The semi-Markov unreliability range evaluator program

The SURE program is a design/validation tool for ultrareliable computer system architectures. The system uses simple algebraic formulas to compute accurate upper and lower bounds for the death state probabilities of a large class of semi-Markov models. The mathematical formulas used in the program were derived from a mathematical theorem proven by Allan White under contract to NASA Langley Research Center. This mathematical theorem is discussed along with the user interface to the SURE program

Minimum permissible leakage resistance established for instrumentation systems

Mathematical formulas are used to determine if, and to what extent, an instrumentation system that has been exposed to the elements should be dried out to restore minimum permissible leakage resistance to ground. Formulas are also derived and used for an intermediate number of systems that are exposed to moisture penetration

Development of a valid mathematical formula or group of formulas to establish within an accuracy of 5 percent the inductance audio range resulting in beryllium coil assemblies Final report

Mathematical formulas to determine net inductance in audio range of both hammer coil and cryogenic sealing coi

Exact formulas for random growth with half-flat initial data

We obtain exact formulas for moments and generating functions of the height function of the asymmetric simple exclusion process at one spatial point, starting from special initial data in which every positive even site is initially occupied. These complement earlier formulas of E. Lee [J. Stat. Phys. 140 (2010) 635-647] but, unlike those formulas, ours are suitable in principle for asymptotics. We also explain how our formulas are related to divergent series formulas for half-flat KPZ of Le Doussal and Calabrese [J. Stat. Mech. 2012 (2012) P06001], which we also recover using the methods of this paper. These generating functions are given as a series without any apparent Fredholm determinant or Pfaffian structure. In the long time limit, formal asymptotics show that the fluctuations are given by the Airy$_{2\to1}$ marginals.Comment: Published at http://dx.doi.org/10.1214/15-AAP1099 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Asymptotic Number of Attractors in the Random Map Model

The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We derive here explicit formulas for the statistical distribution of the number of attractors in the system. As in related results, the number of operations involved by our formulas increases exponentially with n; therefore, they are not directly applicable to study the behavior of systems where n is large. However, our formulas lend themselves to derive useful asymptotic expressions, as we show.Comment: 16 pages, 1 figure. Minor changes. To be published in Journal of Physics A: Mathematical and Genera