A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz invariants, called critical parameters, that measure largeness for infinite-dimensional metric spaces. Basic properties of these invariants are given, and they are estimated for a naturel set of spaces generalizing the usual Hilbert cube. In a second part, we estimate the value of these new invariants in the case of some Wasserstein spaces, as well as the dynamical complexity of push-forward maps. The lower bounds rely on several embedding results; for example we provide bi-Lipschitz embeddings of all powers of any space inside its Wasserstein space, with uniform bound and we prove that the Wasserstein space of a d-manifold has "power-exponential" critical parameter equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 modified according to the referee final remarks ; to appear in Journal of Topology and Analysi

Polarization Gradient Study of Interstellar Medium Turbulence Using The Canadian Galactic Plane Survey

We have investigated the magneto-ionic turbulence in the interstellar medium through spatial gradients of the complex radio polarization vector in the Canadian Galactic Plane Survey (CGPS). The CGPS data cover 1300 square-degrees, over the range ${53^{\circ}}\leq{\ell}\leq{192^{\circ}}$, ${-3^{\circ}}\leq{b}\leq{5^{\circ}}$ with an extension to ${b}={17.5^{\circ}}$ in the range ${101^{\circ}}\leq{\ell}\leq{116^{\circ}}$, and arcminute resolution at 1420 MHz. Previous studies found a correlation between the skewness and kurtosis of the polarization gradient and the Mach number of the turbulence, or assumed this correlation to deduce the Mach number of an observed turbulent region. We present polarization gradient images of the entire CGPS dataset, and analyze the dependence of these images on angular resolution. The polarization gradients are filamentary, and the length of these filaments is largest towards the Galactic anti-center, and smallest towards the inner Galaxy. This may imply that small-scale turbulence is stronger in the inner Galaxy, or that we observe more distant features at low Galactic longitudes. For every resolution studied, the skewness of the polarization gradient is influenced by the edges of bright polarization gradient regions, which are not related to the turbulence revealed by the polarization gradients. We also find that the skewness of the polarization gradient is sensitive to the size of the box used to calculate the skewness, but insensitive to Galactic longitude, implying that the skewness only probes the number and magnitude of the inhomogeneities within the box. We conclude that the skewness and kurtosis of the polarization gradient are not ideal statistics for probing natural magneto-ionic turbulence.Comment: 21 pages, 15 figures, accepted by Ap

The DDO IVC Distance Project: Survey Description and the Distance to G139.6+47.6

We present a detailed analysis of the distance determination for one intermediate Velocity Cloud (IVC G139.6+47.6) from the ongoing DDO IVC Distance Project. Stars along the line of sight to G139.6+47.6 are examined for the presence of sodium absorption attributable to the cloud, and the distance bracket is established by astrometric and spectroscopic parallax measurements of demonstrated foreground and background stars. We detail our strategy regarding target selection, observational setup, and analysis of the data, including a discussion of wavelength calibration and sky subtraction uncertainties. We find a distance estimate of 129 (+/- 10) pc for the lower limit and 257 (+211-33) pc for the upper limit. Given the high number of stars showing absorption due to this IVC, we also discuss the small-scale covering factor of the cloud and the likely significance of non-detections for subsequent observations of this and other similar IVC's. Distance measurements of the remaining targets in the DDO IVC project will be detailed in a companion paper.Comment: 10 pages, 6 figures, LaTe

Electronic states and Landau levels in graphene stacks

We analyze, within a minimal model that allows analytical calculations, the electronic structure and Landau levels of graphene multi-layers with different stacking orders. We find, among other results, that electrostatic effects can induce a strongly divergent density of states in bi- and tri-layers, reminiscent of one-dimensional systems. The density of states at the surface of semi-infinite stacks, on the other hand, may vanish at low energies, or show a band of surface states, depending on the stacking order

Ursinus College Alumni Journal, Fall 1949

Are you a 75-percenter? • President\u27s page • Dinner dance highlights Alumni Day activities • Harry Frosberg appointed general alumni secretary • Ursinus Women\u27s Club gives $1,000 to college • Sellers, Rieser to head Berks County local alumni • R. Claire Frank to preside over York County alumni • 211 receive degrees at 79th commencement • Dr. Paisley assumes post for 40th year • Improved radio station built for college • 947 enroll for 80th year! • Seven new members join faculty and staff • Four programs featured in Ursinus forum • Walter Marsteller builds observatory to house Franklin Institute telescope • Sewage disposal plant nearing completion • Admiral Will retires after 32 years in Navy • Gemmel writes report on iron industry • Rowland Mulford heads Bridgeton, N.J. schools • Dr. Miner assumes new post in west • Pennsylvania German Society meets here; Dr. Fogel receives award • Dr. Livingood goes to Texas University • Millers write chapters for history book • Class of \u2762 convenes at Duryea Hall • News about town: Betsy Grove opens nursery; Ilsa Helfferich in Germany; New fire hall planned • Sports review: Bears bow to Drexel, tie Haverford; Soccer team faces nine-game schedule; Squad of forty-seven vie for hockey berths; Baseball fares best in men\u27s spring sports; Track team improves; Netmen win 1, lose 6; Dennis leads golfers; Harriers condition for championships; Girls\u27 softball team ends 8th no-loss season; Tennis team has poor year • Necrology • News about ourselveshttps://digitalcommons.ursinus.edu/alumnijournal/1036/thumbnail.jp

Surface superconductivity in multilayered rhombohedral graphene: Supercurrent

The supercurrent for the surface superconductivity of a flat-band multilayered rhombohedral graphene is calculated. Despite the absence of dispersion of the excitation spectrum, the supercurrent is finite. The critical current is proportional to the zero-temperature superconducting gap, i.e., to the superconducting critical temperature and to the size of the flat band in the momentum space

The Open Cluster NGC 7789: I. Radial Velocities for Giant Stars

A total of 597 radial-velocity observations for 112 stars in the ~1.6 Gyr old open cluster NGC 7789 have been obtained since 1979 with the radial velocity spectrometer at the Dominion Astrophysical Observatory. The mean cluster radial velocity is -54.9 +/- 0.12 km/s and the dispersion is 0.86 km/s, from 50 constant-velocity stars selected as members from this radial-velocity study and the proper motion study of McNamara and Solomon (1981). Twenty-five stars (32%) among 78 members are possible radial-velocity variable stars, but no orbits are determined because of the sparse sampling. Seventeen stars are radial-velocity non-members, while membership estimates of six stars are uncertain. There is a hint that the observed velocity dispersion falls off at large radius. This may due to the inclusion of long-period binaries preferentially in the central area of the cluster. The known radial-velocity variables also seem to be more concentrated toward the center than members with constant velocity. Although this is significant at only the 85% level, when combined with similar result of Raboud and Mermilliod (1994) for three other clusters, the data strongly support the conclusion that mass segregation is being detected.Comment: 16 pages (including 3 figures) and 3 table