Overview of Wavelet Analysis and Applications to Engineering

Dr. Alessio Medda’s research interest are in digital signal and image processing, mathematical theory and applications. His experience is in signal modeling and analysis for data interpretation and representation applied to a variety of cases.Presented on October 24, 2014 at 1:00 p.m. in the Jesse W. Mason Building, room 3133.Runtime: 65:26 minute

Pellets recovered from stick nests and new diet items of Furnariidae (Aves: Passeriformes)

This is the first record showing eleven species in seven genera of Furnariidae (Aves: Passeriformes) from Argentina that regurgitate pellets. A total of 627 nests of Furnariidae was examined, and from 84 nests (13.3%), 1,329 pellets were recovered. These pellets were found in the closed, domed nests of many Furnariidae, because in comparison to other passerine birds, their nests were used for roosting, especially in the subfamily Synallaxinae. Anumbius annumbi had the highest percentage of nests containing pellets. Food items identified from the pellets provided important new data on the diets of several species of Furnariidae.Fil: Turienzo, Paola Noemí. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Biodiversidad y Biología Experimental; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Di Iorio, Osvaldo Rubén. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Biodiversidad y Biología Experimental; Argentin

A Mirror Theorem for Toric Stacks

We prove a Givental-style mirror theorem for toric Deligne--Mumford stacks X. This determines the genus-zero Gromov--Witten invariants of X in terms of an explicit hypergeometric function, called the I-function, that takes values in the Chen--Ruan orbifold cohomology of X.Comment: 35 pages. v2: key references added. v3: errors corrected; formal setup changed; proofs simplified, clarified, and shortened; references added. v4: references updated. v5: references update

On the structure and applications of the Bondi-Metzner-Sachs group

This work is a pedagogical review dedicated to a modern description of the Bondi-Metzner-Sachs group. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of asymptotic simplicity are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the Bondi-Metzner-Sachs group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the Bondi-Metzner-Sachs group, e.g. its algebra and the possibility to obtain as its subgroup the Poincar\'e group, as we may expect. The paper ends with a review of the Bondi-Metzner-Sachs invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.Comment: 62 pages, 9 figures. Misprints have been amended and two important references have been adde

A fractional Kirchhoff problem involving a singular term and a critical nonlinearity

In this paper we consider the following critical nonlocal problem \left\{\begin{array}{ll} M\left(\displaystyle\iint_{\mathbb{R}^{2N}}\frac{|u(x)-u(y)|^2}{|x-y|^{N+2s}}dxdy\right)(-\Delta)^s u = \displaystyle\frac{\lambda}{u^\gamma}+u^{2^*_s-1}&\quad\mbox{in } \Omega,\\ u>0&\quad\mbox{in } \Omega,\\ u=0&\quad\mbox{in } \mathbb{R}^N\setminus\Omega, \end{array}\right. where $\Omega$ is an open bounded subset of $\mathbb R^N$ with continuous boundary, dimension $N>2s$ with parameter $s\in (0,1)$, $2^*_s=2N/(N-2s)$ is the fractional critical Sobolev exponent, $\lambda>0$ is a real parameter, exponent $\gamma\in(0,1)$, $M$ models a Kirchhoff type coefficient, while $(-\Delta)^s$ is the fractional Laplace operator. In particular, we cover the delicate degenerate case, that is when the Kirchhoff function $M$ is zero at zero. By combining variational methods with an appropriate truncation argument, we provide the existence of two solutions