Non-Lipschitz differentiable functions on slit domains

It is proved the existence of large algebraic structures –including large vector subspaces or infinitely generated free algebras– inside the family of non-Lipschitz differentiable real functions with bounded gradient defined on special non-convex plane domains. In particular, this yields that there are many differentiable functions on plane domains that do not satisfy the Mean Value Theorem.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitividad (MINECO). Españ

Bounded and unbounded polynomials and multilinear forms: Characterizing continuity

In this paper we prove a characterization of continuity for polynomials on a normed space. Namely, we prove that a polynomial is continuous if and only if it maps compact sets into compact sets. We also provide a partial answer to the question as to whether a polynomial is continuous if and only if it transforms connected sets into connected sets. These results motivate the natural question as to how many non-continuous polynomials there are on an infinite dimensional normed space. A problem on the \emph{lineability} of the sets of non-continuous polynomials and multilinear mappings on infinite dimensional normed spaces is answered.Comment: 8 page

Universality of sequences of operators related to Taylor series

In this note, the universality of a sequence of operators associated to the partial sums of the Taylor series of a holomorphic function is investigated. The emphasis is put on the fact that the Taylor series are evaluated at a prescribed point and the variable is the center of the expansion. The dynamics of the sequence of operators linked to the partial sums of a power series that is not generated by an entire function is also studied.Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Economía y Competitividad (MINECO). Españ

Synthesis and photochemical study of a new norbornadiene-derivative with potential as a molecular system for the storage of solar-thermal energy

Norbornadiene derivatives (NBD) have recently emerged as a promising alternative in the development of molecular systems for the storage of solar-thermal energy (MOST). In these systems, the energy is stored in the form of chemical bonds by photoisomerization reactions, and the stored energy can be released on demand in the form of heat. In this contribution, we present results regarding the photochemical behavior of a new NBD, i.e., 2-cyano-3-((4 (diethylamino)phenyl)ethinyl)norbornadiene (NBD1). This compound contains an electron-withdrawing group (CN), and an electron-donor group (ethinyl-derivative) in one of the double bonds of the bicycle-ring. As a consequence, a conjugated push-pull system was obtained, with led to an absorption band peaked at the visible region. The irradiation of NBD1 in toluene solution promotes the formation of the quadricyclane isomer, for which a maximum at about 310 nm was detected. Photoconversion seems to proceed almost quantitatively after ca. 30 minutes of irradiation.Agencia Nacional de Investigación e Innovació

Censo Nacional de último año de la educación técnico profesional 2009 : metodología y resultados generales

El presente volumen describe la metodología utilizada para la realización del Censo Nacional de Último Año de ETP (2009) donde se documentan las principales tareas vinculadas a la preparación del operativo, al relevamiento del campo y el procesamiento de datos. Así mismo, se ofrece una descripción general de los alumnos que han sido censados, resaltando los principales rasgos del alumnado: características demográficas, socioeconómicas, trayectorias escolares y expectativas de inserción a futuro

Lineability in sequence and function spaces

It is proved the existence of large algebraic structures –including large vector subspaces or infinitely generated free algebras– inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family of nonconstant differentiable real functions vanishing on dense sets, and the family of non-continuous separately continuous real functions. Lineability in special spaces of sequences is also investigated. Some of our findings complete or extend a number of results by several authors.Programa de Doutorado Sanduíche no Exterior (Coordenação de aperfeiçoamento de pessoal de nivel superior)Plan Andaluz de Investigación (Junta de Andalucía)Ministerio de Ciencia e Innovació