39,077 research outputs found

    Art, Science, Cartography, and the Eye of the Beholder

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    Numerical Calculation of Bessel Functions

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    A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The Trapezoidal Rule, applied to suitable integral representations, may become the method of choice for evaluation of the many Special Functions of mathematical physics.Comment: 10 page

    The Low-z Intergalactic Medium. III. HI and Metal Absorbers at z<0.4

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    We conduct an ultraviolet (HST and FUSE) spectroscopic survey of HI (Lyman lines) and seven metal ions (OVI, NV, CIV, CIII, SiIV, SiIII, FeIII) in the low-redshift intergalactic medium (IGM) at z<0.4. We analyzed 650 Lya absorbers over redshift pathlength Delta z=5.27, detecting numerous absorbers: 83 OVI systems, 39 CIII, 53 SiIII, 24 CIV, 24 NV, and so on. Our survey yields distributions in column density and estimates of the IGM baryon content and metallicities of C, N, O in the IGM. In the low-z IGM, we have accounted for ~40% of the baryons: 30% in the photoionized Lya forest and 10% in the (T=10^5-6 K) warm-hot intergalactic medium (WHIM) traced by OVI. Statistical metallicities of C, N, O ions are consistent with the canonical (z=0) value of 10% solar, with considerable scatter. Improved statistics for weak OVI absorbers allows us to estimate Omega_WHIM/Omega_b=0.073+-0.008 down to logN_OVI=13.4. NV absorption is well-correlated with OVI and both ions show similarly steep power-law indices dN/dz N^-beta with beta_OVI beta_NV 2 while beta_HI=1.7. We conclude that OVI and NV are reliable tracers of the portion of the WHIM at T=10^5-6 K. CIV may be present in both collisional and photoionized phases; N_CIV correlates poorly with both N_HI and N_OVI and beta_HI<beta_CIV<beta_OVI. The ions CIII, SiIII, and SiIV are well correlated with HI and show patterns typical of photoionization. Adjacent ion stages of the same element (CIII/IV and SiIII/IV) provide useful constraints on the photoionization parameter, logU=-1.5+-0.5. Comparison of SiIV and CIV with high-z surveys shows a modest increase in line density, consistent with increasing IGM metallicity at recent epochs.Comment: Submitted to ApJ, 27 pages in ApJ format (figure and discussion added

    The Mission Doctors Association, Inc.

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    An intrinsic homotopy for intersecting algebraic varieties

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    Recently we developed a diagonal homotopy method to compute a numerical representation of all positive dimensional components in the intersection of two irreducible algebraic sets. In this paper, we rewrite this diagonal homotopy in intrinsic coordinates, which reduces the number of variables, typically in half. This has the potential to save a significant amount of computation, especially in the iterative solving portion of the homotopy path tracker. There numerical experiments all show a speedup of about a factor two
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