Integers represented as a sum of primes and powers of two

It is shown that every sufficiently large even integer is a sum of two primes and exactly 13 powers of 2. Under the Generalized Rieman Hypothesis one can replace 13 by 7. Unlike previous work on this problem, the proof avoids numerical calculations with explicit zero-free regions of Dirichlet L-functions. The argument uses a new technique to bound the measure of the set on which the exponential sum formed from powers of 2 is large.Comment: 32 Pages; typos correcte

Recommendations for NASA research and development in artificial intelligence

Basic artificial intelligence (AI) research, AI applications, engineering, institutional management, and previously impractical missions enabled by AI are discussed

Evaluation of a low-density polyimide foam in a dynamic, high temperature environment

A low density polyimide foam material was tested in an arc tunnel to determine its potential for heat shield application on aerospace vehicles. The results show that the material has some reuse potential at surface temperatures as high as 750 K. When a black refractory paint was applied to the surface of the material, the surface recession was negligible at 750 K. An analytical thermal conductivity was derived for this material which, combined with measured thermal property values, can be used to make preliminary design thickness calculations for heat shield applications

Surface recession characteristics of a cryogenic insulation subjected to arc-tunnel heating

Specimens of a cryogenic insulation, proposed for use on the space shuttle external tank, were tested in an arc tunnel over a range of heating rates, pressures, and enthalpies corresponding to the shuttle ascent environment. A regression analysis was used to correlate the test data. Correlation equations involving surface recession rate as a function of heating rate, pressure, and enthalpy were developed. These equations can be used to make total surface recession predictions for shuttle ascent flight environments

Permutation groups, simple groups and sieve methods

We show that the number of integers n ≤ x which occur as indices of subgroups of nonabelian finite simple groups, excluding that of An-1 in An, is ∼ hx/log x, for some given constant h. This might be regarded as a noncommutative analogue of the Prime Number Theorem (which counts indices n ≤ x of subgroups of abelian simple groups). We conclude that for most positive integers n, the only quasiprimitive permutation groups of degree n are Sn and An in their natural action. This extends a similar result for primitive permutation groups obtained by Cameron, Neumann and Teague in 1982. Our proof combines group-theoretic and number-theoretic methods. In particular, we use the classification of finite simple groups, and we also apply sieve methods to estimate the size of some interesting sets of primes

Comparative health and safety assessment of the SPS and alternative electrical generation systems

A comparative analysis of health and safety risks is presented for the Satellite Power System and five alternative baseload electrical generation systems: a low-Btu coal gasification system with an open-cycle gas turbine combined with a steam topping cycle; a light water fission reactor system without fuel reprocessing; a liquid metal fast breeder fission reactor system; a central station terrestrial photovoltaic system; and a first generation fusion system with magnetic confinement. For comparison, risk from a decentralized roof-top photovoltaic system with battery storage is also evaluated. Quantified estimates of public and occupational risks within ranges of uncertainty were developed for each phase of the energy system. The potential significance of related major health and safety issues that remain unquantitied are also discussed

Confidence regions for the multinomial parameter with small sample size

Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many applications, the construction of a confidence region for p when n is small is crucial. This concrete challenging problem has a long history. It is well known that the confidence regions built from asymptotic statistics do not have good coverage when n is small. On the other hand, most available methods providing non-asymptotic regions with controlled coverage are limited to the binomial case d=2. In the present work, we propose a new method valid for any d>1. This method provides confidence regions with controlled coverage and small volume, and consists of the inversion of the "covering collection"' associated with level-sets of the likelihood. The behavior when d/n tends to infinity remains an interesting open problem beyond the scope of this work.Comment: Accepted for publication in Journal of the American Statistical Association (JASA

Boundary States and Black Hole Entropy

Black hole entropy is derived from a sum over boundary states. The boundary states are labeled by energy and momentum surface densities, and parametrized by the boundary metric. The sum over state labels is expressed as a functional integral with measure determined by the density of states. The sum over metrics is expressed as a functional integral with measure determined by the universal expression for the inverse temperature gradient at the horizon. The analysis applies to any stationary, nonextreme black hole in any theory of gravitational and matter fields.Comment: 4 pages, Revte