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

(M-theory-)Killing spinors on symmetric spaces

We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form $D= \nabla + \Omega$ in a purely algebraic and algorithmic way, where $\Omega : TM \rightarrow \Lambda^*(TM)$ is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e. $(M,g,F)$ with $(M,g)$ a symmetric space and $F$ an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.Comment: Updated abstract for clarity. Added missing geometries to section 6. Main result stand

Detection and imaging of the oxygen deficiency in single crystalline YBa2_{\text{2}}Cu3_{\text{3}}O7−δ_{\text{7}-\delta} thin films using a positron beam

Single crystalline YBa$_{\text{2}}$Cu$_{\text{3}}$O$_{\text{7}-\delta}$ (YBCO) thin films were grown by pulsed laser deposition (PLD) in order to probe the oxygen deficiency $\delta$ using a mono-energetic positron beam. The sample set covered a large range of $\delta$ (0.191<$\delta$<0.791) yielding a variation of the critical temperature $T_{\text{c}}$ between 25 and 90\,K. We found a linear correlation between the Doppler broadening of the positron electron annihilation line and $\delta$ determined by X-ray diffraction (XRD). Both, the origin of the found correlation and the influence of metallic vacancies, were examined with the aid of ab-initio calculations that allowed us (i) to exclude the presence of Y vacancies and (ii) to ensure that positrons still probe $\delta$ despite the potential presence of Ba or Cu vacancies. In addition, by scanning with the positron beam the spatial variation of $\delta$ could be analyzed. It was found to fluctuate with a standard deviation of up to $0.079(5)$ within a single YBCO film

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

Emotional Intelligence and its consequences for occupational and life satisfaction - Emotional Intelligence in the context of irrational beliefs

According to Albert Ellis' theory of Rational Emotive Behavior Therapy irrational beliefs (IB) lead to maladaptive emotions. A central component of irrationality is the denial of one's own possibilities to control important aspects of life. A specific IB is that one cannot control and thus cannot avoid certain emotion states. Emotion research considers regulative emotion control a pivotal component of the concept of emotional intelligence (EI). A negative association between IB and EI can thus be theoretically derived from both concepts. Furthermore both should be related to life satisfaction. We examined the relationship between IB and EI using standardized questionnaire instruments and the predictive value of both concepts regarding life satisfaction. We found a significant negative correlation between both conceptions (r = -.21). Life satisfaction and occupational satisfaction are better predicted by IB. R² increases from .04 to .12 when both concepts are incorporated in regression analysis

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

Conformal Structures Associated to Generic Rank 2 Distributions on 5-Manifolds – Characterization and Killing-Field Decomposition

Given a maximally non-integrable 2-distribution D on a 5-manifold M, it was discovered by P. Nurowski that one can naturally associate a conformal structure [g]D of signature (2,3) on M. We show that those conformal structures [g]D which come about by this construction are characterized by the existence of a normal conformal Killing 2-form which is locally decomposable and satisfies a genericity condition. We further show that every conformal Killing field of [g]D can be decomposed into a symmetry of D and an almost Einstein scale of [g]D