Astrometry with the Hubble Space Telescope: Trigonometric Parallaxes of Selected Hyads

We present absolute parallaxes and proper motions for seven members of the Hyades open cluster, pre-selected to lie in the core of the cluster. Our data come from archival astrometric data from FGS 3, and newer data for 3 Hyads from FGS 1R, both white-light interferometers on the Hubble Space Telescope (HST). We obtain member parallaxes from six individual Fine Guidance Sensor (FGS) fields and use the field containing van Altena 622 and van Altena 627 (= HIP 21138) as an example. Proper motions, spectral classifications and VJHK photometry of the stars comprising the astrometric refer- ence frames provide spectrophotometric estimates of reference star absolute parallaxes. Introducing these into our model as observations with error, we determine absolute parallaxes for each Hyad. The parallax of vA 627 is significantly improved by including a perturbation orbit for this previously known spectroscopic binary, now an astrometric binary. Compared to our original (1997) determina- tions, a combination of new data, updated calibration, and improved analysis lowered the individual parallax errors by an average factor of 4.5. Comparing parallaxes of the four stars contained in the Hipparcos catalog, we obtain an average factor of 11 times improvement with the HST . With these new results, we also have better agreement with Hipparcos for the four stars in common. These new parallaxes provide an average distance for these seven members, = 47.5 pc, for the core a \pm 1 - {\sigma} dispersion depth of 3.6 pc, and a minimum depth from individual components of 16.0 \pm 0.9 pc. Absolute magnitudes for each member are compared to established main sequences, with excellent agreement. We obtain a weighted average distance modulus for the core of the Hyades of m-M=3.376 \pm 0.01, a value close to the previous Hipparcos values, m-M=3.33\pm 0.02.Comment: 21 pages, 7 figures, Astronomical Journal, accepted 2011-3-

Hardy-Orlicz spaces of conformal densities

We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.Comment: 12 page

On the distribution law in locally rapidly fluctuating fields which are steady when averaged over a sufficient time interval

Thomas(1) and later Fermi(2) have attempted to determine the time average electrical potential around the nucleus of a heavy atom. They treat the electrons as if they formed an ideal degenerate Fermi gas which becomes statistically distributed in the steady field due to the nucleus plus the locally rapidly fluctuating field due to the electrons themselves. This method is apparently fully justified and it is hard to see, at first, why the numerical solutions given by the above writers turn out to be so roughly approximate, especially for heavy atoms with many electrons. The following investigation purports to show that the roughness of the method is due to the unjustified, except for approximation purposes, use of the statistical distribution law of an ideal gas in a steady field in the case where the field is steady only when averaged over a sufficiently long time interval and is locally fluctuating

Whose International Law?: Sovereignty and Non-State Groups

This is the first of three keynote panels at this 88th Annual Meeting, under the overarching theme of The Transformation of Sovereignty

Computational reverse mathematics and foundational analysis

Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational analysis, which explores the limits of different foundations for mathematics in a formally precise manner. This paper gives a detailed account of the motivations and methodology of foundational analysis, which have heretofore been largely left implicit in the practice. It then shows how this account can be fruitfully applied in the evaluation of major foundational approaches by a careful examination of two case studies: a partial realization of Hilbert's program due to Simpson [1988], and predicativism in the extended form due to Feferman and Sch\"{u}tte. Shore [2010, 2013] proposes that equivalences in reverse mathematics be proved in the same way as inequivalences, namely by considering only $\omega$-models of the systems in question. Shore refers to this approach as computational reverse mathematics. This paper shows that despite some attractive features, computational reverse mathematics is inappropriate for foundational analysis, for two major reasons. Firstly, the computable entailment relation employed in computational reverse mathematics does not preserve justification for the foundational programs above. Secondly, computable entailment is a $\Pi^1_1$ complete relation, and hence employing it commits one to theoretical resources which outstrip those available within any foundational approach that is proof-theoretically weaker than $\Pi^1_1\text{-}\mathsf{CA}_0$.Comment: Submitted. 41 page

A Grotian Tradition of Theory and Practice: Grotius, Law, and Moral Skepticism in the Thought of Hedley Bull

This paper describes a system that incrementally constructs an increasingly accurate road map from GPS traces from a single vehicle. The resulting road map contains information about the road such as road gradient which can be used by functions in a heavy vehicle to drive more effectively. The system is supposed to run on an embedded system in a heavy vehicle and is therefore design to require as little working memory and processing time as possible.Pre- and post processing techniques that counters GPS noise, random movements and improve the quality of the road map are also described, for example tunnel estimation where GPS signals are missing. An aging method, designed for data from a single vehicle, that eventually removes closed and rarely used roads is proposed.A comparison between the constructed road map and a commercial one shows that the algorithms described creates a very accurate roadmap. The performance of the system is evaluated and it is concluded that it would be possible to run it on an embedded system in a heavyvehicle