68,483 research outputs found

    The Algebra of Strand Splitting. II. A Presentation for the Braid Group on One Strand

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    Presentations are computed for a braided version BV of Thompson's group V and for V itself showing that there is an Artin group/Coxeter group relation between them. The presentation for V is obtained from that for BV by declaring all that all generators are involutions.Comment: 15 page

    Nonparametric maximum likelihood estimation of probability densities by penalty function methods

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    When it is known a priori exactly to which finite dimensional manifold the probability density function gives rise to a set of samples, the parametric maximum likelihood estimation procedure leads to poor estimates and is unstable; while the nonparametric maximum likelihood procedure is undefined. A very general theory of maximum penalized likelihood estimation which should avoid many of these difficulties is presented. It is demonstrated that each reproducing kernel Hilbert space leads, in a very natural way, to a maximum penalized likelihood estimator and that a well-known class of reproducing kernel Hilbert spaces gives polynomial splines as the nonparametric maximum penalized likelihood estimates

    Constraints on z~10 Galaxies from the Deepest HST NICMOS Fields

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    We use all available fields with deep NICMOS imaging to search for J dropouts (H<28) at z~10. Our primary data set for this search were the two J+H NICMOS parallel fields taken with the ACS HUDF. The 5 sigma limiting mags were 28.6 in J and 28.5 in H. Several shallower fields were also used: J+H NICMOS frames available over the HDF North, the HDF South NICMOS parallel, and the ACS HUDF. The primary selection criterion was (J-H)>1.8. 11 such sources were found in all search fields using this criterion. 8 of these were clearly ruled out as credible z~10 sources, either as a result of detections (>2 sigma) blueward of J or their colors redward of the break (H-K~1.5). The nature of the 3 remaining sources could not be determined from the data. The number appears consistent with the expected contamination from low-z interlopers. Analysis of the stacked images for the 3 candidates also suggests contamination. Regardless of their true redshifts, the actual number of z~10 sources must be <=3. To assess the significance of these results, two lower redshift samples (a z~3.8 B-dropout and z~6 i-dropout sample) were projected to z~8-12 using a (1+z)^{-1} size scaling. They were added to the image frames, and the selection repeated, giving 15.6 and 4.8 J-dropouts, respectively. This suggests that to the limit of this probe (0.3 L*) there has been evolution from z~3.8 and possibly from z~6. This is consistent with the strong evolution already noted at z~6 and z~7.5 relative to z~3-4. Even assuming that 3 sources from this probe are at z~10, the rest-frame continuum UV (~1500 A) luminosity density at z~10 (integrated down to 0.3 L*) is just 0.19_{-0.09}^{+0.13}x that at z~3.8 (or 0.19_{-0.10}^{+0.15}x including cosmic variance). However, if none of our sources is at z~10, this ratio has a 1 sigma upper limit of 0.07. (abridged)Comment: 13 pages, 3 figures, 2 tables, accepted for publication in the Astrophysical Journal Letter

    Chemical propulsion research at MSFC

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    Chemical propulsion research reviews at Marshall Space Flight Cente

    How does breakup influence the total fusion of 6,7^{6,7}Li at the Coulomb barrier?

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    Total (complete + incomplete) fusion excitation functions of 6,7^{6,7}Li on 59^{59}Co and 209^{209}Bi targets around the Coulomb barrier are obtained using a new continuum discretized coupled channel (CDCC) method of calculating fusion. The relative importance of breakup and bound-state structure effects on total fusion is particularly investigated. The effect of breakup on fusion can be observed in the total fusion excitation function. The breakup enhances the total fusion at energies just around the barrier, whereas it hardly affects the total fusion at energies well above the barrier. The difference between the experimental total fusion cross sections for 6,7^{6,7}Li on 59^{59}Co is notably caused by breakup, but this is not the case for the 209^{209}Bi target.Comment: 9 pages, 9 figures, Submitted to Phys. Rev.

    Laser cooling in the Penning trap: an analytical model for cooling rates in the presence of an axializing field

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    Ions stored in Penning traps may have useful applications in the field of quantum information processing. There are, however, difficulties associated with the laser cooling of one of the radial motions of ions in these traps, namely the magnetron motion. The application of a small radio-frequency quadrupolar electric potential resonant with the sum of the two radial motional frequencies has been shown to couple these motions and to lead to more efficient laser cooling. We present an analytical model that enables us to determine laser cooling rates in the presence of such an 'axializing' field. It is found that this field leads to an averaging of the laser cooling rates for the two motions and hence improves the overall laser cooling efficiency. The model also predicts shifts in the motional frequencies due to the axializing field that are in qualitative agreement with those measured in recent experiments. It is possible to determine laser cooling rates experimentally by studying the phase response of the cooled ions to a near resonant excitation field. Using the model developed in this paper, we study the expected phase response when an axializing field is present.Comment: 22 pages, 7 figure
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