A Complete Finite Equational Axiomatisation of the Fracterm Calculus for Common Meadows

We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error flag $\bot$ whose main purpose is to always return a value for division. To rings and fields we add a division operator $x/y$ and study a class of algebras called \textit{common meadows} wherein $x/0 = \bot$. The set of equations true in all common meadows is named the \textit{fracterm calculus of common meadows}. We give a finite equational axiomatisation of the fracterm calculus of common meadows and prove that it is complete and that the fracterm calculus is decidable

Square root meadows

Let Q_0 denote the rational numbers expanded to a meadow by totalizing inversion such that 0^{-1}=0. Q_0 can be expanded by a total sign function s that extracts the sign of a rational number. In this paper we discuss an extension Q_0(s ,\sqrt) of the signed rationals in which every number has a unique square root.Comment: 9 page

Inversive Meadows and Divisive Meadows

Inversive meadows are commutative rings with a multiplicative identity element and a total multiplicative inverse operation whose value at 0 is 0. Divisive meadows are inversive meadows with the multiplicative inverse operation replaced by a division operation. We give finite equational specifications of the class of all inversive meadows and the class of all divisive meadows. It depends on the angle from which they are viewed whether inversive meadows or divisive meadows must be considered more basic. We show that inversive and divisive meadows of rational numbers can be obtained as initial algebras of finite equational specifications. In the spirit of Peacock's arithmetical algebra, we study variants of inversive and divisive meadows without an additive identity element and/or an additive inverse operation. We propose simple constructions of variants of inversive and divisive meadows with a partial multiplicative inverse or division operation from inversive and divisive meadows. Divisive meadows are more basic if these variants are considered as well. We give a simple account of how mathematicians deal with 1 / 0, in which meadows and a customary convention among mathematicians play prominent parts, and we make plausible that a convincing account, starting from the popular computer science viewpoint that 1 / 0 is undefined, by means of some logic of partial functions is not attainable.Comment: 18 pages; error corrected; 29 pages, combined with arXiv:0909.2088 [math.RA] and arXiv:0909.5271 [math.RA

Differential Meadows

A meadow is a zero totalised field (0^{-1}=0), and a cancellation meadow is a meadow without proper zero divisors. In this paper we consider differential meadows, i.e., meadows equipped with differentiation operators. We give an equational axiomatization of these operators and thus obtain a finite basis for differential cancellation meadows. Using the Zariski topology we prove the existence of a differential cancellation meadow.Comment: 8 pages, 2 table

Meadow enriched ACP process algebras

We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow enriched ACP process algebra, which is a simple generalization of the notion of an ACP process algebra to processes in which data are involved. In meadow enriched ACP process algebras, the mathematical structure for data is a meadow.Comment: 8 pages; correction in Table

Baseline marine benthic surveys in the Maltese Islands (Central Mediterranean)

Extract from: MEDCOAST 97 : Proceedings of the Third International Conference on the Mediterranean Coastal Environment, Qawra, Malta / E. Ozhan (editor), (1997)During the period 1991 to 1997, extensive baseline studies of the submarine geomorphology, infralittoral habitats, macrobenthic assemblages, and demersal fish fauna, were carried out in 14 different sites around the Maltese Islands, using conventional SCUBA diving techniques. These were made as part of assessments of the environmental impact of existing or proposed projects, or in order to produce an inventory of coastal resources. In total, these surveys covered a sea-bed area of ca. 7.55Km² and a coastline length of ca 24 km, and represent the most extensive biological surveys of the marine environment carried out to date in the Maltese Islands. The results of these surveys have been presented as maps showing the type, location, and spatial extent of these physical and biological features. The Peres & Picard (1964) scheme, as adapted by Pen~s (1967; 1982) was used to classify and characterize the benthic assemblages recorded during the surveys. Our results show that, in tenus of spatial extent, the most important macrobenthic assemblages are the communities of photophilic 'algae on hard substrata, meadows of the sea-grass Posidonia oceanica and communities of bare well-sorted sand. For all these, many subtypes and facies exist, depending on the light intensity, hydrodynamic conditions, microtopography, sediment granulometry and other edaphic factors, and anthropic influences, including pollution. Other assemblages with a limited spatial distribution include meadows of the sea-grass (vmodocea nodosa and of the Lessepsian immigrant Halophila stipu/acea on sandy bottoms, the assemblages of boulder fields which are complexes of photophilic and sciaphilic communities, and those of marine caves. Our maps are supplemented by descriptions of the different habitats and macrobenthjc assemblages, species lists, and semi-quantitative data on percentage cover for the dominant macroalgae, shoot density counts for sea-grass meadows, and population density counts for the main macrofaunal species. These maps and data-sets are intended to be used (i) for assessing the status of habitats, species assemblages, and individual species, around the Maltese Islands in order to recommend appropriate measures for their conservation, including inclusion in red data lists; (ii) for designation of marine protected areas; and (iii) as baselines against which future monitoring studies and surveys can be compared.peer-reviewe

Structural analyses of features in cultural landscapes based on historical cadastral maps and GIS

A landscape may appear to be ancient and to contain old man-made structures even if this is not the whole truth. Structures are moved, removed, replaced and added over the years. New users introduce new land use and management regimes. In Norway, information from land consolidation processes is crucially important in gaining a better understanding of the history, dynamics and development of farms, identifying older traces of human activity and selecting important areas for protection and management. When cadastral maps are transformed, common points are needed during the transformation process and for testing the accuracy of the final transformation. It is often difficult to find enough common points to satisfy statistical requirements. Paper I presents a simple method using buffers based on linear features to evaluate whether or not the accuracy of the transformation results is better than the known accuracy of the source. Papers II, III and IV show how digitised and geographically referenced historical cadastral maps can be used to reconstruct the situation at various dates back to the 19th century, and for some information back to the 16th century. The digitised cadastral map provides a snapshot of the situation at the time of the land consolidation process, and the information is considered to be very exact. Paper IV also demonstrates how a DEM (digital elevation model) can add significantly to an understanding of the information contained in the land consolidation material. The use of digitised cadastral maps reveals that many man-made structures generally perceived as old, because they are constructed using traditional techniques, in fact date from after the land consolidation process. One aim of the new European Landscape Convention is to promote landscape protection, management and planning. It therefore requires identification of landscapes and analysis of their characteristics and the forces and pressures transforming them. Using land consolidation material in a GIS makes it possible to document changes in a landscape and improve understanding of the pressures behind these changes

Division by zero in non-involutive meadows

Meadows have been proposed as alternatives for fields with a purely equational axiomatization. At the basis of meadows lies the decision to make the multiplicative inverse operation total by imposing that the multiplicative inverse of zero is zero. Thus, the multiplicative inverse operation of a meadow is an involution. In this paper, we study `non-involutive meadows', i.e.\ variants of meadows in which the multiplicative inverse of zero is not zero, and pay special attention to non-involutive meadows in which the multiplicative inverse of zero is one.Comment: 14 page

Tuplix Calculus

We introduce a calculus for tuplices, which are expressions that generalize matrices and vectors. Tuplices have an underlying data type for quantities that are taken from a zero-totalized field. We start with the core tuplix calculus CTC for entries and tests, which are combined using conjunctive composition. We define a standard model and prove that CTC is relatively complete with respect to it. The core calculus is extended with operators for choice, information hiding, scalar multiplication, clearing and encapsulation. We provide two examples of applications; one on incremental financial budgeting, and one on modular financial budget design.Comment: 22 page

Not only the butterflies: managing ants on road verges to benefit Phengaris (Maculinea) butterflies

Obligate myrmecophilic butterfly species, such as Phengaris (Maculinea) teleius and P. nausithous, have narrow habitat requirements. Living as a caterpillar in the nests of the ant species Myrmica scabrinodis and M. rubra, respectively, they can only survive on sites with both host ants and the host plant Great Burnet Sanguisorba officinalis. After having been reintroduced into a nature reserve in the Netherlands in 1990, both butterfly species expanded their distribution to linear landscape elements such as road verges and ditch edges outside this reserve. As additional habitat of both butterfly species, vegetation management of these landscape elements became important. Our results show that a management beneficial for Phengaris butterflies should aim to increase the nest density of Myrmica species, at the same time reducing the density of nests of the competitor Lasius niger or at least keeping them at a low density. Unfavourable grassland management under which L. niger thrives, includes not mowing or flail-cutting the grass, or depositing dredgings along the side of the ditch. Management favourable for the two Myrmica species differs, demanding some flexibility if both species are to benefit. M. scabrinodis is best supported with early mowing of the road verge vegetation or late mowing in the nature reserve, both of which result in an open vegetation and warm microclimate. In contrast, the nest sites of M. rubra should be left undisturbed during the summer, and mown in late autumn. Mowing of butterfly habitat should be avoided between mid-June and mid-September as this would remove the flowerheads of the Sanguisorba plants, on which the butterflies lay their eggs