Recently, finite state automata, via the advent of hyperbolic and automatic groups, have become a powerful tool in geometric group theory. This paper develops a geometric approach to automata theory, analogous to various techniques used in combinatorial group theory, to solve various problems on the overlap between group theory and monoid theory. For instance, we give a geometric algorithm for computing the closure of a rational language in the profinite topology of a free group. We introduce some geometric notions for automata and show that certain important classes of monoids can be described in terms of the geometry of their Cayley graphs. A long standing open question, to which the answer was only known in the simplest of cases (and even then was non-trivial), is whether it is true, for a pseudovariety of groups , that a -trivial co-extension of a group in must divide a semidirect product of a -trivial monoid and a group in . We show the answer is affirmative if is closed under extension, and may be negative otherwise.
As a support for writing software, a comprehensive set of problem oriented languages appears preferable to any so-called universal language, as soon as static checking is sufficient to ensure type correctness of the mixed language program. We lay the basis for a mixed language system where this requirement is fulfilled. The general outline of the system is first sketched. Detailed consideration is then given to our basic constructs for establishing communication between languages, namely standard types and foreign types. Abstract types, such as defined in CLU, are finally shown to be a particular class of foreign types. 相似文献
In this work we introduce PRIN-3D (PRoto-code for Internal
flows modeled by Navier-Stokes equations in 3-Dimensions),
a new high level algebraic language (Matlab$^®$) based code, by discussing some fundamental aspects regarding its basic solving kernel and by describing the design of an innovative advection scheme. The main focus was on
designing a memory and computationally efficient code that, due to the typical
conciseness of the Matlab coding language, could allow for fast and effective implementation of new models or algorithms. Innovative numerical methods are discussed in the paper. The pressure equation
is derived with a quasi-segregation technique leading to an iterative scheme obtained within the framework of a global preconditioning procedure. Different levels of parallelization are obtainable by exploiting special
pressure variable ordering patterns that lead to a block-structured Poisson-like
matrix. Moreover, the new advection scheme has the potential of a controllable artificial diffusivity. Preliminary results are shown including a fully three-dimensional internal
laminar flow evolving in a relatively complex geometry and a 3D methane-air flame simulated with the aid of libraries based on the Flamelet model. 相似文献
This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016, programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first-year courses than a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination). 相似文献
From the point of view of a price-taking hydropower producer participating in the day-ahead power market, market prices are highly uncertain. The present paper provides a model for determining optimal bidding strategies taking this uncertainty into account. In particular, market price scenarios are generated and a stochastic mixed-integer linear programming model that involves both hydropower production and physical trading aspects is developed. The idea is to explore the effects of including uncertainty explicitly into optimization by comparing the stochastic approach to a deterministic approach. The model is illustrated with data from a Norwegian hydropower producer and the Nordic power market at Nord Pool. 相似文献