Conservative tolerance and confidence limits

Extension of exponential tolerance and confidence limits to class of distributions with monotone failure rat

Relative chronology of Martian volcanoes

Impact cratering is one of the major geological processes that has affected the Martian surface throughout the planet's history. The frequency of craters within particular size ranges provides information about the formation ages and obliterative episodes of Martian geologic units. The Barlow chronology was extended by measuring small craters on the volcanoes and a number of standard terrain units. Inclusions of smaller craters in units previously analyzed by Barlow allowed for a more direct comparison between the size-frequency distribution data for volcanoes and established chronology. During this study, 11,486 craters were mapped and identified in the 1.5 to 8 km diameter range in selected regions of Mars. The results are summarized in this three page report and give a more precise estimate of the relative chronology of the Martian volcanoes. Also, the results of this study lend further support to the increasing evidence that volcanism has been a dominant geologic force throughout Martian history

Tolerance and confidence limits for classes of distributions based on failure rate

Tolerance and confidence limits for classes of distributions based on failure rate

Full-scale aerodynamic characteristics of a propellar installed on a small twin-engine aircraft wing panel

Full-scale measurements of shaft thrust and torque were made. Wind-tunnel speeds and blade angles were set for full-scale flight conditions. Excellent quality measurements were obtained of the thrust coefficient, the power coefficient, and the propeller efficiency for various values of the advance ratio and the blade incidence angle at 3/4-blade radius. A conventional propeller theory found in the literature was applied to the present results. Although thrust, power, and efficiency were somewhat overpredicted, the advance ratio for maximum efficiency was predicted quite accurately. It was found that, for some conditions, spinner drag could be significant. A simple correction that was based on the spinner base pressure substantially accounted for the changes in efficiency that resulted from this cause

Reliability growth during a development testing program

Binomial and trinomial mathematical models for reliability growth studies - statistical analysis of system failure

Modified Paouris inequality

The Paouris inequality gives the large deviation estimate for Euclidean norms of log-concave vectors. We present a modified version of it and show how the new inequality may be applied to derive tail estimates of l_r-norms and suprema of norms of coordinate projections of isotropic log-concave vectors.Comment: 14 page

The timing and location of dust formation in the remnant of SN 1987A

The discovery with the {\it Herschel Space Observatory} of bright far infrared and submm emission from the ejecta of the core collapse supernova SN\,1987A has been interpreted as indicating the presence of some 0.4--0.7\,M$_\odot$ of dust. We have constructed radiative transfer models of the ejecta to fit optical to far-infrared observations from the literature at epochs between 615 days and 24 years after the explosion, to determine when and where this unexpectedly large amount of dust formed. We find that the observations by day 1153 are consistent with the presence of 3$\times$10$^{-3}$M$_\odot$ of dust. Although this is a larger amount than has previously been considered possible at this epoch, it is still very small compared to the amount present in the remnant after 24 years, and significantly higher dust masses at the earlier epochs are firmly ruled out by the observations, indicating that the majority of the dust must have formed at very late times. By 8515-9200 days after the explosion, 0.6--0.8\,M$_\odot$ of dust is present, and dust grains with radii greater than 2\,$\mu$m are required to obtain a fit to the observed SED. This suggests that the dust mass increase at late times was caused by accretion onto and coagulation of the dust grains formed at earlier epochs. These findings provide further confirmation that core collapse supernovae can create large quantities of dust, and indicate that the reason for small dust masses being estimated in many cases is that the vast majority of the dust forms long after most supernovae have been detectable at mid-infrared wavelengths.Comment: 13 pages, 16 figures. Accepted for publication in MNRA

Structured total least norm and approximate GCDs of inexact polynomials

The determination of an approximate greatest common divisor (GCD) of two inexact polynomials f=f(y) and g=g(y) arises in several applications, including signal processing and control. This approximate GCD can be obtained by computing a structured low rank approximation S*(f,g) of the Sylvester resultant matrix S(f,g). In this paper, the method of structured total least norm (STLN) is used to compute a low rank approximation of S(f,g), and it is shown that important issues that have a considerable effect on the approximate GCD have not been considered. For example, the established works only yield one matrix S*(f,g), and therefore one approximate GCD, but it is shown in this paper that a family of structured low rank approximations can be computed, each member of which yields a different approximate GCD. Examples that illustrate the importance of these and other issues are presented