The support of the logarithmic equilibrium measure on sets of revolution in R3\R^3

For surfaces of revolution $B$ in $\R^3$, we investigate the limit distribution of minimum energy point masses on $B$ that interact according to the logarithmic potential $\log (1/r)$, where $r$ is the Euclidean distance between points. We show that such limit distributions are supported only on the ``out-most'' portion of the surface (e.g., for a torus, only on that portion of the surface with positive curvature). Our analysis proceeds by reducing the problem to the complex plane where a non-singular potential kernel arises whose level lines are ellipses

The (B0+?)+O6 system FN CMa: A case for tidal-pulsational interaction?

FN CMa is visually double with a separation of about 0.6arcsec. Sixty high-cadence VLT/UVES spectra permit the A and B components to be disentangled, as the relative contribution of each star to the total light entering the spectrograph fluctuates between exposures due to changes in seeing. Component A exhibits rapid line-profile variations, leading us to attribute the photometric variability seen by HIPPARCOS (with a derived P=0.08866d) to this component. From a total of 122 archival and new echelle spectra it is shown that component A is an SB1 binary with an orbital period of 117.55 days. The eccentricity of 0.6 may result in tidal modulation of the pulsation(s) of component Aa.Comment: 2 pages, 1 figure, IAUS 272 - Active OB Stars: Structure, Evolution, Mass Loss and Critical Limit

Design Trade Study for a 4-Meter Off-Axis Primary Mirror Substrate and Mount for the Habitable-Zone Exoplanet Direct Imaging Mission

An extensive trade study was conducted to evaluate primary mirror substrate design architectures for the HabEx mission baseline 4-meter off-axis telescope. The studys purpose is not to produce a final design, but rather to established a design methodology for matching the mirrors properties (mass and stiffness) with the missions optical performance specifications (static dynamic wavefront error, WFE). The study systematically compares the effect of proven design elements (closed-back vs. open-back vs. partial-back; meniscus vs. flat back vs. shaped back; etc.), which can be implemented with proven space mirror materials (ULE and Zerodur), on static and dynamic WFE. Additionally, the study compares static and dynamic WFE of each substrate point design integrated onto three and six point mounts

Price setting in the euro area: Some stylised facts from Individual Producer Price Data

This paper documents producer price setting in 6 countries of the euro area: Germany, France, Italy, Spain, Belgium and Portugal. It collects evidence from available studies on each of those countries and also provides new evidence. These studies use monthly producer price data. The following five stylised facts emerge consistently across countries. First, producer prices change infrequently: each month around 21% of prices change. Second, there is substantial cross-sector heterogeneity in the frequency of price changes: prices change very often in the energy sector, less often in food and intermediate goods and least often in non-durable non- food and durable goods. Third, countries have a similar ranking of industries in terms of frequency of price changes. Fourth, there is no evidence of downward nominal rigidity: price changes are for about 45% decreases and 55% increases. Fifth, price changes are sizeable compared to the inflation rate. The paper also examines the factors driving producer price changes. It finds that costs structure, competition, seasonality, inflation and attractive pricing all play a role in driving producer price changes. In addition producer prices tend to be more flexible than consumer prices.

The topological classification of one-dimensional symmetric quantum walks

We give a topological classification of quantum walks on an infinite 1D lattice, which obey one of the discrete symmetry groups of the tenfold way, have a gap around some eigenvalues at symmetry protected points, and satisfy a mild locality condition. No translation invariance is assumed. The classification is parameterized by three indices, taking values in a group, which is either trivial, the group of integers, or the group of integers modulo 2, depending on the type of symmetry. The classification is complete in the sense that two walks have the same indices if and only if they can be connected by a norm continuous path along which all the mentioned properties remain valid. Of the three indices, two are related to the asymptotic behaviour far to the right and far to the left, respectively. These are also stable under compact perturbations. The third index is sensitive to those compact perturbations which cannot be contracted to a trivial one. The results apply to the Hamiltonian case as well. In this case all compact perturbations can be contracted, so the third index is not defined. Our classification extends the one known in the translation invariant case, where the asymptotic right and left indices add up to zero, and the third one vanishes, leaving effectively only one independent index. When two translationally invariant bulks with distinct indices are joined, the left and right asymptotic indices of the joined walk are thereby fixed, and there must be eigenvalues at $1$ or $-1$ (bulk-boundary correspondence). Their location is governed by the third index. We also discuss how the theory applies to finite lattices, with suitable homogeneity assumptions.Comment: 36 pages, 7 figure

Influence of Core and Hexapod Geometry, and Local Reinforcement on the Performance of Ultra-Lightweight ULE Mirror

The Habitable Exoplanet Observatory (HabEx) mission has unique optical performance requirements which drive the mirror design process beyond the traditional criteria. While mass and stiffness are still important, the response to inertia loading (expressed in terms of Zernike coefficients) to omni-directional excitation dominates the effort. While a Zerodur mirror is the current baseline, as mass budgets change, a ULE design is being studied as a potential alternative. This trade study looked at over 264 design variations using the Arnold Mirror Modeler and ANSYS(c) to investigate the influence of various design elements, including: substrate thickness, core cell size, hexapod geometry and local reinforcement. Design 'goodness' was evaluated based on the mirror's inertial deformation response to omni-directional input. This response was calculated via RSSing Zernike polynomial responses to (XYZ) accelerations