Testing equality of variances in the analysis of repeated measurements

The problem of comparing the precisions of two instruments using repeated measurements can be cast as an extension of the Pitman-Morgan problem of testing equality of variances of a bivariate normal distribution. Hawkins (1981) decomposes the hypothesis of equal variances in this model into two subhypotheses for which simple tests exist. For the overall hypothesis he proposes to combine the tests of the subhypotheses using Fisher's method and empirically compares the component tests and their combination with the likelihood ratio test. In this paper an attempt is made to resolve some discrepancies and puzzling conclusions in Hawkins's study and to propose simple modifications.\ud \ud The new tests are compared to the tests discussed by Hawkins and to each other both in terms of the finite sample power (estimated by Monte Carlo simulation) and theoretically in terms of asymptotic relative efficiencies

Control of composition and structure for molybdenum nitride films synthesized using ion beam assisted deposition

The purpose of the research described in this article was to synthesize molybdenum nitride films with well‐defined structures and stoichiometries using ion beam assisted deposition (IBAD). Approximately 400 nm thick films were prepared by the evaporative deposition of molybdenum while simultaneously bombarding the growing film with low energy (250–1000 eV) nitrogen ions. The effects of ion‐to‐atom arrival rate ratio, ion angle of incidence, and ion energy on the film composition and phase constituents were examined. The film nitrogen to molybdenum stoichiometry increased linearly with increasing arrival rate ratio irrespective of the ion energy and varied significantly with changes in the ion angle of incidence. The latter was interpreted based on sputtering and reflection effects. The phase constituents were functions of all of the deposition parameters investigated. We propose that a single parameter, the effective energy density per deposited atom, can account for the effects of ion energy, mass, and angle of incidence. The effective energy density is approximately the ion energy divided by the ion range. The range incorporates the effects of ion mass and angle of incidence, as well as the energy. For low energy ions the energy density per depositing atom is proportional to E1/2, a dependence that it shares with other models that have been developed to account for phase formation during IBAD. The advantage of the energy density treatment is that it has a more obvious influence on the temperature in the growth zone, a factor controlling phase formation. © 1995 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69720/2/JAPIAU-77-10-5138-1.pd

Ion-beam-assisted deposition of molybdenum nitride films

A series of molybdenum nitride films was synthesized by electron beam evaporative deposition of molybdenum, with simultaneous bombardment by nitrogen ions from a Kaufman ion source. The nitrogen ions were accelerated to 500 or 1000 eV. The film compositions and structures were determined using Rutherford backscattering spectrometry and X-ray diffraction respectively. Effective reflection and sputtering coefficients for nitrogen incident on the molybdenum nitride surfaces were extracted from the data. These coefficients were used to calibrate the deposition system and allowed the deposition of molybdenum nitride films with control of the nitrogen atom concentration to +/-2.3 at.%. In general, the films were polycrystalline with a high degree of texturing. The phases found in order of increasing measured nitrogen content were as follows: [gamma]-Mo2N (f.c.c.), [beta]-Mo16N7 (b.c.t.), B1-MoN (f.c.c.) then [delta]-MoN (h.c.p.).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31418/1/0000335.pd

Constraints on the χ_(c1) versus χ_(c2) polarizations in proton-proton collisions at √s = 8 TeV

The polarizations of promptly produced χ_(c1) and χ_(c2) mesons are studied using data collected by the CMS experiment at the LHC, in proton-proton collisions at √s=8  TeV. The χ_c states are reconstructed via their radiative decays χ_c → J/ψγ, with the photons being measured through conversions to e⁺e⁻, which allows the two states to be well resolved. The polarizations are measured in the helicity frame, through the analysis of the χ_(c2) to χ_(c1) yield ratio as a function of the polar or azimuthal angle of the positive muon emitted in the J/ψ → μ⁺μ⁻ decay, in three bins of J/ψ transverse momentum. While no differences are seen between the two states in terms of azimuthal decay angle distributions, they are observed to have significantly different polar anisotropies. The measurement favors a scenario where at least one of the two states is strongly polarized along the helicity quantization axis, in agreement with nonrelativistic quantum chromodynamics predictions. This is the first measurement of significantly polarized quarkonia produced at high transverse momentum