show that we are able to estimate analysis increments that improve the two-day forecast using only four backward integrations with the tangent linear model. Copyright © 2011 Royal Meteorological Society

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

Piano Performance at the New York Trade School

A piano player is shown performing at the New York Trade School. He is likely playing on a piano tuned or built by students in the Piano Crafts Department at the school. Black and white photograph.

Piano Crafts Department

Students are shown working on pianos in various states of construction in the Piano Crafts Department at the New York Trade School. Black and white photograph.

Piano Tuning Classroom

A Wissner piano is shown in a piano tuning classroom at the New York Trade School. Wissner pianos were manufactured in Brooklyn from 1878 until the company went out of business at the start of World War II. Black and white photograph.