Saddlepoint approximation for moment generating functions of truncated random variables

We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the application of saddlepoint approximations to certain distributions determined by truncated random variables. Two important statistical applications are the following: the approximation of certain multivariate cumulative distribution functions; and the approximation of passage time distributions in ion channel models which incorporate time interval omission. We derive two types of representation for the MGF of a truncated random variable. One of these representations is obtained by exponential tilting. The second type of representation, which has two versions, is referred to as an exponential convolution representation. Each representation motivates a different approximation. It turns out that each of the three approximations is extremely accurate in those cases ``to which it is suited.'' Moreover, there is a simple rule of thumb for deciding which approximation to use in a given case, and if this rule is followed, then our numerical and theoretical results indicate that the resulting approximation will be extremely accurate.Comment: Published at http://dx.doi.org/10.1214/009053604000000689 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A dynamical symmetry breaking model in Weyl space

The dynamical process following the breaking of Weyl geometry to Riemannian geometry is considered by studying the motion of de Sitter bubbles in a Weyl vacuum. The bubbles are given in terms of an exact, spherically symmetric thin shell solution to the Einstein equations in a Weyl-Dirac theory with a time-dependent scalar field of the form beta = f(t)/r. The dynamical solutions obtained lead to a number of possible applications. An important feature of the thin shell model is the manner in which beta provides a connection between the interior and exterior geometries since information about the exterior geometry is contained in the boundary conditions for beta.Comment: 18 pages, RevTex, to be published in J. Math. Phy

NASA Low-Speed Centrifugal Compressor for Fundamental Research

A centrifugal compressor facility being built by the NASA Lewis Research Center is described; its purpose is to obtain benchmark experimental data for internal flow code verification and modeling. The facility will be heavily instrumented with standard pressure and temperature probes and have provisions for flow visualization and laser Doppler velocimetry. The facility will accommodate rotational speeds to 2400 rpm and will be rated at pressures to 1.25 atm. The initial compressor stage for testing is geometrically and dynamically representative of modern high-performance stages with the exception of Mach number levels. Design exit tip speed for the initial stage is 500 ft/sec with a pressure ratio of 1.17. The rotor exit backsweep is 55 deg from radial

Engine restart and thermodynamic analysis of Apollo spacecraft engine tests, volume 1

Thermodynamic performance test analyses for Apollo spacecraft ascent, descent, and service propulsion system engines to define hypergol engine restart limit

Resistance to Fracture of Two All-Ceramic Crown Materials Following Endodontic Access

Statement of problem There is currently no protocol for managing endodontic access openings for all-ceramic crowns. A direct restorative material is generally used to repair the access opening, rendering a repaired crown as the definitive restoration. This endodontic procedure, however, may weaken the restoration or initiate microcracks that may propagate, resulting in premature failure of the restoration. Purpose The purpose of this in vitro study was to evaluate how an endodontic access opening prepared through an all-ceramic crown altered the structural integrity of the ceramic, and the effect of a repair of this access on the load to failure of an all-ceramic crown. Material and methods Twenty-four alumina (Procera) and 24 zirconia (Procera) crowns were fabricated and cemented (Rely X Luting Plus Cement) onto duplicate epoxy resin dies. Twelve crowns of each were accessed to simulate root canal treatment therapy. Surface defects of all accessed specimens were evaluated with an environmental scanning electron microscope. The specimens were repaired with a porcelain repair system (standard adhesive resin/composite resin protocol) and were loaded to failure in a universal testing machine. Observations made visually and microscopically noted veneer delamination from the core, core fracture, shear within the veneer porcelain, or a combination thereof. A Kruskal-Wallis test was used to determine if a significant difference (α=.05) in load to failure existed between the 4 groups, and a Mann-Whitney test with a Bonferroni correction (P Results All specimens exhibited edge chipping around the access openings. Some displayed larger chips within the veneering porcelain, and 4 zirconia crowns showed radial crack formation. There was a significant difference in load to failure among all groups with the exception of the alumina intact and repaired specimens (P=.695). The alumina crowns generally showed fracture of the coping with the veneering porcelain still bonded to the core, whereas the zirconia copings tended not to fracture but experienced veneering porcelain delamination. Conclusion Endodontic access through all-ceramic crowns resulted in a significant loss of strength in the zirconia specimens but not in the alumina specimens

The Development of a Direct Homologous Radioimmunoassay for Serum Cortisol

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