The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

Bayesian inference in spherical linear models: robustness and conjugate analysis

AbstractThe early work of Zellner on the multivariate Student-t linear model has been extended to Bayesian inference for linear models with dependent non-normal error terms, particularly through various papers by Osiewalski, Steel and coworkers. This article provides a full Bayesian analysis for a spherical linear model. The density generator of the spherical distribution is here allowed to depend both on the precision parameter φ and on the regression coefficients β. Another distinctive aspect of this paper is that proper priors for the precision parameter are discussed.The normal-chi-squared family of prior distributions is extended to a new class, which allows the posterior analysis to be carried out analytically. On the other hand, a direct joint modelling of the data vector and of the parameters leads to conjugate distributions for the regression and the precision parameters, both individually and jointly. It is shown that some model specifications lead to Bayes estimators that do not depend on the choice of the density generator, in agreement with previous results obtained in the literature under different assumptions. Finally, the distribution theory developed to tackle the main problem is useful on its own right

Adventures of a tidally induced bar

Using N-body simulations, we study the properties of a bar induced in a discy dwarf galaxy as a result of tidal interaction with the Milky Way. The bar forms at the first pericentre passage and survives until the end of the evolution at 10 Gyr. Fourier decomposition of the bar reveals that only even modes are significant and preserve a hierarchy so that the bar mode is always the strongest. They show a characteristic profile with a maximum, similar to simulated bars forming in isolated galaxies and observed bars in real galaxies. We adopt the maximum of the bar mode as a measure of the bar strength and we estimate the bar length by comparing the density profiles along the bar and perpendicular to it. The bar strength and the bar length decrease with time, mainly at pericentres, as a result of tidal torques acting at those times and not to secular evolution. The pattern speed of the bar varies significantly on a time-scale of 1 Gyr and is controlled by the orientation of the tidal torque from the Milky Way. The bar is never tidally locked, but we discover a hint of a 5/2 orbital resonance between the third and fourth pericentre passage. The speed of the bar decreases in the long run so that the bar changes from initially rather fast to slow in the later stages. The boxy/peanut shape is present for some time and its occurrence is preceded by a short period of buckling instability

Las creencias del profesor universitario como factor de calidad en la enseñanza.

El estudio de las creencias docentes ha sido objeto de diversos análisis durante los últimos años debido al creciente interés que se observa por el campo de la enseñanza reflexiva, por los procesos de pensamiento del profesor y por la relación entre estos y las características de la enseñanza. En el ámbito universitario es un tema trascendente, ya que las creencias ejercen influencia en el modo de estructurar y organizar la propia actividad educativa. Este estudio tiene como objetivos, analizar las creencias del docente considerando que representan la base conceptual, personal, subjetiva y dinámica con impacto significativo en el desempeño del docente en la clase. También, observar e identificar el modo en que el profesor conceptualiza su propio proceso de enseñanza con los cambios e innovaciones que se producen. A tal fin, se aplica un cuestionario estructurado a docentes de carreras de Ingeniería de la Facultad de Tecnología de la UNCa. Los resultados muestran que las creencias, actitudes y conocimientos de los docentes son fundamentales para dar respuesta a las necesidades de la clase.\ud Palabras clave: creencias- enseñanza- cambios- docentes\u

Galaxy cluster mergers as triggers for the formation of jellyfish galaxies: case study of the A901/2 system

The A901/2 system is a rare case of galaxy cluster interaction, in which two galaxy clusters and two smaller groups are seen in route of collision with each other simultaneously. Within each of the four substructures, several galaxies with features indicative of jellyfish morphologies have been observed. In this paper, we propose a hydrodynamic model for the merger as a whole, compatible with its diffuse X-ray emission, and correlate the gas properties in this model with the locations of the jellyfish galaxy candidates in the real system. We find that jellyfish galaxies seem to be preferentially located near a boundary inside each subcluster where diffuse gas moving along with the subcluster and diffuse gas from the remainder of the system meet. The velocity change in those boundaries is such that a factor of up to $\sim$1000 increase in the ram pressure takes place within a few hundred kpc, which could trigger the high rate of gas loss necessary for a jellyfish morphology to emerge. A theoretical treatment of ram pressure stripping in the environment of galaxy cluster mergers has not been presented in the literature so far; we propose that this could be a common scenario for the formation of jellyfish morphologies in such systems.Comment: Accepted for publication in MNRAS. 10 pages, 9 figure

Stationary solutions of the nonlinear Schr\"odinger equation with fast-decay potentials concentrating around local maxima

We study positive bound states for the equation $$- \epsilon^2 \Delta u + Vu = u^p, \qquad \text{in $\mathbf{R}^N$},$$ where $\epsilon > 0$ is a real parameter, $\frac{N}{N-2} < p < \frac{N+2}{N-2}$ and $V$ is a nonnegative potential. Using purely variational techniques, we find solutions which concentrate at local maxima of the potential $V$ without any restriction on the potential.Comment: 25 pages, reformatted the abstract for MathJa

Sign-changing tower of bubbles for a sinh-Poisson equation with asymmetric exponents

Motivated by the statistical mechanics description of stationary 2D-turbulence, for a sinh-Poisson type equation with asymmetric nonlinearity, we construct a concentrating solution sequence in the form of a tower of singular Liouville bubbles, each of which has a different degeneracy exponent. The asymmetry parameter $\gamma\in(0,1]$ corresponds to the ratio between the intensity of the negatively rotating vortices and the intensity of the positively rotating vortices. Our solutions correspond to a superposition of highly concentrated vortex configurations of alternating orientation; they extend in a nontrivial way some known results for $\gamma=1$. Thus, by analyzing the case $\gamma\neq1$ we emphasize specific properties of the physically relevant parameter $\gamma$ in the vortex concentration phenomena

The SUMO project I. A survey of multiple populations in globular clusters

We present a general overview and the first results of the SUMO project (a SUrvey of Multiple pOpulations in Globular Clusters). The objective of this survey is the study of multiple stellar populations in the largest sample of globular clusters homogeneously analysed to date. To this aim we obtained high signal-to-noise (S/N>50) photometry for main sequence stars with mass down to ~0.5 M_SUN in a large sample of clusters using both archival and proprietary U, B, V, and I data from ground-based telescopes. In this paper, we focus on the occurrence of multiple stellar populations in twenty three clusters. We have defined a new photometric index cubi= (U-B)-(B-I), that turns out to be very effective for identifying multiple sequences along the red giant branch (RGB). We found that in the V-cubi diagram all clusters presented in this paper show broadened or multimodal RGBs, with the presence of two or more components. We found a direct connection with the chemical properties of different sequences, that display different abundances of light elements (O, Na, C, N, and Al). The cubi index is also a powerful tool to identify distinct sequences of stars along the horizontal branch and, for the first time in the case of NGC104 (47 Tuc), along the asymptotic giant branch. Our results demonstrate that i) the presence of more than two stellar populations is a common feature among globular clusters, as already highlighted in previous work; ii) multiple sequences with different chemical contents can be easily identified by using standard Johnson photometry obtained with ground-based facilities; iii) in the study of GC multiple stellar populations the cubi index is alternative to spectroscopy, and has the advantage of larger statistics.Comment: 23 pages, 20 figures, accepted for publication in MNRA