55,094 research outputs found

    Reverse Engineering from Assembler to Formal Specifications via Program Transformations

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    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

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    Number of Pages: 4Integrative BiologyGeological Science

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

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    The behaviour of real zeroes of the Hurwitz zeta function ζ(s,a)=r=0(a+r)sa>0\zeta (s,a)=\sum_{r=0}^{\infty}(a+r)^{-s}\qquad\qquad a > 0 is investigated. It is shown that ζ(s,a)\zeta (s,a) has no real zeroes (s=σ,a)(s=\sigma,a) in the region a>σ2πe+14πelog(σ)+1a >\frac{-\sigma}{2\pi e}+\frac{1}{4\pi e}\log (-\sigma) +1 for large negative σ\sigma. In the region 0<a<σ2πe0 < a < \frac{-\sigma}{2\pi e} the zeroes are asymptotically located at the lines σ+4a+2m=0\sigma + 4a + 2m =0 with integer mm. If N(p)N(p) is the number of real zeroes of ζ(p,a)\zeta(-p,a) with given pp then limpN(p)p=1πe.\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 Bn(x)B_n(x) for large nn is asymptotically equal to 2nπe\frac{2n}{\pi e}.Comment: 9 pages, 2 figure

    In search for a perfect shape of polyhedra: Buffon transformation

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    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 BB-regular polyhedra. The main result is the proof of existence of star-shaped affine BB-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

    Trends in fatal car-occupant accidents

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    An empirical model for protostellar collapse

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    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

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    Unravelling complex systems

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