Generalized splines in ℝn and optimal control

We give a new time-dependent definition of spline curves in ℝn, which extends a recent definition of vector-valued splines introduced by Rodrigues and Silva Leite for the time-independent case. Previous results are based on a variational approach, with lengthy arguments, which do not cover the non-autonomous situation. We show that the previous results are a consequence of the Pontryagin maximum principle, and are easily generalized using the methods of optimal control. Main result asserts that vector-valued splines are related to the Pontryagin extremals of a non-autonomous linear-quadratic optimal control problem

A Multiwavelength Investigation of Unidentified EGRET Sources

Statistical studies indicate that the 271 point sources of high-energy gamma rays belong to two groups: a Galactic population and an isotropic extragalactic population. Many unidentified extragalactic sources are certainly blazars, and it is the intention of this work to uncover gamma-ray blazars missed by previous attempts. Until recently, searches for blazar counterparts to unidentified EGRET sources have focused on finding AGN that have 5-GHz radio flux densities S_5 near or above 1 Jy. However, the recent blazar identification of 3EG J2006-2321 (S_5 = 260 mJy) and other work suggest that careful studies of weaker flat-spectrum sources may be fruitful. In this spirit, error circles of 4 high-latitude unidentified EGRET sources have been searched for 5-GHz sources. The gamma-ray sources are 3EG J1133+0033, 3EG J1212+2304, 3EG J1222+2315, and 3EG J1227+4302. Within the error contours of each of the four sources are found 6 radio candidates; by observing the positions of the radio sources with the 0.81-m Tenagra II telescope it is determined that 14 of these 24 radio sources have optical counterparts with R < 22. Eight of these from two different EGRET sources have been observed in the B, V, and R bands in more than one epoch and the analysis of these data is ongoing. Any sources that are found to be variable will be the objects of multi-epoch polarimetry studies.Comment: 6 pages, 2 tables. To appear in Astrophysics & Space Scienc

Delta rho pi interaction leading to N* and Delta* resonances

We have performed a calculation for the three body $\Delta \rho \pi$ system by using the fixed center approximation to Faddeev equations, taking the interaction between $\Delta$ and $\rho$, $\Delta$ and$\pi$, and $\rho$ and $\pi$ from the chiral unitary approach. We find several peaks in the modulus squared of the three-body scattering amplitude, indicating the existence of resonances, which can be associated to known $I=1/2, 3/2$ and $J^P=1/2^+, 3/2^+$ and $5/2^+$ baryon states.Comment: Presented at the 21st European Conference on Few-Body Problems in Physics, Salamanca, Spain, 30 August - 3 September 201

GLAST Large Area Telescope Multiwavelength Planning

Gamma-ray astrophysics depends in many ways on multiwavelength studies. The Gamma-ray Large Area Space Telescope (GLAST) Large Area Telescope (LAT) Collaboration has started multiwavelength planning well before the scheduled 2007 launch of the observatory. Some of the high-priority multiwavelength needs include: (1) availability of contemporaneous radio and X-ray timing of pulsars; (2) expansion of blazar catalogs, including redshift measurements; (3) improved observations of molecular clouds, especially at high galactic latitudes; (4) simultaneous broad-spectrum blazar monitoring; (5) characterization of gamma-ray transients, including gamma ray bursts; (6) radio, optical, X-ray and TeV counterpart searches for reliable and effective sources identification and characterization. Several of these activities are needed to be in place before launch

Turbulent luminance in impassioned van Gogh paintings

We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation

Three-Body approach to the K^- d Scattering Length in Particle Basis

We report on the first calculation of the scattering length A_{K^-d} based on a relativistic three-body approach where the two-body input amplitudes coupled to the Kbar N channels have been obtained with the chiral SU(3) constraint, but with isospin symmetry breaking effects taken into account. Results are compared with a recent calculation applying a similar set of two-body amplitudes,based on the fixed center approximation, considered as a good approximation for a loosely bound target, and for which we find significant deviations from the exact three-body results. Effects of the hyperon-nucleon interaction, and deuteron $D$-wave component are also evaluated.Comment: 5 pages, Submitted to Phys. Rev.

Towards a population of HMXB/NS microquasars as counterparts of low-latitude unidentified EGRET sources

The discovery of the microquasar LS 5039 well within the 95% conficence contour of the Unidentified EGRET Source (UES) 3EG J1824-1514 was a major step towards the possible association between microquasars (MQs) and UESs. The recent discovery of precessing relativistic radio jets in LS I +61 303, a source associated for long time with 2CG 135+01 and with the UES 3EG J0241+6103, has given further support to this idea. Finally, the very recently proposed association between the microquasar candidate AX J1639.0-4642 and the UES 3EG J1639-4702 points towards a population of High Mass X-ray Binary (HMXB)/Neutron Star (NS) microquasars as counterparts of low-latitude unidentified EGRET sources.Comment: 12 pages, 7 figures. Proceedings of the Conference "The Multiwavelength Approach to Unidentified Gamma-ray Sources", to appear in the journal Astrophysics and Space Scienc

The distribution of transit durations for Kepler planet candidates and implications for their orbital eccentricities

‘In these times, during the rise in the popularity of institutional repositories, the Society does not forbid authors from depositing their work in such repositories. However, the AAS regards the deposit of scholarly work in such repositories to be a decision of the individual scholar, as long as the individual's actions respect the diligence of the journals and their reviewers.’ Original article can be found at : http://iopscience.iop.org/ Copyright American Astronomical SocietyDoppler planet searches have discovered that giant planets follow orbits with a wide range of orbital eccentricities, revolutionizing theories of planet formation. The discovery of hundreds of exoplanet candidates by NASA's Kepler mission enables astronomers to characterize the eccentricity distribution of small exoplanets. Measuring the eccentricity of individual planets is only practical in favorable cases that are amenable to complementary techniques (e.g., radial velocities, transit timing variations, occultation photometry). Yet even in the absence of individual eccentricities, it is possible to study the distribution of eccentricities based on the distribution of transit durations (relative to the maximum transit duration for a circular orbit). We analyze the transit duration distribution of Kepler planet candidates. We find that for host stars with T > 5100 K we cannot invert this to infer the eccentricity distribution at this time due to uncertainties and possible systematics in the host star densities. With this limitation in mind, we compare the observed transit duration distribution with models to rule out extreme distributions. If we assume a Rayleigh eccentricity distribution for Kepler planet candidates, then we find best fits with a mean eccentricity of 0.1-0.25 for host stars with T ≤ 5100 K. We compare the transit duration distribution for different subsets of Kepler planet candidates and discuss tentative trends with planetary radius and multiplicity. High-precision spectroscopic follow-up observations for a large sample of host stars will be required to confirm which trends are real and which are the results of systematic errors in stellar radii. Finally, we identify planet candidates that must be eccentric or have a significantly underestimated stellar radius.Peer reviewedFinal Accepted Versio

Theoretical study of incoherent phi photoproduction on a deuteron target

We study the photoproduction of phi mesons in deuteron, paying attention to the modification of the cross section from bound protons to the free ones with the aim of comparing with recent results at LEPS. For this purpose we take into account Fermi motion in single scattering and rescattering of the phi to account for phi absorption on a second nucleon as well as the rescattering of the proton. We find that the contribution of the double scattering is much smaller than the typical cross section of gamma p to phi p in free space, which implies a very small screening of the phi production in deuteron. The contribution from the proton rescattering, on the other hand, is found to be not negligible compared to the cross section of gamma p to phi p in free space, and leads to a moderate reduction of the phi photoproduction cross section on a deuteron at forward angles if LEPS set up is taken into account. The Fermi motion allows contribution of the single scattering in regions forbidden by phase space in the free case. In particular, we find that for momentum transferred squared close to the maximum value, the Fermi motion changes drastically the shape of d sigma / dt, to the point that the ratio of this cross section to the free one becomes very sensitive to the precise value of t chosen, or the size of the bin used in an experimental analysis. Hence, this particular region of t does not seem the most indicated to find effects of a possible phi absorption in the deuteron. This reaction is studied theoretically as a function of t and the effect of the experimental angular cuts at LEPS is also discussed, providing guidelines for future experimental analyses of the reaction.Comment: 17 pages, 16 figure