Detecting flat normal cones using Segre classes

Given a flat, projective morphism $Y \to T$ from an equidimensional scheme to a nonsingular curve and a subscheme $Z$ of $Y$, we give conditions under which specialization of the Segre class $s(N_{Z}Y)$ of the normal cone of $Z$ in $Y$ implies flatness of the normal cone. We apply this result to study when the relative tangent star cone of a flat family is flat.Comment: LaTeX, 11 pages, no figure

Tangential Quantum Cohomology of Arbitrary Order

J. Kock has previously defined a tangency quantum product on formal power series with coefficients in the cohomology ring of any smooth projective variety, and thus a ring that generalizes the quantum cohomology ring. We further generalize Kock's construction by defining a dth-order contact product and establishing its associativity.Comment: 18 pages, LaTeX. We correct our paper to work in the correct context, viz., using numerical equivalence (rather than rational equivalence) and explicitly mentioning the Novikov rin

Interactive cutting path analysis programs

The operation of numerically controlled machine tools is interactively simulated. Four programs were developed to graphically display the cutting paths for a Monarch lathe, Cintimatic mill, Strippit sheet metal punch, and the wiring path for a Standard wire wrap machine. These programs are run on a IMLAC PDS-ID graphic display system under the DOS-3 disk operating system. The cutting path analysis programs accept input via both paper tape and disk file

On the Non-Gaussianity Observed in the COBE-DMR Sky Maps

In this paper we pursue the origin of the non-Gaussianity determined by a bispectrum analysis of the COBE-DMR 4-year sky maps. The robustness of the statistic is demonstrated by the rebinning of the data into 12 coordinate systems. By computing the bispectrum statistic as a function of various data partitions - by channel, frequency, and time interval, we show that the observed non-Gaussian signal is driven by the 53 GHz data. This frequency dependence strongly rejects the hypothesis that the signal is cosmological in origin. A jack-knife analysis of the coadded 53 and 90 GHz sky maps reveals those sky pixels to which the bispectrum statistic is particularly sensitive. We find that by removing data from the 53 GHz sky maps for periods of time during which a known systematic effect perturbs the 31 GHz channels, the amplitudes of the bispectrum coefficients become completely consistent with that expected for a Gaussian sky. We conclude that the non-Gaussian signal detected by the normalised bispectrum statistic in the publicly available DMR sky maps is due to a systematic artifact. The impact of removing the affected data on estimates of the normalisation of simple models of cosmological anisotropy is negligible.Comment: 14 pages, plus 8 Postscript and 3 GIF figures. LaTeX2e document using AASTeX v5.0 macros. Revised version accepted for publication in the Astrophysical Journal: small changes to the text, minor modifications to figures 1 and

Assessment worlds colliding? Negotiating between discourses of assessment on an online open course

Using the badged open course, Taking your first steps into Higher Education, this case study examines how assessment on online open courses draws on concepts of assessment used within formal and informal learning. Our experience was that assessment used within open courses, such as massive open online courses, is primarily determined by the requirements of quality assurance processes to award a digital badge or statement of participation as well as what is technologically possible. However, this disregards much recent work in universities that use assessment in support of learning. We suggest that designers of online open courses should pay greater attention to the relationship of assessment and learning to improve participant course completion

Dynamics of ``Small Galaxies'' in the Hubble Deep Field

We have previously found in the Hubble Deep Field a significant angular correlation of faint, high color-redshift objects on scales below one arcsecond, or several kiloparsecs in metric size. We examine the correlation and nearest neighbor statistics to conclude that 38% of these objects in the HDF have a companion within one arcsecond, three times the number expected in a random distribution with the same number of objects. We examine three dynamical scenarios for these object multiplets: 1) the objects are star-forming regions within normal galaxies, whose disks have been relatively dimmed by K-correction and surface brightness dimming; 2) they are fragments merging into large galaxies; 3) they are satellites accreting onto normal L_* galaxies. We find that hypothesis 1 is most tenable. First, large galaxies in the process of a merger formation would have accumulated too much mass in their centers (5e12 M_sun inside 2 kpc) to correspond to present day objects. Second, accretion by dynamical friction occurs with a predictable density vs. radius slope, not seen among the faint HDF objects. Since the dynamical friction time is roughly (1 Gyr), a steady-state should have been reached by redshift z < 5. Star-forming regions within galaxies clearly present no dynamical problems. Since large spirals would still appear as such in the HDF, we favor a scenario in which the faint compact sources in the HDF are giant starforming regions within small normal galaxies, such as Magellanic irregulars. Finally we checked that reduction in mass-to-light from induced star-formation cannot alone explain the luminosity overdensity.Comment: AASTeX 4.0 (preprint), 4 PostScript figure