A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

Retired galaxies: not to be forgotten in the quest of the star formation -- AGN connection

We propose a fresh look at the Main Galaxy Sample of the Sloan Digital Sky Survey by packing the galaxies in stellar mass and redshift bins. We show how important it is to consider the emission-line equivalent widths, in addition to the commonly used emission-line ratios, to properly identify retired galaxies (i.e. galaxies that have stopped forming stars and are ionized by their old stellar populations) and not mistake them for galaxies with low-level nuclear activity. We find that the proportion of star-forming galaxies decreases with decreasing redshift in each mass bin, while that of retired galaxies increases. Galaxies with $M_\star > 10^{11.5} M_\odot$ have formed all their stars at redshift larger than 0.4. The population of AGN hosts is never dominant for galaxy masses larger than $10^{10} M_\odot$. We warn about the effects of stacking galaxy spectra to discuss galaxy properties. We estimate the lifetimes of active galactic nuclei (AGN) relying entirely on demographic arguments --- i.e. without any assumption on the AGN radiative properties. We find upper-limit lifetimes of about 1--5 Gyr for detectable AGN in galaxies with masses between $10^{10}$--$10^{12} M_\odot$. The lifetimes of the AGN-dominated phases are a few $10^8$ yr. Finally, we compare the star-formation histories of star-forming, AGN and retired galaxies as obtained by the spectral synthesis code STARLIGHT. Once the AGN is turned on it inhibits star formation for the next $\sim$ 0.1 Gyr in galaxies with masses around $10^{10} M_\odot$, $\sim$ 1 Gyr in galaxies with masses around $10^{11} M_\odot$.Comment: accepted for MNRAS figure resolution has been degraded with respect to what will be published in MNRA

Oscillatory dynamics of a superconductor vortex lattice in high amplitude ac magnetic fields

In this work we study by ac susceptibility measurements the evolution of the solid vortex lattice mobility under oscillating forces. Previous work had already shown that in YBCO single crystals, below the melting transition, a temporarily symmetric magnetic ac field (e.g. sinusoidal, square, triangular) can heal the vortex lattice (VL) and increase its mobility, but a temporarily asymmetric one (e.g. sawtooth) of the same amplitude can tear the lattice into a more pinned disordered state. In this work we present evidence that the mobility of the VL is reduced for large vortex displacements, in agreement with predictions of recent simulations. We show that with large symmetric oscillating fields both an initially ordered or an initially disordered VL configuration evolve towards a less mobile lattice, supporting the scenario of plastic flow.Comment: 5 pages, 4 figures. To appear in Phys. Rev.

Evaluation of areas prepared for planting using LANDSAT data

Three different algorithms (SINGLE-CELL, MAXVER and MEDIA K) were used to automatically interpret data from LANDSAT observations of an area of Ribeirao Preto, Brazil. Photographic transparencies were obtained, projected and visually interpreted. The results show that: (1) the MAXVER algorithm presented a better classification performance; (2) verification of the changes in cultivated areas using data from the three different acquisition dates was possible; (3) the water bodies, degraded lands, urban areas, and fallow fields were frequently mistaken by cultivated soils; and (4) the use of projected photographic transparencies furnished satisfactory results, besides reducing the time spent on the image-100 system

On stochastic sea of the standard map

Consider a generic one-parameter unfolding of a homoclinic tangency of an area preserving surface diffeomorphism. We show that for many parameters (residual subset in an open set approaching the critical value) the corresponding diffeomorphism has a transitive invariant set $\Omega$ of full Hausdorff dimension. The set $\Omega$ is a topological limit of hyperbolic sets and is accumulated by elliptic islands. As an application we prove that stochastic sea of the standard map has full Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure