Stability of branched pull-back projective foliations

We prove that, if $n\geq 3$, a singular foliation $\mathcal{F}$ on $\mathbb P^n$ which can be written as pull-back, where $\mathcal{G}$ is a foliation in ${\mathbb P^2}$ of degree $d\geq2$ with one or three invariant lines in general position and $f:{\mathbb P^n}--->{\mathbb P^2}$, $deg(f)=\nu\geq2,$ is an appropriated rational map, is stable under holomorphic deformations. As a consequence we conclude that the closure of the sets $\{\mathcal {F}= f^{*}(\mathcal{G})\}$ are new irreducible components of the space of holomorphic foliations of certain degrees.Comment: arXiv admin note: substantial text overlap with arXiv:1503.07827, arXiv:1503.0071

Branched pull-back components of the space of codimension 1 foliations on Pn\mathbb P^n

Let $\mathcal{F}$ be written as $f^{*}\mathcal{G}$, where $\mathcal{G}$ is a foliation in ${\mathbb P^2}$ with three invariant lines in general position, say $(XYZ)=0$, and $f:{\mathbb P^n}--->{\mathbb P^2}$, $f=(F^\alpha_{0}:F^\beta_{1}:F^\gamma_{2})$ is a nonlinear rational map. Using local stability results of singular holomorphic foliations, we prove that: if $n\geq 3$, the foliation $\mathcal{F}$ is globally stable under holomorphic deformations. As a consequence we obtain new irreducible componentes for the space of codimension one foliations on $\mathbb P^n$. We present also a result which characterizes holomorphic foliations on ${\mathbb P^n}, n\geq 3$ which can be obtained as a pull back of foliations on ${\mathbb P^2}$ of degree $d\geq2$ with three invariant lines in general position.Comment: arXiv admin note: text overlap with arXiv:1503.0071

Irreducible components of the space of foliations by surfaces

Let $\mathcal{F}$ be written as $f^{*}(\mathcal{G})$, where $\mathcal{G}$ is a $1$-dimensional foliation on ${\mathbb P^{n-1}}$ and $f:{\mathbb P^n}--->{\mathbb P^{n-1}}$ a non-linear generic rational map. We use local stability results of singular holomorphic foliations, to prove that: if $n\geq 4$, a foliation $\mathcal{F}$ by complex surfaces on $\mathbb P^n$ is globally stable under holomorphic deformations. As a consequence, we obtain irreducible components for the space of two-dimensional foliations in $\mathbb P^n$. We present also a result which characterizes holomorphic foliations on ${\mathbb P^n}, n\geq 4$ which can be obtained as a pull back of 1- foliations in ${\mathbb P^{n-1}}$ of degree $d\geq2$

Achieving Super-Resolution in Multi-Rate Sampling Systems via Efficient Semidefinite Programming

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral estimation in multi-rate sampling systems. It shows that, under the existence of a common supporting grid, and under a minimal separation constraint, the frequencies of a spectrally sparse signal can be exactly jointly recovered from the output of a semidefinite program (SDP). The algorithmic complexity of this approach is discussed, and an equivalent SDP of minimal dimension is derived by extending the Gram parametrization properties of sparse trigonometric polynomials

Persistence in the Zero-Temperature Dynamics of the Random Ising Ferromagnet on a Voronoi-Delaunay lattice

The zero-temperature Glauber dynamic is used to investigate the persistence probability $P(t)$ in the randomic two-dimensional ferromagnetic Ising model on a Voronoi-Delaunay tessellation. We consider the coupling factor $J$ varying with the distance $r$ between the first neighbors to be $J(r) \propto e^{-\alpha r}$, with $\alpha \ge 0$. The persistence probability of spins flip, that does not depends on time $t$, is found to decay to a non-zero value $P(\infty)$ depending on the parameter $\alpha$. Nevertheless, the quantity $p(t)=P(t)-P(\infty)$ decays exponentially to zero over long times. Furthermore, the fraction of spins that do not change at a time $t$ is a monotonically increasing function of the parameter $\alpha$. Our results are consistent with the ones obtained for the diluted ferromagnetic Ising model on a square lattice.Comment: 3 pages, 3 Figure

Critical behavior of the 3D-Ising model on a poissonian random lattice

The single-cluster Monte Carlo algorithm and the reweighting technique are used to simulate the 3D-ferromagnetic Ising model on three dimensional Voronoi-Delaunay lattices. It is assumed that the coupling factor $J$ varies with the distance $r$ between the first neighbors as $J(r) \propto e^{-ar}$, with $a \ge 0$. The critical exponents $\gamma/\nu$, $\beta/\nu$, and $\nu$ are calculated, and according to the present estimates for the critical exponents, we argue that this random system belongs to the same universality class of the pure three-dimensional ferromegnetic Ising model.Comment: 4 pages, 5 figure

System-environment correlations for dephasing two-qubit states coupled to thermal baths

Based on the exact dynamics of a two-qubit system and environment, we investigate system-environment (SE) quantum and classical correlations. The coupling is chosen to represent a dephasing channel for one of the qubits and the environment is a proper thermal bath. First we discuss the general issue of dilation for qubit phase damping. Based on the usual thermal bath of harmonic oscillators, we derive criteria of separability and entanglement between an initial $X$ state and the environment. Applying these criteria to initial Werner states, we find that entanglement between the system and environment is built up in time for temperatures below a certain critical temperature $T_{\mathrm{crit}}$. On the other hand, the total state remains separable during those short times that are relevant for decoherence and loss of entanglement in the two-qubit state. Close to $T_{\mathrm{crit}}$ the SE correlations oscillate between separable and entangled. Even though these oscillations are also observed in the entanglement between the two qubits, no simple relation between the loss of entanglement in the two-qubit system and the build-up of entanglement between the system and environment is found.Comment: 10 pages, published versio

PN and galactic chemical evolution

Recent applications of PN to the study of galactic chemical evolution are reviewed, such as PN and stellar populations, abundance gradients, including their space and time variations, determination of the He/H radial gradient and of the helium-to-metals enrichment ratio, and the [O/Fe] x [Fe/H] relation in the solar neighbourhood and in the galactic bulge.Comment: 8 pages, 3 postscript figures, TeX, uses psfig.sty, to be published in: Planetary Nebulae and their Role in the Universe, IAU Symposium 209, edited by R. Sutherland, S. Kwok, M. Dopita, ASP (2002) also available at http://www.iagusp.usp.br/~maciel/index.htm

Pull-back components of the space of foliations of codimension ≥2\ge2

We present a new list of irreducible components for the space of k-dimensional holomorphic foliations on $\mathbb P^{n}$, $n\geq3$, $k\ge2$. They are associated to pull-back of dimension one foliations on $\mathbb P^{n-k+1}$ by non-linear rational maps

Metallicity gradients in the Milky Way

Radial metallicity gradients are observed in the disks of the Milky Way and in several other spiral galaxies. In the case of the Milky Way, many objects can be used to determine the gradients, such as HII regions, B stars, Cepheids, open clusters and planetary nebulae. Several elements can be studied, such as oxygen, sulphur, neon, and argon in photoionized nebulae, and iron and other elements in cepheids, open clusters and stars. As a consequence, the number of observational characteristics inferred from the study of abundance gradients is very large, so that in the past few years they have become one of the main observational constraints of chemical evolution models. In this paper, we present some recent observational evidences of abundance gradients based on several classes of objects. We will focus on (i) the magnitude of the gradients, (ii) the space variations, and (iii) the evidences of a time variation of the abundance gradients. Some comments on recent theoretical models are also given, in an effort to highlight their predictions concerning abundance gradients and their variations.Comment: 8 pages, 3 figures, uses iaus.cls, in press, IAU Symp. 265, Chemical abundances in the Universe: Connecting the first Stars to Planets, Ed. K. Cunha, M. Spite, B. Barbu