8 research outputs found
Imbrex geometries
We introduce an axiom on strong parapolar spaces of diameter 2, which arises
naturally in the framework of Hjelmslev geometries. This way, we characterize
the Hjelmslev-Moufang plane and its relatives (line Grassmannians, certain
half-spin geometries and Segre geometries). At the same time we provide a more
general framework for a Lemma of Cohen, which is widely used to study parapolar
spaces. As an application, if the geometries are embedded in projective space,
we provide a common characterization of (projections of) Segre varieties, line
Grassmann varieties, half-spin varieties of low rank, and the exceptional
variety by means of a local condition on tangent spaces
On exceptional Lie geometries
Parapolar spaces are point-line geometries introduced as a geometric approach to (exceptional) algebraic groups. We characterize a wide class of Lie geometries as parapolar spaces satisfying a simple intersection property. In particular, many of the exceptional Lie incidence geometries occur. In an appendix, we extend our result to the locally disconnected case and discuss the locally disconnected case of some other well-known characterizations
Characterisations and classifications in the theory of parapolar spaces
This thesis in incidence geometry is divided into two parts, which can both be linked to the geometries of the Freudenthal-Tits magic square.
The first and main part consists of an axiomatic characterisation of certain plane geometries, defined via the Veronese mapping using degenerate quadratic alternative algebras (over any field) with a radical that is (as a ring) generated by a single element. This extends and complements earlier results of Schillewaert and Van Maldeghem, who considered such geometries over non-degenerate quadratic alternative algebras.
The second and smaller part deals with a classification of parapolar spaces exhibiting the feature that the dimensions of intersections of pairs of symplecta cannot take all possible sensible values, with the only further requirement that, if the parapolar spaces have symplecta of rank 2, then they are strong. This part is based on a joint work with Schillewaert, Van Maldeghem and Victoor
La "stereotomia scientifica" in Amédée François Frézier
Cut-stone constructions are made of pre-hewn blocks dry assembled on top of each other. Owing to the formal complexity characteristic of these works, in order to design them it is necessary to have knowledge of the theory of lines, surfaces and their properties, as well as knowledge of the representation methods capable of rendering them on a plane surface. This knowledge set makes stereotomy the science that anticipates, in terms of theory and tools, modern descriptive geometry. These are the reasons for seeking the beginnings of descriptive geometry in stereotomy, that is, the reasons for the transformation of the mason's art of cutting stone into a bona fide science. Frézier's work fits among the last theoretical essays prior to the géométrie descriptive of Gaspard Monge. It is a treaty on solid geometry, devoted to the shape of the bodies, their intersections and the graphical methods necessary to represent them on a plane. In it the author draws up a rigorous theory that puts in place over two centuries of knowledge and experimentation on the subject of cutting stones
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Time-lapse Geophysical Investigations over Known Archaeological Features Using Electrical Resistivity Imaging and Earth Resistance
Electrical methods of geophysical survey are known to produce results that are hard to predict at different times of the year, and under differing weather conditions. This is a problem which can lead to misinterpretation of archaeological features under investigation. The dynamic relationship between a ‘natural’ soil matrix and an archaeological feature is a complex one, which greatly affects the success of the feature’s detection when using active electrical methods of geophysical survey. This study has monitored the gradual variation of measured resistivity over a selection of study areas. By targeting difficult to find, and often ‘missing’ electrical anomalies of known archaeological features, this study has increased the understanding of both the detection and interpretation capabilities of such geophysical surveys.
A 16 month time-lapse study over 4 archaeological features has taken place to investigate the aforementioned detection problem across different soils and environments. In addition to the commonly used Twin-Probe earth resistance survey, electrical resistivity imaging (ERI) and quadrature electro-magnetic induction (EMI) were also utilised to explore the problem. Statistical analyses have provided a novel interpretation, which has yielded new insights into how the detection of archaeological features is influenced by the relationship between the target feature and the surrounding ‘natural’ soils.
The study has highlighted both the complexity and previous misconceptions around the predictability of the electrical methods. The analysis has confirmed that each site provides an individual and nuanced situation, the variation clearly relating to the composition of the soils (particularly pore size) and the local weather history. The wide range of reasons behind survey success at each specific study site has been revealed. The outcomes have shown that a simplistic model of seasonality is not universally applicable to the electrical detection of archaeological features. This has led to the development of a method for quantifying survey success, enabling a deeper understanding of the unique way in which each site is affected by the interaction of local environmental and geological conditions
Una aproximación multidisciplinar al estudio de las fallas activas, los terremotos y el riesgo sísmico : 2ª Reunión Ibérica sobre Fallas Activas y Paleosismología : celebrada del 22 al 24 de octubre de 2014, en Lorca
Depto. de Geodinámica, Estratigrafía y PaleontologíaFac. de Ciencias GeológicasTRUEpu