Infinitary rewriting: meta-theory and convergence

When infinitary rewriting was introduced by Kaplan et.al. at the beginning of the 1990s, its term universe was explained as the metric completion of a metric on finite terms. The motivation for this connection to topology was that it allowed to import other well-studied notions from metric spaces, in particular the notion of convergence as a replacement for normalisation. This paper generalises the approach by parameterising it with a term metric, and applying the process of metric completion not only to terms but also to operations on and relations between terms. The resulting meta-theory is studied, leading to a revised notion of infinitary rewrite system. For these systems a method is devised to prove their convergence

Statistical investigation of geometrical properties of discontinuities case study: Cavern of rodbar lorestan pumped storage power plant

The geometrical parameters of 639 discontinuities that surveyed in powerhouse cavern of Rodbar Lorestan pumped storage power plant project have been investigated by scanline and areal sampling methods. As regards the processing and correction of bias types, one bedding and three joint sets are existed in the site. The tectonic activities and direction of principal stresses have caused for each of trace length and spacing characteristics, the probability distribution function of joint sets differ to each other as regards their genetic types. The calculated mean trace length by scanline and areal method are very close together for one joint set and for another one the difference is 28%. The actual intensity differences between circular and rectangle sampling windows for joint sets J1 and J2 are 7% and 38%, respectively. Meanwhile, the calculation of volumetric intensity by various methods shows the estimation of this characteristic is very difficult in the field