Superisolated Surface Singularities

In this survey, we review part of the theory of superisolated surface singularities (SIS) and its applications including some new and recent developments. The class of SIS singularities is, in some sense, the simplest class of germs of normal surface singularities. Namely, their tangent cones are reduced curves and the geometry and topology of the SIS singularities can be deduced from them. Thus this class \emph{contains}, in a canonical way, all the complex projective plane curve theory, which gives a series of nice examples and counterexamples. They were introduced by I. Luengo to show the non-smoothness of the $\mu$-constant stratum and have been used to answer negatively some other interesting open questions. We review them and the new results on normal surface singularities whose link are rational homology spheres. We also discuss some positive results which have been proved for SIS singularities.Comment: Survey article for the Proceedings of the Conference "Singularities and Computer Algebra" on Occasion of Gert-Martin Greuel's 60th Birthday, LMS Lecture Notes (to appear

What Can Explain Excess Smoothness and Sensitivity of State-Level Consumption?

This article estimates marginal propensities to consume (MPC) out of current and lagged income for U.S. states using panel data regressions that control for time-specific and state-level fixed effects. The MPCs vary across states, in particular, the MPC out of current income is higher in states where income is more persistent and the MPC out of lagged income is lower in agricultural states. Several models of individual consumer behavior are analyzed and simulated in order to isolate a model which is able to match the estimated MPCs well.Permanent Income, Credit Rationing, Precautionary saving, Time-Aggregation, Durable Goods, Risk Sharing.

Quasi-ordinary singularities and Newton trees

In this paper we study some properties of the class of nu-quasi-ordinary hypersurface singularities. They are defined by a very mild condition on its (projected) Newton polygon. We associate with them a Newton tree and characterize quasi-ordinary hypersurface singularities among nu-quasi-ordinary hypersurface singularities in terms of their Newton tree. A formula to compute the discriminant of a quasi-ordinary Weierstrass polynomial in terms of the decorations of its Newton tree is given. This allows to compute the discriminant avoiding the use of determinants and even for non Weierstrass prepared polynomials. This is important for applications like algorithmic resolutions. We compare the Newton tree of a quasi-ordinary singularity and those of its curve transversal sections. We show that the Newton trees of the transversal sections do not give the tree of the quasi-ordinary singularity in general. It does if we know that the Newton tree of the quasi-ordinary singularity has only one arrow.Comment: 32 page

Quasi-ordinary power series and their zeta functions

The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser motivic zeta function $Z_{\text{DL}}(h,T)$ of a quasi-ordinary power series $h$ of arbitrary dimension over an algebraically closed field of characteristic zero from its characteristic exponents without using embedded resolution of singularities. This allows us to effectively represent $Z_{\text{DL}}(h,T)=P(T)/Q(T)$ such that almost all the candidate poles given by $Q(T)$ are poles. Anyway, these candidate poles give eigenvalues of the monodromy action of the complex of nearby cycles on $h^{-1}(0).$ In particular we prove in this case the monodromy conjecture made by Denef-Loeser for the local motivic zeta function and the local topological zeta function. As a consequence, if $h$ is a quasi-ordinary polynomial defined over a number field we prove the Igusa monodromy conjecture for its local Igusa zeta function.Comment: 74 page

Optomechanical strong coupling between a single cavity photon and a single atom

Single atoms coupled to a cavity offer unique opportunities as quantum optomechanical devices because of their small mass and strong interaction with light. A particular regime of interest in optomechanics is that of "single-photon strong coupling," where motional displacements on the order of the zero-point uncertainty are sufficient to shift the cavity resonance frequency by more than its linewidth. In many cavity QED platforms, however, this is unfeasible due to the large cavity linewidth. Here, we propose an alternative route in such systems, which instead relies on the coupling of atomic motion to the much narrower cavity-dressed atomic resonance frequency. We discuss and optimize the conditions in which the scattering properties of single photons from the atom-cavity system become highly entangled with the atomic motional wave function. We also analyze the prominent observable features of this optomechanical strong coupling, which include a per-photon motional heating that is significantly larger than the single-photon recoil energy, as well as mechanically-induced oscillations in time of the second-order correlation function of the emitted light. This physics should be realizable in current experimental setups, such as trapped atoms coupled to photonic crystal cavities, and more broadly opens the door to realizing qualitatively different phenomena beyond what has been observed in optomechanical systems thus far.Comment: 14 pages, 6 figure

Pulsed electric fields as a green technology for the extraction of bioactive compounds from thinned peach by-products

Thinned fruits are agricultural by-products which nowadays have few economic or environmental benefits. However, previous studies have revealed that these immature fruits have a large amount of antioxidant compounds. The aim of this study was to evaluate whether pulsed electric fields (PEF) might be a suitable green technology for enhancing the extraction of phenols, flavonoids and antioxidant compounds from fresh thinned peaches, thus reducing the use of methanol. Moreover, response surface methodology has been used to determine the optimal PEF treatment conditions, observing that the solvent is the main factor. The highest amounts of bioactive compounds were extracted using 80% methanol and no PEF. Methanol combined with PEF produced a negative effect on the extraction yield. However, the use of water as a solvent increased the amount of total bioactive compounds and individual phenols (chlorogenic acid, coumaric acid and neochlorogenic acid). Thus, PEF-assisted extraction of bioactive compounds from thinned peach fruits using water as a solvent is an alternative to conventional extraction methods which require dried products, large amounts of organic solvents and long extraction times

La biografía literaria. La inquisición: Invención de identidades femeninas

Se expone la fundamentación teórica que defiende Mijail Bajtín (1979) en torno a las biografías literarias. Se investiga la semejanza de esta metodología con la búsqueda del escritor Benjamín Jarnés y como ejemplo se analiza la biografía novelada de Sor Patrocinio. La Monja de las Llagas (1929) cuyo biógrafo, Benjamín Jarnés, destaca lo más signi- ficativo del personaje y revela los refinados métodos de la Inquisición, maestros en la devaluación del discurso femenino. The theoretical foundation defended by Mijail Bajtín (1979) regarding literary biographies is explained. The similarity of this methodology to that of the research carried out by the writer Benjamín Jarnés is investigated and as an example the biography of Sor Patrocinio. La Monja de las Llagas (1929) (Sister Patrocinio. The Nun with the Sores) is analysed. The biographer of this novel, Benjamín Jarnés, highlights the most significant features of this character and reveals the refined methods used by the Inquisition, the members of which were masters of devaluating feminine discourse

Stability of liquid bridges between twisted elliptical disks

The influence in the stability of long liquid bridges supported between two elliptical-shaped disks of their main axis relative orientation is investigated. A numerical continuation method capable of finding equilibrium shapes, both stable and unstable, is used to calculate a series of equilibrium shapes supported by disks of increasing eccentricity for different relative orientation of the disks axis. The stable or unstable character of each of the shapes is calculated to determine the position of the stability limit and its characte