Galois groups over function fields of positive characteristic
We describe examples motivated by the work of Serre and Abhyankar.
math.NT↗
arXiv subjects
John Conway
Publications and source records attributed to John Conway.
The Strong Free Will Theorem
We strengthen "The Free Will Theorem" [1] in several ways, by replacing the axiom FIN by a weaker axiom MIN, and also by allowing the particles' responses to depend on past half-spaces rather than on on past light cones. This change allows us to directly apply our theorem to relativistic theories of the GRW type.
quant-ph↗
Thou Shalt Not Clone One Bit!
We prove a no-triplets theorem for spin 1 particles, which implies a strengthened form of the no-cloning theorem.
quant-ph↗
Reply to Comments of Bassi, Ghirardi, and Tumulka on the Free Will Theorem
We show that the authors in the title have erred in claiming that our axiom FIN is false by conflating it with Bell locality. We also argue that the predictions of quantum mechanics, and in particular EPR, are fully Lorentz invariant, whereas the Free Will Theorem shows that theories with a mechanism of reduction, such as GRW, cannot be made fully invariant.
quant-ph↗
On Adler's "Conway-Kochen Twin Argument"
We respond to Stephen Adler's comments on our paper "The Free Will Theorem",and add some further observations.
quant-ph↗
The Free Will Theorem
On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.
quant-ph↗
Interval estimation in the presence of nuisance parameters. 1. Bayesian approach
We address the common problem of calculating intervals in the presence of systematic uncertainties. We aim to investigate several approaches, but here describe just a Bayesian technique for setting upper limits. The particular example we study is that of inferring the rate of a Poisson process when there are uncertainties on the acceptance and the background. Limit calculating software associated with this work is available in the form of C functions.
physics.data-an↗
The Apparent Host Galaxy of PKS 1413+135: HST, ASCA and VLBA Observations
PKS 1413+135 (z=0.24671) is one of very few radio-loud AGN with an apparent spiral host galaxy. Previous authors have attributed its nearly exponential infrared cutoff to heavy absorption but have been unable to place tight limits on the absorber or its location in the optical galaxy. In addition, doubts remain about the relationship of the AGN to the optical galaxy given the observed lack of re-emitted radiation. We present new HST, ASCA and VLBA observations which throw significant new light on these issues. The HST observations reveal an extrremely red color (V-H = 6.9 mag) for the active nucleus of PKS 1413+135, requiring both a spectral turnover at a few microns due to synchrotron aging and a GMC-sized absorber. We derive an intrinsic column N_H = 4.6^{+2.1}_{-1.6} times 10^{22}cm^{-2} and covering fraction f = 0.12^{+0.07}_{-0.05}. As the GMC is likely in the disk of the optical galaxy, our sightline is rather unlikely (P ~ 2 times 10^{-4}). The properties of the GMC typical of GMCs in our own galaxy. The HI absorber appears centered 25 milliarcseconds away from the nucleus, while the X-ray and nearly all of the molecular absorbers must cover the nucleus, implying a complicated geometry and cloud structure, with a molecular core along our line of sight to the nucleus. Interestingly, the HST/NICMOS data require the AGN to be decentered relative to the optical galaxy by 13 +/- 4 milliarcseconds. This could be interpreted as suggestive of an AGN location far in the background compared to the optical galaxy, but it can also be explained by obscuration and/or nuclear structure, which is more consistent with the observed lack of multiple images.
astro-ph↗
Host Galaxies, Obscuration and Nuclear Structure of Three Nearby Compact Symmetric Objects
We present 3-band HST imaging of three z</=0.1 compact symmetric objects (CSOs): 4C 31.04, 1946+708 and 1146+596. These objects were chosen on the basis of proximity to Earth as well as HI 21 cm absorption. The inner H-band isophotes of these galaxies are well fit by "nuker" models, typical of nearby ellipticals. Each shows a significant flattening in the isophotal profile at radii ~0.5", as well as variations in ellipticity and PA. However, neither is uncommon for elliptical galaxies. All three show modest departures from nuker models at radii of 1-5 $h_{60}^{-1}$ kpc. Each shows large, well distributed dust features, which are somewhat concentrated in the nuclear regions in features which resemble disks or tori. The amount of dust in these galaxies is about 10 times higher than normal for ellipticals and radio galaxy hosts. The nuclear dust disks tend to be oriented roughly perpendicular to the radio axis. One galaxy, 4C31.04, exhibits bright nuclear regions well-aligned with the radio axis, while another, 1146+596, shows a significant near-IR excess resembling a stellar bar along its dust disk. The combination of outwardly normal isophotal profiles with significant variations in PA and ellipticity is consistent with the host galaxies being relatively recent merger remnants, with the mergers having occurred >/= 10^8 years ago. Such a merger could have "triggered" the current activity in these objects, but our data require a significant time delay between the merger and the onset of nuclear activity. However, these data are also consistent with the hypothesis that the onset of nuclear activity in radio galaxies is due to relatively minor "feeding" events and/or the formation of "bars within bars", which would disturb the internal kinematics only slightly.
astro-ph↗
On Three-Dimensional Space Groups
An entirely new and independent enumeration of the crystallographic space groups is given, based on obtaining the groups as fibrations over the plane crystallographic groups, when this is possible. For the 35 ``irreducible'' groups for which it is not, an independent method is used that has the advantage of elucidating their subgroup relationships. Each space group is given a short ``fibrifold name'' which, much like the orbifold names for two-dimensional groups, while being only specified up to isotopy, contains enough information to allow the construction of the group from the name.
math.MG↗