55,094 research outputs found

### 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

### In search for a perfect shape of polyhedra: Buffon transformation

For an arbitrary polygon consider a new one by joining the centres of
consecutive edges. Iteration of this procedure leads to a shape which is affine
equivalent to a regular polygon. This regularisation effect is usually ascribed
to Count Buffon (1707-1788). We discuss a natural analogue of this procedure
for 3-dimensional polyhedra, which leads to a new notion of affine $B$-regular
polyhedra. The main result is the proof of existence of star-shaped affine
$B$-regular polyhedra with prescribed combinatorial structure, under partial
symmetry and simpliciality assumptions. The proof is based on deep results from
spectral graph theory due to Colin de Verdiere and Lovasz.Comment: Slightly revised version with added example of pentakis dodecahedro

### 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
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