Discussion of "Objective Priors: An Introduction for Frequentists" by M. Ghosh

Discussion of "Objective Priors: An Introduction for Frequentists" by M. Ghosh [arXiv:1108.2120]Comment: Published in at http://dx.doi.org/10.1214/11-STS338A the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

The rectilinear local crossing number of KnK_n

We determine ${\bar{\rm{lcr}}}(K_n)$, the rectilinear local crossing number of the complete graph $K_n$ for every $n$. More precisely, for every $n \notin \{8, 14 \},$ $${\bar{\rm{lcr}}}(K_n)=\left\lceil \frac{1}{2} \left( n-3-\left\lceil \frac{n-3}{3} \right\rceil \right) \left\lceil \frac{n-3}{3} \right\rceil \right\rceil,$$ ${\bar{\rm{lcr}}}(K_8)=4$, and ${\bar{\rm{lcr}}}(K_{14})=15$.Comment: 6 Figures. Changes from v1: Added keywords, MSC2010 codes, a single formula to consider all cases together, and the resolution of the case n=14 that remained as a conjecture on the previous version. Changes from v2: A minor error in Lemma 2 was corrected. Some typos were fixed. Figure 1 was eliminated and Figures 2 and 5 were improved slightly. The last section was split into two section

Comment on "Harold Jeffreys's Theory of Probability Revisited"

Comment on "Harold Jeffreys's Theory of Probability Revisited" [arXiv:0804.3173]Comment: Published in at http://dx.doi.org/10.1214/09-STS284E the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Analysis of pressure blips in aft-finocyl solid rocket motor

Ballistic anomalies have frequently occurred during the firing of several solid rocket motors (SRMs) (Inertial Upper Stage, Space Shuttle Redesigned SRM (RSRM) and Titan IV SRM Upgrade (SRMU)), producing even relevant and unexpected variations of the SRM pressure trace from its nominal profile. This paper has the purpose to provide a numerical analysis of the following possible causes of ballistic anomalies in SRMs: an inert object discharge, a slag ejection, and an unexpected increase in the propellant burning rate or in the combustion surface. The SRM configuration under investigation is an aft-finocyl SRM with a first-stage/small booster design. The numerical simulations are performed with a quasi-one-dimensional (Q1D) unsteady model of the SRM internal ballistics, properly tailored to model each possible cause of the ballistic anomalies. The results have shown that a classification based on the head-end pressure (HEP) signature, relating each other the HEP shape and the ballistic anomaly cause, can be made. For each cause of ballistic anomalies, a deepened discussion of the parameters driving the HEP signatures is provided, as well as qualitative and quantitative assessments of the resultant pressure signals