The Ontological Import of Adding Proper Classes

In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content

New classes of nonlinearly self-adjoint evolution equations of third- and fifth-order

In a recent communication Nail Ibragimov introduced the concept of nonlinearly self-adjoint differential equation [N. H. Ibragimov, Nonlinear self-adjointness and conservation laws, J. Phys. A: Math. Theor., vol. 44, 432002, 8 pp., (2011)]. In the present communication a nonlinear self-adjoint classification of a general class of fifth-order evolution equation with time dependent coefficients is presented. As a result five subclasses of nonlinearly self-adjoint equations of fifth-order and four subclasses of nonlinearly self-adjoint equations of third-order are obtained. From the Ibragimov's theorem on conservation laws [N. H. Ibragimov, A new conservation theorem, J. Math. Anal. Appl., vol. 333, 311--328, (2007)] conservation laws for some of these equations are established

Radio pulsar binaries in globular clusters: their orbital eccentricities and stellar interactions

High sensitivity searches of globular clusters (GC) for radio pulsars by improved pulsar search algorithms and sustained pulsar timing observations have so far yielded some 140 pulsars in more than two dozen GCs. The observed distribution of orbital eccentricity and period of binary radio pulsars in GCs have imprints of the past interaction between single pulsars and binary systems or of binary pulsars and single passing non-compact stars. It is seen that GCs have different groups of pulsars. These may have arisen out of exchange or merger of a component of the binary with the incoming star or a "fly-by" in which the original binary remains intact but undergoes a change of eccentricity and orbital period. We consider the genesis of the distribution of pulsars using analytical and computational tools such as STARLAB, which performs numerical scattering experiments with direct N-body integration. Cluster pulsars with intermediate eccentricities can mostly be accounted for by fly-bys whereas those with high eccentricities are likely to be the result of exchanges and/or mergers of single stars with the binary companion of the pulsar, although there are a few objects which do not easily fit into this description. The corresponding distribution for galactic field pulsars shows notable differences from the GC pulsar orbital period and eccentricity distribution. The long orbital period pulsars in the galactic field with frozen out low eccentricities are largely missing from the globular clusters, and we show that ionization of these systems in GCs cannot alone account for the peculiarities.Comment: Accepted for publication in Ap

Self-adjoint sub-classes of third and fourth-order evolution equations

In this work a class of self-adjoint quasilinear third-order evolution equations is determined. Some conservation laws of them are established and a generalization on a self-adjoint class of fourth-order evolution equations is presented

On What Counts as a Translation

In this article, instead of taking a particular method as translation, we ask: what does one expect to do with a translation? The answer to this question will reveal, though, that none of the first order methods are capable of fully represent the required transference of ontological commitments. Lastly, we will show that this view on translation enlarge considerably the scope of translatable, and, therefore, ontologically comparable theories

Application of moderate deviation techniques to prove Sinai's Theorem on RWRE

We apply the techniques developed in Comets and Popov (2003) to present a new proof to Sinai's theorem (Sinai, 1982) on one-dimensional random walk in random environment (RWRE), working in a scale-free way to avoid rescaling arguments and splitting the proof in two independent parts: a quenched one, related to the measure $P_\omega$ conditioned on a fixed, typical realization $\omega$ of the environment, and an annealed one, related to the product measure $\mathbb{P}$ of the environment $\omega$. The quenched part still holds even if we use another measure (possibly dependent) for the environment.Comment: 17 pages, 3 figures, 5 annexe

The Pulsar Population in Globular Clusters and in the Galaxy

In this paper, I review some of the basic properties of the pulsar population in globular clusters (GCs) and compare it with the the Galactic disk population. The neutron stars (NSs) in GCs were likely formed - and appear to continue forming - in highly symmetric supernovae (SNe), likely from accretion-induced collapse (AIC). I review the many pulsar finds and discuss some particularly well populated GCs and why they are so. I then discuss some particularly interesting objects, like millisecond pulsars (MSPs) with eccentric orbits, which were heavily perturbed by passing stars. Some of these systems, like NGC 1851A and NGC 6544B, are almost certainly the result of exchange interactions, i.e., they are witnesses to the very same processes that created the large population of MSPs in the first place. I also review briefly the problem posed by the presence of young pulsars in GCs (with a special emphasis on a sub-class of young pulsars, the super-energetic MSPs), which suggest continuing formation of NSs in low-velocity SNe. In the final section, I discuss the possibility of an analogous population in the Galaxy and highlight a particularly interesting case, PSR J1903+0327, where the primary neutron star appears to have formed with a small-velocity kick and small fractional mass loss. Systems with primary NSs formed in electron-capture SNe should constitute a distinct low-velocity Galactic population akin in many respects to the GC population. Current high-resolution surveys of the Galactic plane should be able to detect it clearly.Comment: Proceedings of IAUS 291 "Neutron Stars and Pulsars: Challenges and Opportunities after 80 years", J. van Leeuwen (ed.); 8 pages, Accepted versio

Calming down the seas: the near collapse of an Atlantic coastal fishery

For years now the estimates of the consequences of overfishing for marine ecosystems have differed greatly within the scientific community^1^. The use of commercial catch statistics to estimate tendencies has been much criticised^2^, but alternative information sources with long time series are rare. Here we employ the historic archive (1953-2007) of the recreational spearfishery in Galicia (NW Spain), which does not have the problems common to other fishery registers, to estimate long-term changes in coastal ecosystems. Using generalized additive regression models (GAM) we estimated decreases of around 83% in the abundances of coastal fish over the last 50 years. In the same period the average body size decreased by 36%. In addition, the relative catch frequency has decreased for the most valuable commercial species. Commercial overfishing has brought these ecosystems so close to the brink of collapse that it is necessary to implement measures that ensure their recovery