Projective BGG equations, algebraic sets, and compactifications of Einstein geometries

For curved projective manifolds we introduce a notion of a normal tractor frame field, based around any point. This leads to canonical systems of (redundant) coordinates that generalise the usual homogeneous coordinates on projective space. These give preferred local maps to the model projective space that encode geometric contact with the model to a level that is optimal, in a suitable sense. In terms of the trivialisations arising from the special frames, normal solutions of classes of natural linear PDE (so-called first BGG equations) are shown to be necessarily polynomial in the generalised homogeneous coordinates; the polynomial system is the pull back of a polynomial system that solves the corresponding problem on the model. Thus questions concerning the zero locus of solutions, as well as related finer geometric and smooth data, are reduced to a study of the corresponding polynomial systems and algebraic sets. We show that a normal solution determines a canonical manifold stratification that reflects an orbit decomposition of the model. Applications include the construction of structures that are analogues of Poincare-Einstein manifolds.Comment: 22 page

Holonomy reductions of Cartan geometries and curved orbit decompositions

We develop a holonomy reduction procedure for general Cartan geometries. We show that, given a reduction of holonomy, the underlying manifold naturally decomposes into a disjoint union of initial submanifolds. Each such submanifold corresponds to an orbit of the holonomy group on the modelling homogeneous space and carries a canonical induced Cartan geometry. The result can therefore be understood as a `curved orbit decomposition'. The theory is then applied to the study of several invariant overdetermined differential equations in projective, conformal and CR-geometry. This makes use of an equivalent description of solutions to these equations as parallel sections of a tractor bundle. In projective geometry we study a third order differential equation that governs the existence of a compatible Einstein metric. In CR-geometry we discuss an invariant equation that governs the existence of a compatible K\"{a}hler-Einstein metric.Comment: v2: major revision; 30 pages v3: final version to appear in Duke Math.

A possible solution of the grain boundary problem for applications of high-Tc superconductors

It is shown that the critical current density of high-Tc wires can be greatly enhanced by using a threefold approach, which consists of grain alignment, doping, and optimization of the grain architecture. According to model calculations, current densities of 4x10^6 A/cm2 can be achieved for an average grain alignment of 10 degree at 77K. Based on this approach, a road to competitive high-Tc cables is proposed.Comment: 3 pages, 5 figure

The twistor spinors of generic 2- and 3-distributions

Generic distributions on 5- and 6-manifolds give rise to conformal structures that were discovered by P. Nurowski resp. R. Bryant. We describe both as Fefferman-type constructions and show that for orientable distributions one obtains conformal spin structures. The resulting conformal spin geometries are then characterized by their conformal holonomy and equivalently by the existence of a twistor spinor which satisfies a genericity condition. Moreover, we show that given such a twistor spinor we can decompose a conformal Killing field of the structure. We obtain explicit formulas relating conformal Killing fields, almost Einstein structures and twistor spinors.Comment: 26 page

\u3ci\u3eAgave\u3c/i\u3e Chewing and Dental Wear: Evidence from Quids

Agave quid chewing is examined as a potential contributing behavior to hunter-gatherer dental wear. It has previously been hypothesized that the contribution of Agave quid chewing to dental wear would be observed in communities wherever phytolith-rich desert succulents were part of subsistence. Previous analysis of coprolites from a prehistoric agricultural site, La Cueva de los Muertos Chiquitos in Durango, Mexico, showed that Agave was a consistent part of a diverse diet. Therefore, quids recovered at this site ought to be useful materials to test the hypothesis that dental wear was related to desert succulent consumption. The quids recovered from the site were found to be largely derived from chewing Agave. In this study, the quids were found to be especially rich in phytoliths, and analysis of dental casts made from impressions left in the quids revealed flat wear and dental attrition similar to that of Agave-reliant hunter-gatherers. Based on evidence obtained from the analysis of quids, taken in combination with results from previous studies, it is determined that Agave quid chewing was a likely contributing factor to dental wear in this population. As such, our method provides an additional avenue of dental research in areas where quids are present

Role of magnetic and orbital ordering at the metal-insulator transition in NdNiO3

Soft x-ray resonant scattering at the Ni L2,3 edges is used to test models of magnetic and orbital-ordering below the metal-insulator transition in NdNiO3. The large branching ratio of the L3 to L2 intensities of the (1/2,0,1/2) reflection and the observed azimuthal angle and polarization dependence originates from a non collinear magnetic structure. The absence of an orbital signal and the non collinear magnetic structure show that the nickelates are materials for which orbital ordering is absent at the metal-insulator transition.Comment: 10 pages, 4 figures, Physical Review B rapid communication, to be publishe

Empirical competence-testing: A psychometric examination of the German version of the Emotional Competence Inventory

The “Emotional Competence Inventory“ (ECI 2.0) by Goleman and Boyatzis assesses emotional intelligence (EI) in organizational context by means of 72 items in 4 clusters (self-awareness, self- management, social awareness, social skills) which at large consist of 18 competencies. Our study examines the psychometric properties of the first German translation of this instrument in two different surveys (N = 236). If all items are included in reliability analysis the ECI is reliable (Cronbach’s Alpha = .90), whereas the reliability of the four sub dimensions is much smaller (Alpha = .62 - .81). For 43 items the corrected item-total correlation with its own scale is higher than correlations with the other three clusters. Convergent validity was examined by using another EI instrument (Wong & Law, 2002). We found a significant correlation between the two instruments (r = .41). The German version of the ECI seems to be quite useful, although the high reliability is achieved by a large number of items. Possibilities of improvement are discussed

Using a multi-level tailored design process to develop a customer satisfaction survey for university evaluation

A multi-level procedure is described in order to develop a total quality management survey tool in the field of engineering academia. As a first step a review of available evaluation tools for universities is conducted, resulting in over 150 items used for evaluation purposes. Secondly all dimensions of educational evaluation used in previous research are summarized, resulting in 15 dimensions. In a third step, items are assigned to the dimensions, overlapping items were combined or removed, and item content and dimensions were adjusted to the specific conditions of the target faculty. Fourthly, the resulting twelve dimensions were used in first, investigative interviews in the target population. Results indicate that eleven dimensions sufficiently mapped all aspects of evaluation. After revising the items to improve understanding in a fifth step cognitive pretests were conducted. The final revision resulted in 83 items assigned to eleven dimensions