The Search for Maximal Values of min(A,B,C) / gcd(A,B,C) for A^x + B^y = C^z

This paper answers a question asked by Ed Pegg Jr. in 2001: "What is the maximal value of min(A,B,C)/ gcd(A,B,C) for A^x + B^y = C^z with A,B,C >= 1; x,y,z >= 3?" Equations of this form are analyzed, showing how they map to exponential Diophantine equations with coprime bases. A search algorithm is provided to find the largest min/gcd value within a given equation range. The algorithm precalculates a multi-gigabyte lookup table of power residue information that is used to eliminate over 99% of inputs with a single array lookup and without any further calculations. On inputs that pass this test, the algorithm then performs further power residue tests, avoiding modular powering by using lookups into precalculated tables, and avoiding division by using multiplicative inverses. This algorithm is used to show the largest min/gcd value for all equations with C^z <= 2^100.Comment: Body: 16 pages, Appendices: 11 pages, 5 tables, 1 figur

Deployment mechanisms on Pioneer Venus probes

Deployment mechanisms were developed to position scientific instruments during probe descent into the Venus atmosphere. Each mechanism includes a provision for pyrotechnic release of the enclosure door, negator springs for positive deployment torque, and an active damper using a shunted dc motor. The deployment time requirement is under 2 seconds, and the deployment shock must be less than 100 g's. The mechanism is completely dry lubricated and constructed mainly of titanium for high strength and high temperature stability. The mechanism was qualified for descent decelerations up to 565 g's and for instrument alignment up to 940 F. The mechanism requirements, the hardware design details, the analytical simulations, and the qualification testing are described

Surface trapping and leakage of low-frequency g-modes in rotating early-type stars -- I. Qualitative analysis

A qualitative study of the surface trapping of low-frequency non-radial g-modes in rotating early-type stars is undertaken within the Cowling, adiabatic and traditional approximations. It is demonstrated that, at frequencies below a cut-off, waves cannot be fully trapped within the star, and will leak through the surface. Expressions for the cut-off frequency are derived in both the non-rotating and rotating cases; it is found from these expressions that the cut-off frequency increases with the rotation rate for all but prograde sectoral modes. The results are of possible relevance to the 53 Per and SPB classes of variable star, which exhibit pulsation frequencies of the same order of magnitude as the cut-off frequencies found for the stellar model. It is suggested that observations either of an upper limit on variability periods (corresponding to the cut-off), or of line-profile variations due to leaking modes, may permit asteroseismological studies of the outer layers of these systems.Comment: 8 pages, 2 figures, to be published in MNRA

Hidden supersymmetry of domain walls and cosmologies

We show that all domain-wall solutions of gravity coupled to scalar fields for which the worldvolume geometry is Minkowski or anti-de Sitter admit Killing spinors, and satisfy corresponding first-order equations involving a superpotential determined by the solution. By analytic continuation, all flat or closed FLRW cosmologies are shown to satisfy similar first-order equations arising from the existence of ``pseudo-Killing'' spinors.Comment: 4 pages, v2:minor improvements, refs added, version to appear in PR

"Who receives statins? Variations in physicians’ prescribing patterns for patients with coronary heart disease, dyslipidemia, and diabetes"

Our objective is to estimate the extent to which clinical and non-clinical factors are associated with physicians’ prescribing patterns for statins. The data are from the National Ambulatory Medical Care Survey for the period 1992 through 2004. The three samples examined included more than 14,000 patients who were diagnosed with coronary heart disease, high cholesterol, or diabetes, individuals who are most likely to benefit from being prescribed a statin drug. Using a multinomial logit framework, we find disparities in prescribing patterns based on non-clinical factors. Namely, whites and patients who have private insurance are more likely to be prescribed a statin than nonwhites and those with public insurance. Also, even though a large increase occurred in the uptake of statins over the period 1992 to 2004, our results for 2004 show that only about 50 percent of patients diagnosed with coronary heart disease were prescribed a statin. Because coronary heart disease is the leading cause of death in the U.S. and currently is estimated to cost over $150 billion annually in the U.S. in direct and indirect costs, observed differences in prescribing patterns along these dimensions is troubling and should be part of discussions dealing with health care reform.Pharmaceuticals; Statins; Equity in Physician Prescribing Patterns; Insurance

Influence of correlated visual cues on auditory signal detection

Influence of correlated visual cues on auditory signal detectio