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

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

Optimum design for BB84 quantum key distribution in tree-type passive optical networks

We show that there is a tradeoff between the useful key distribution bit rate and the total length of deployed fiber in tree-type passive optical networks for BB84 quantum key distribution applications. A two stage splitting architecture where one splitting is carried in the central office and a second in the outside plant and figure of merit to account for the tradeoff are proposed. We find that there is an optimum solution for the splitting ratios of both stages in the case of Photon Number Splitting (PNS) attacks and Decoy State transmission. We then analyze the effects of the different relevant physical parameters of the PON on the optimum solution.Comment: Published in the Journal of the Optical Society of America

Excitation of g modes in Wolf-Rayet stars by a deep opacity bump

We examine the stability of l=1 and l=2 g modes in a pair of nitrogen-rich Wolf-Rayet stellar models characterized by differing hydrogen abundances. We find that modes with intermediate radial orders are destabilized by a kappa mechanism operating on an opacity bump at an envelope temperature log T ~ 6.25. This `deep opacity bump' is due primarily to L-shell bound-free transitions of iron. Periods of the unstable modes span ~ 11-21 hr in the model containing some hydrogen, and ~ 3-12 hr in the hydrogen-depleted model. Based on the latter finding, we suggest that self-excited g modes may be the source of the 9.8 hr-periodic variation of WR 123 recently reported by Lefevre et al. (2005).Comment: 5 pages, 3 figures, accepted by MNRAS letter

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

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