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

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

Robust dx2-y2 pairing symmetry in high-temperature superconductors

Although initially quite controversial, it has been widely accepted that the Cooper pairs in optimally doped cuprate superconductors have predominantly dx2-y2 wavefunction symmetry. The controversy has now shifted to whether the high-Tc pairing symmetry changes away from optimal doping. Here we present phase-sensitive tricrystal experiments on three cuprate systems: Y0.7Ca0.3Ba2Cu3O7-x (Ca-doped Y-123), La2-xSrxCuO4 (La-214) and Bi2Sr2CaCu2O8+x (Bi-2212),with doping levels covering the underdoped, optimal and overdoped regions. Our work implies that time-reversal invariant, predominantly dx2-y2 pairing symmetry is robust over a large variation in doping, and underscores the important role of on-site Coulomb repulsion in the making of high-temperature superconductivity.Comment: 4 pages, 4 figure

Spatial homogeneity and doping dependence of quasiparticle tunneling spectra in cuprate superconductors

Scanning tunneling spectroscopy (STS) studies reveal long-range (similar to 100 nm) spatial homogeneity in optimally and underdoped superconducting YBa2Cu3O7-delta (YBCO) single crystals and thin films, and macroscopic spatial modulations in overdoped (Y0.7Ca0.3)BaCu3O7-delta (Ca-YBCO) epitaxial films. In contrast, STS on an optimally doped YBa2(Cu0.9934Zn0.0026Mg0.004)(3)O-6.9 single crystal exhibits strong spatial modulations and suppression of superconductivity over a microscopic scale near the Zn or Mg impurity sites, and the global pairing potential is also reduced relative to that of optimally doped YBCO, suggesting strong pair-breaking effects of the non-magnetic impurities. The spectral characteristics are consistent with d(x2-y2) pairing symmetry for the optimally and underdoped YBCO, and with (d(x2-y2) + s) for the overdoped Ca-YBCO. The doping-dependent pairing symmetry suggests interesting changes in the superconducting ground state, and is consistent with the presence of nodal quasiparticles for all doping levels. The maximum energy gap Delta (d) is non-monotonic with the doping level, while the (2 Delta (d)/k(B)T(c)) ratio increases with decreasing doping. The similarities and contrasts between the spectra of YBCO and of Bi2Sr2CaCu2O8+x are discussed

The Molecular Switch of Telomere Phages: High Binding Specificity of the PY54 Cro Lytic Repressor to a Single Operator Site

Temperate bacteriophages possess a molecular switch, which regulates the lytic and lysogenic growth. The genomes of the temperate telomere phages N15, PY54 and ɸKO2 harbor a primary immunity region (immB) comprising genes for the prophage repressor, the lytic repressor and a putative antiterminator. The roles of these products are thought to be similar to those of the lambda proteins CI, Cro and Q, respectively. Moreover, the gene order and the location of several operator sites in the prototype telomere phage N15 and in ɸKO2 are also reminiscent of lambda-like phages. By contrast, in silico analyses revealed the presence of only one operator (O$_{\rm{R}}$3) in PY54. The purified PY54 Cro protein was used for EMSA studies demonstrating that it exclusively binds to a 16-bp palindromic site (O$_{\rm{R}}$3) upstream of the prophage repressor gene. The O$_{\rm{R}}$3 operator sequences of PY54 and ɸKO2/N15 only differ by their peripheral base pairs, which are responsible for Cro specificity. PY54 cI and cro transcription is regulated by highly active promoters initiating the synthesis of a homogenious species of leaderless mRNA. The location of the PY54 Cro binding site and of the identified promoters suggests that the lytic repressor suppresses cI transcription but not its own synthesis. The results indicate an unexpected diversity of the growth regulation mechanisms in lambda-related phages

Two-dimensional electron liquid state at LaAlO3-SrTiO3 interfaces

Using tunneling spectroscopy we have measured the spectral density of states of the mobile, two-dimensional electron system generated at the LaAlO3-SrTiO3 interface. As shown by the density of states the interface electron system differs qualitatively, first, from the electron systems of the materials defining the interface and, second, from the two-dimensional electron gases formed at interfaces between conventional semiconductors

Diodes with Breakdown Voltages Enhanced by the Metal-Insulator Transition of LaAlO3_3-SrTiO3_3 Interfaces

Using the metal-insulator transition that takes place as a function of carrier density at the LaAlO$_3$-SrTiO$_3$ interface, oxide diodes have been fabricated with room-temperature breakdown voltages of up to 200 V. With applied voltage, the capacitance of the diodes changes by a factor of 150. The diodes are robust and operate at temperatures up to 270 C

The moral muteness of managers: an Anglo-American phenomenon? German and British managers and their moral reasoning about environmental sustainability in business

Several studies in the Anglo-American context have indicated that managers present themselves as morally neutral employees who act only in the best interest of the company by employing objective skills. The reluctance of managers to use moral arguments in business is further accentuated in the now common argument presented as a neutral fact that the company must always prioritise shareholder value. These and other commercial aims are seen as an objective reality in business, whilst questions about sustainability, environmental problems or fair trade are seen as emotional or moral ones; a phenomenon described as ‘moral muteness’. This research explores whether this ‘moral muteness’ is an Anglo-American phenomenon and/or whether managers in other countries - in this case Germany - might express themselves in a different way. The focus is on moral arguments around environmental sustainability and the implications of this study for cross-cultural management. This article is based on a qualitative, comparative cross-cultural study of British and German managers in the Food Retail and Energy Sectors. In line with the studies mentioned above, British managers placed a strong emphasis on their moral neutrality. In contrast, German managers tended to use moral arguments when discussing corporate greening, often giving such arguments more weight than financial arguments. Overall, the study suggests that the ‘moral muteness’ of managers is a British phenomenon and quite distinct from the German approach. The article ends in a short exploration of how this understanding can help managers better manage people, organisations and change across cultures