The algebra of rewriting for presentations of inverse monoids

We describe a formalism, using groupoids, for the study of rewriting for presentations of inverse monoids, that is based on the Squier complex construction for monoid presentations. We introduce the class of pseudoregular groupoids, an example of which now arises as the fundamental groupoid of our version of the Squier complex. A further key ingredient is the factorisation of the presentation map from a free inverse monoid as the composition of an idempotent pure map and an idempotent separating map. The relation module of a presentation is then defined as the abelianised kernel of this idempotent separating map. We then use the properties of idempotent separating maps to derive a free presentation of the relation module. The construction of its kernel - the module of identities - uses further facts about pseudoregular groupoids.Comment: 22 page

Generic Ada code in the NASA space station command, control and communications environment

The results of efforts to apply powerful Ada constructs to the formatted message handling process are described. The goal of these efforts was to extend the state-of-technology in message handling while at the same time producing production-quality, reusable code. The first effort was initiated in September, 1984 and delivered in April, 1985. That product, the Generic Message Handling Facility, met initial goals, was reused, and is available in the Ada Repository on ARPANET. However, it became apparent during its development that the initial approach to building a message handler template was not optimal. As a result of this initial effort, several alternate approaches were identified, and research is now on-going to identify an improved product. The ultimate goal is to be able to instantly build a message handling system for any message format given a specification of that message format. The problem lies in how to specify the message format, and one that is done, how to use that information to build the message handler. Message handling systems and message types are described. The initial efforts, its results and its shortcomings are detailed. The approach now being taken to build a system which will be significantly easier to implement, and once implemented, easier to use, is described. Finally, conclusions are offered

The Teaching of Pupils Who Experience Difficulties in Learning in a Spanish Classroom in Two Government Secondary Schools in Trinidad, West Indies

This study investigates the teaching approaches used with pupils who experience difficulties in learning in a Spanish classroom in two secondary schools in Trinidad, West Indies. Much literature focuses on teaching approaches for pupils with clearly defined special educational needs or on teaching approaches in general. Pupils who experience difficulties in learning, however, represent an amorphous category and research regarding teaching approaches for this less defined group of pupils is scarcer. Spanish is a core subject in most secondary schools in Trinidad and Tobago. As a foreign language, however, Spanish is different to other subjects as it represents the acquisition of another linguistic system. The acquisition of grammatical and communicative competencies may therefore be the goal of teaching approaches but these may be problematic areas for pupils who experience difficulties in learning. The teaching approaches used with these pupils were under investigation in this study. This study adopts a qualitative approach which incorporates a dual case study design. The cases are represented by one urban and one rural secondary school. The participants are the pupils and Spanish teachers of a selected form two class within each school. Non-participant classroom observations, semi-structured interviews with teachers and pupils, task-based interviews with pupils were used to collect data. The study spanned 12 weeks in the first term of the 2017-2018 academic year. The time in the field was divided into three phases. Phase one represented a Reconnaissance Phase which facilitated acquaintance with the context of each case. During this phase, the practices of each school were observed. Phase two represented a formal data collection phase. At the end of Phase two, the data was preliminarily analysed and data collection methods were adapted for Phase three. The findings of this study suggest that teaching approaches with pupils who experience difficulties in learning vary according to a number of factors: composition of the class; teacher perceptions of pupil ability and the degree of difficulties pupils face; and teacher perceptions of the most effective methods to acquire competency in a foreign language. Key issues arose from this study: the role of English and vocabulary; learner issues such as interest, engagement and pupil learning responsibility; and impact of lack of school resources on teaching approaches and preparation for national standardized tests. The findings suggest that teaching approaches with pupils who experience difficulties in learning are hinged on teacher perceptions, learner behaviour and school and Ministry of Education constraints

Eyelid development, fusion and subsequent reopening in the mouse

The process of eyelid development was studied in the mouse. The critical events occur between about 15.5 d postcoitum (p.c.) and 12 d after birth, and were studied by conventional histology and by scanning electron microscopy. At about 15.5 d p.c. the cornea of the eye is clearly visible with the primitive eyelids being represented by protruding ridges of epithelium at its periphery. Over the next 24 h, eyelid development proceeds to the stage when the cornea is completely covered by the fused eyelids. Periderm cells stream in to fill the gap between the developing eyelids. Their proliferative activity is such that they produce a cellular excrescence on the outer surface of the line of fusion of the eyelids. This excrescence had almost disappeared by about 17.5 d p.c. Keratinisation is first evident at this stage on the surface of the eyelids and passes continuously from one eyelid to the other. Evidence of epidermal differentiation is more clearly seen in the newborn, where a distinctive stratum granulosum now occupies about one third of its entire thickness. Within the subjacent dermis, hair follicles are differentiating. By about 5 d after birth, a thick layer of keratin extends without interruption across the junctional region. While a noticeable surface indentation overlies the latter, a similar depression is only seen on the conjunctival surface by about 10 d after birth. Keratinisation is also observed to extend in from the epidermal surface to involve the entire region between the 2 eyelids at about this time.(ABSTRACT TRUNCATED AT 250 WORDS

MHD Mode Conversion around a 2D Magnetic Null Point

Mode conversion occurs when a wave passes through a region where the sound and Alfven speeds are equal. At this point there is a resonance, which allows some of the incident wave to be converted into a different mode. We study this phenomenon in the vicinity of a two-dimensional, coronal null point. As a wave approaches the null it passes from low- to high-beta plasma, allowing conversion to take place. We simulate this numerically by sending in a slow magnetoacoustic wave from the upper boundary; as this passes through the conversion layer a fast wave can clearly be seen propagating ahead. Numerical simulations combined with an analytical WKB investigation allow us to determine and track both the incident and converted waves throughout the domain.Comment: 4 pages, 2 figure