Reverse Engineering from Assembler to Formal Specifications via Program Transformations

The FermaT transformation system, based on research carried out over the last sixteen years at Durham University, De Montfort University and Software Migrations Ltd., is an industrial-strength formal transformation engine with many applications in program comprehension and language migration. This paper is a case study which uses automated plus manually-directed transformations and abstractions to convert an IBM 370 Assembler code program into a very high-level abstract specification.Comment: 10 page

Terrapene ornata

Number of Pages: 4Integrative BiologyGeological Science

On the real zeroes of the Hurwitz zeta-function and Bernoulli polynomials

The behaviour of real zeroes of the Hurwitz zeta function $$\zeta (s,a)=\sum_{r=0}^{\infty}(a+r)^{-s}\qquad\qquad a > 0$$ is investigated. It is shown that $\zeta (s,a)$ has no real zeroes $(s=\sigma,a)$ in the region $a >\frac{-\sigma}{2\pi e}+\frac{1}{4\pi e}\log (-\sigma) +1$ for large negative $\sigma$. In the region $0 < a < \frac{-\sigma}{2\pi e}$ the zeroes are asymptotically located at the lines $\sigma + 4a + 2m =0$ with integer $m$. If $N(p)$ is the number of real zeroes of $\zeta(-p,a)$ with given $p$ then $$\lim_{p\to\infty}\frac{N(p)}{p}=\frac{1}{\pi e}.$$ As a corollary we have a simple proof of Inkeri's result that the number of real roots of the classical Bernoulli polynomials $B_n(x)$ for large $n$ is asymptotically equal to $\frac{2n}{\pi e}$.Comment: 9 pages, 2 figure

An empirical model for protostellar collapse

We propose a new analytic model for the initial conditions of protostellar collapse in relatively isolated regions of star formation. The model is non-magnetic, and is based on a Plummer-like radial density profile as its initial condition. It fits: the observed density profiles of pre-stellar cores and Class 0 protostars; recent observations in pre-stellar cores of roughly constant contraction velocities over a wide range of radii; and the lifetimes and accretion rates derived for Class 0 and Class I protostars. However, the model is very simple, having in effect only 2 free parameters, and so should provide a useful framework for interpreting observations of pre-stellar cores and protostars, and for calculations of radiation transport and time-dependent chemistry. As an example, we model the pre-stellar core L1544.Comment: To appear in Astrophysical Journal, Jan 20th, 2001. 18 pages incl. 3 fig

Multiple-input multiple-output least-squares constant modulus algorithms

Published versio

On the Running of the Cosmological Constant in Quantum General Relativity

We present arguments that show what the running of the cosmological constant means when quantum general relativity is formulated following the prescription developed by Feynman.Comment: 5 page