The BL-Lac gamma-ray blazar PKS 0447-439 as a probable member of a group of galaxies at z=0.343

The BL-Lac blazar PKS 0447-439 is one of the brightest HE gamma-ray sources that were first detected by Fermi-LAT. It was also detected by H.E.S.S. at VHE gamma-rays, which allowed constraining the redshift of PKS 0447-439 by considering the attenuation caused by gamma-ray interactions with ambient photons in the extragalactic background light (EBL). This constraint agreed with color-magnitude and spectroscopic redshift constraints (0.179 < z < 0.56), Recently, however, a much higher redshift was proposed for this blazar (z > 1.2). This value was debated because if true, it would imply either that the relevant absorption processes of gamma-rays are not well understood or that the EBL is dramatically different from what is believed today. This high redshift was not confirmed by three independent new spectroscopic observations at high signal-to-noise ratios. Given that BL-Lac are typically hosted by elliptical galaxies, which in turn are associated with groups, we aim to find the host group of galaxies of PKS 0447-439. The ultimate goal is to estimate a redshift for this blazar. Spectra of twenty-one objects in the field of view of PKS 0447-439 were obtained with the Gemini Multi-Object Spectrograph. Based on the redshifts and coordinates of these galaxies, we searched for groups of galaxies. Using a deep catalog of groups, we studied the probability of finding by chance a group of galaxies in the line of sight of PKS 0447-439. We identified a group of galaxies that was not previously cataloged at z = 0.343 with seven members, a virial radius of 0.42 Mpc, and a velocity dispersion of 622 km s^-1. We found that the probability of the host galaxy of PKS 0447-439 to be a member of the new group is >= 97%. Therefore, we propose to adopt z = 0.343 +- 0.002 as the most likely redshift for PKS 0447-439.Comment: Accepted for publication in A&

Pensioner poverty over the next decade: what role for tax and benefit reform?

Recent falls in poverty amongst those aged 65 and over are unlikely to continue after 2007-08, even after the implementation of the proposals outlined in the Government's Pensions White Paper. This report looks at the prospects for pensioner poverty in England over the next decade. The authors find that that the proportion of those aged 65 and over living in poverty is set to remain at its current level - around one-in-five - between 2007-08 and 2017-18. This is despite the overall increase in the generosity of state pensions arising from the Pensions White Paper, and the fact that younger cohorts are expected to have more private pension income and higher employment rates at older ages than those preceding them

Integration of differential equations by C∞\mathcal{C}^{\infty}-structures

Several integrability problems of differential equations are addressed by using the concept of $\mathcal{C}^{\infty}$-structure, a recent generalization of the notion of solvable structure. Specifically, the integration procedure associated with $\mathcal{C}^{\infty}$-structures is used to integrate to a Lotka-Volterra model and several differential equations that lack sufficient Lie point symmetries and cannot be solved using conventional methods

On the relation between standard and μ\mu-symmetries for PDEs

We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We give in particular a result concerning the relationship between $\mu$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $\mu$-symmetries and nonlocal standard symmetries.Comment: 25 pages, no figures, latex. to be published in J. Phys.

On the complete integrability of a nonlinear oscillator from group theoretical perspective

In this paper, we investigate the integrability aspects of a physically important nonlinear oscillator which lacks sufficient number of Lie point symmetries but can be integrated by quadrature. We explore the hidden symmetry, construct a second integral and derive the general solution of this oscillator by employing the recently introduced $\lambda$-symmetry approach and thereby establish the complete integrability of this nonlinear oscillator equation from a group theoretical perspective.Comment: 15 page

C∞\mathcal{C}^{\infty}-structures in the integration of involutive distributions

For a system of ordinary differential equations (ODEs) or, more generally, an involutive distribution of vector fields, the problem of its integration is considered. Among the many approaches to this problem, solvable structures provide a systematic procedure of integration via Pfaffian equations that are integrable by quadratures. In this paper structures more general than solvable structures (named cinf-structures) are considered. The symmetry condition in the concept of solvable structure is weakened for cinf-structures by requiring their vector fields be just cinf-symmetries. For cinf-structures there is also an integration procedure, but the corresponding Pfaffian equations, although completely integrable, are not necessarily integrable by quadratures. The well-known result on the relationship between integrating factors and Lie point symmetries for first-order ODEs is generalized for cinf-structures and involutive distributions of arbitrary corank by introducing symmetrizing factors. The role of these symmetrizing factors on the integrability by quadratures of the Pfaffian equations associated with the \cinf-structure is also established. Some examples that show how these objects and results can be applied in practice are also presented