An analytic solution to the Busemann-Petty problem on sections of convex bodies

We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in R^n with the Fourier transform of powers of the radial function of the body. A parallel section function (or (n-1)-dimensional X-ray) gives the ((n-1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characterization of intersection bodies in R^n and leads to a unified analytic solution to the Busemann-Petty problem: Suppose that K and L are two origin-symmetric convex bodies in R^n such that the ((n-1)-dimensional) volume of each central hyperplane section of K is smaller than the volume of the corresponding section of L; is the (n-dimensional) volume of K smaller than the volume of L? In conjunction with earlier established connections between the Busemann-Petty problem, intersection bodies, and positive definite distributions, our formula shows that the answer to the problem depends on the behavior of the (n-2)-nd derivative of the parallel section functions. The affirmative answer to the Busemann-Petty problem for n\le 4 and the negative answer for n\ge 5 now follow from the fact that convexity controls the second derivatives, but does not control the derivatives of higher orders.Comment: 13 pages, published versio

Vibrational intensity distributions for continuum photoionization of oxygen

Results from measurements of vibrational intensity distributions for continuum photoionization of O2 are reported. Measurements were made using the 584 and 304 A He lines. The photoionization cross section of O2 shows a substantial dip in magnitude over a 20 A band centered about 590 A; thus the possibility exists that a 584 A photoelectron spectrum of O2 includes an autoionized contribution and the vibrational intensity distributions may not correspond to those of continuum ionization. Oxygen photoionization cross section shows no structure around 304 A and purley continuum ionization is expected

On the ionization potential of molecular oxygen

The ionization potential of O2 was measured by the technique of high resolution photoelectron spectroscopy taking into account the influence of rotational structure on the shape of the vibrational bands. A value of 12.071 + or - .001 eV (1027.1 + or - 0.1 A) was found for the ionization potential. A lowering of the ionization potential caused by a branch-head when delta N = -2 gave an appearance potential for ionization of 12.068 + or - .001 eV (1027.4 + or - 0.1 A)

Vibrational intensity distributions in the photoelectron spectrum of hydrogen

The intensity distribution over the H2(+) vibrational levels up to a quantum number of 15 was measured for H2 photoelectron spectra at a photon wavelength of 584 A. The data show reasonable agreement with recent calculations only in the quantum number of 0 through 8. The higher levels are populated significantly lower than predicted by theory

Photoionization branching ratios and vibrational intensity distribution for N2, CO; and CO2 between 53 and 75 nm

The probability of radiation producing ions in specific electronic and vibrational levels was documented. For example, when a narrow band-pass of solar ionizing photons is incident on an atmospheric species it is now possible to describe, accurately, how the radiant energy is shared among the various electronic states of the ions produced. The molecules studied were N2, CO, and CO2. These molecules were photoionized by radiation between 53 and 75 nm. The effects of autoionization are discussed and continuum vibrational intensities are tabulated and compared with theoretical Franck-Condon factors where available. The branching ratios and partial cross sections for ionization into various electronic states are tabulated

Independent Orbiter Assessment (IOA): Assessment of instrumental subsystem FMEA/CIL

The McDonnell Douglas Astronautics Company (MDAC) was selected in June 1986 to perform an Independent Orbiter Assessment (IOA) of the Failure Modes and Effects Analysis (FMEA) and Critical Items List (CIL). The IOA effort first completed an analysis of the Instrumentation hardware, generating draft failure modes and potential critical items. To preserve independence, this analysis was accomplished without reliance upon the results contained within the NASA FMEA/CIL documentation. The IOA results were then compared to the NASA FMEA/CIL baseline. A resolution of each discrepancy from the comparison is provided through additional analysis as required. The results of that comparison for the Orbiter Instrumentation hardware are documented. The IOA product for Instrumentation analysis consisted of 107 failure mode worksheets that resulted in 22 critical items being identified. Comparison was made to the Pre 51-L NASA baseline with 14 Post 51-L FMEAs added, which consists of 96 FMEAs and 18 CIL items. This comparison produced agreement on all but 25 FMEAs which caused differences in 5 CIL items

Collecting efficiency of a cylindrical mirror electron energy analyzer with preretarding lens

The electron collecting efficiency of a cylindrical mirror energy analyzer incorporating retardation of the electrons prior to analysis has been determined over the range 0 to 30 eV by two methods. The first method requires the use of a vacuum ultraviolet monochromator to produce monoenergetic electrons of different energies; the second method involves measuring the energy-brightness relationship of the retarding optics and should be applicable to any deflection analyzer with pre-retarding optics. The results of the two methods are compared and the limitations of the latter method are discussed

New Prospects in Fixed Target Searches for Dark Forces with the SeaQuest Experiment at Fermilab

An intense, 120 GeV proton beam incident on an extremely long, iron target generates enormous numbers of light-mass particles that also decay within that target. If one of these particles decays to a final state with a hidden gauge boson, or if such a particle is produced as a result of the initial collision, then that weakly interacting, hidden-sector particle may traverse the remainder of the target and be detected downstream through its possible decay to an $e^+e^-$, $\mu^+\mu^-$, or $\pi^+\pi^-$ final state. These conditions can be realized through an extension of the SeaQuest experiment at Fermilab, and in this initial investigation we consider how it can serve as an ultrasensitive probe of hidden vector gauge forces, both Abelian and non-Abelian. A light, weakly coupled hidden sector may well explain the dark matter established through astrophysical observations, and the proposed search can provide tangible evidence for its existence --- or, alternatively, constrain a "sea" of possibilities.Comment: 14 pages, 8 figures; improved sensitivity analysis and cross-checks; small shifts in the expected limits; conclusions unchanged; refs. adde

Study of methods for the improvement of bacterial transport media

A series of 500 transport media recipes was tested for ability to hold pure cultures of Streptococcus equisimilus, Corynebacterium equi, Neisseria perflava, and Haemophilus parainfluenzae for 21 days. Stuart Medium Base with 0.4% agar was used as the control medium for this and the other experiments in the investigation. At the end of the holding period inoculated transport media were quantitatively assayed, and the control media were assayed immediately after inoculation. Three vials of each medium were inoculated with an organism, and each vial's medium was diluted and spread on duplicate plates. Assay media for this experiment included Brain Heart Infusion,(BHIA) Tryptic Soy Agar, and BHIA with 1% Isovitalex enrichment