Regularity for almost minimizers with free boundary

In this paper we study the local regularity of almost minimizers of the functional \begin{equation*} J(u)=\int_\Omega |\nabla u(x)|^2 +q^2_+(x)\chi_{\{u>0\}}(x) +q^2_-(x)\chi_{\{u<0\}}(x) \end{equation*} where $q_\pm \in L^\infty(\Omega)$. Almost minimizers do not satisfy a PDE or a monotonicity formula like minimizers do (see \cite{AC}, \cite{ACF}, \cite{CJK}, \cite{W}). Nevertheless we succeed in proving that they are locally Lipschitz, which is the optimal regularity for minimizers

Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions

In this work we introduce the use of powerful tools from geometric measure theory (GMT) to study problems related to the size and structure of sets of mutual absolute continuity for the harmonic measure $\omega^+$ of a domain $\Omega=\Omega^+\subset\mathbb{R}^n$ and the harmonic measure $\omega^-$ of $\Omega^-$, $\Omega^-=$int$(\Omega^c)$, in dimension $n\ge 3$

TAPON: a two-phase machine learning approach for semantic labelling

Through semantic labelling we enrich structured information from sources such as HTML pages, tables, or JSON files, with labels to integrate it into a local ontology. This process involves measuring some features of the information and then nding the classes that best describe it. The problem with current techniques is that they do not model relationships between classes. Their features fall short when some classes have very similar structures or textual formats. In order to deal with this problem, we have devised TAPON: a new semantic labelling technique that computes novel features that take into account the relationships. TAPON computes these features by means of a two-phase approach. In the first phase, we compute simple features and obtain a preliminary set of labels (hints). In the second phase, we inject our novel features and obtain a refined set of labels. Our experimental results show that our technique, thanks to our rich feature catalogue and novel modelling, achieves higher accuracy than other state-of-the-art techniques.Ministerio de Economía y Competitividad TIN2016-75394-

Fluidized bed as a solid precursor delivery system in a chemical vapor deposition reactor

Chemical vapor deposition (CVD) using precursors that are solids at operating temperatures and pressures, presents challenges due to their relatively low vapor pressures. In addition, the sublimation rates of solid state precursors in fixed bed reactors vary with particle and bed morphology. In a recent patent application, the use of fluidized bed (FB) technology has been proposed to provide high, reliable, and reproducible flux of such precursors in CVD processes. In the present contribution, we first focus on the reactor design which must satisfy fluidization,sublimation and CVD reactor feeding constraints. Then, we report masstransport results on the sublimation of aluminium acetylacetonate, a common precursor for the CVD of alumina films. Finally, we discuss the efficiency of the precursor feeding rate, we address advantages and drawbacks of the invention and we propose design modifications in order to meet the process requirements

¿Crean valor los fondos de inversión colectiva colombianos enfocados en acciones?

Esta investigación evalúa el desempeño de 73 fondos de inversión colectiva (FIC) colombianos enfocados en acciones de 2005 a 2015 -- Para cuantificar el valor generado por estos fondos en comparación con sus respectivos activos de referencia (“benchmarks”), se calcula el alfa de Jensen mediante dos metodologías de regresión: Mínimos Cuadrados Ordinarios (MCO) y Regresión por Cuantiles -- También se analiza si estos fondos muestran evidencia de “market timing” o no, utilizando dos modelos: efecto cuadrático y variable binaria interactiva -- De igual manera, nuestro estudio propone la creación de una empresa privada en Colombia que provea a los inversores de información precisa sobre las características y desempeño histórico de estos fondos de inversión colectiva, como lo hace Morningstar Inc. en Estados Unidos -- Esto permitiría a los inversores seleccionar los fondos con mejores perspectivas y, como es de esperarse, haría este mercado más eficiente y atractivo para nuevos inversores potencialesIn this research we evaluate the performance of 73 Colombian stock mutual funds from 2005 to 2015 -- To quantify the value added by these funds compared to their respective benchmarks, Jensen’s alpha is calculated using two regression methodologies: Ordinary Least Squares (OLS) and Quantile Regression -- We also analyze whether these funds show any evidence of market timing -- We recommend the creation of a private firm in Colombia that would provide investors with accurate information about the features and historical performance of Colombian mutual funds, as Morningstar Inc. does in the USA -- This would enable investors to choose the best fund options andmake the mutural fund market more efficient and appealing to new potential investor

The Solar Internetwork. II. Magnetic Flux Appearance and Disappearance Rates

Small-scale internetwork magnetic fields are important ingredients of the quiet Sun. In this paper we analyze how they appear and disappear on the solar surface. Using high resolution Hinode magnetograms, we follow the evolution of individual magnetic elements in the interior of two supergranular cells at the disk center. From up to 38 hr of continuous measurements, we show that magnetic flux appears in internetwork regions at a rate of $120\pm3$ Mx cm$^{-2}$ day$^{-1}$ ($3.7 \pm 0.4 \times 10^{24}$ Mx day$^{-1}$ over the entire solar surface). Flux disappears from the internetwork at a rate of $125 \pm 6$ Mx cm$^{-2}$ day$^{-1}$ ($3.9\pm 0.5 \times 10^{24}$ Mx day$^{-1}$) through fading of magnetic elements, cancellation between opposite-polarity features, and interactions with network patches, which converts internetwork elements into network features. Most of the flux is lost through fading and interactions with the network, at nearly the same rate of about 50 Mx cm$^{-2}$ day$^{-1}$. Our results demonstrate that the sources and sinks of internetwork magnetic flux are well balanced. Using the instantaneous flux appearance and disappearance rates, we successfully reproduce the time evolution of the total unsigned flux in the two supergranular cells.Comment: 8 pages, 6 figures. Accepted in ApJ. An animation of the right panel of Figure 1 is available at http://spg.iaa.es/pub/downloads/gosic/figure1_right_panel.ta