Partial orders on partial isometries

This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spaces of analytic functions. For large classes of partial isometries these spaces can be realized as the well-known model subspaces and deBranges-Rovnyak spaces. This characterization is applied to investigate properties of these pre-orders and the equivalence classes they generate.Comment: 30 pages. To appear in Journal of Operator Theor

Anisotropic focusing characteristics of micro-domain structures within crystalline Sr_0.61Ba_0.39Nb₂O₆ : the crystal ball

We report the anisotropic focusing characteristics of a spherically configured region of micro-domains that have been induced within a cubic shaped crystal of Ce:doped Sr0.61Ba0.39Nb2O6. The internal spherical structure focuses extraordinary polarised light, but not ordinary polarised. The spherical region, which is easily observed via scattering, is formed as the crystal cools down, after a repoling cycle through the Curie temperature, with an applied field. Analytic modelling of the thermal gradients that exist within the crystal during cooling reveals a small (< 1°) temperature difference between the central and outside regions. The similarity in shape between these temperature profiles and the observed scattering region suggests a possible mechanism for the growth of this spherical micro-domained structure

The Relevance of the Value Relevance Literature for Financial Accounting Standard Setting

In this paper we critically evaluate the standard-setting inferences that can be drawn from value relevance research studies that are motivated by standard setting. Our evaluation concentrates on the theories of accounting, standard setting and valuation that underlie those inferences. Unless those underlying theories are descriptive of accounting, standard setting and valuation, the value-relevance literature\u27s reported associations between accounting numbers and common equity valuations have limited implications or inferences for standard setting; they are mere associations. We argue that the underlying theories are not descriptive and hence drawing standard-setting inferences is difficult

Static and dynamic XY-like short-range order in a frustrated magnet with exchange disorder

A single crystal of the Co2+ based pyrochlore NaCaCo2F7 was studied by inelastic neutron scattering. This frustrated magnet with quenched exchange disorder remains in a strongly correlated paramagnetic state down to one 60th of the Curie-Weiss temperature. Below T_f = 2.4 K, diffuse elastic scattering develops and comprises 30 +/- 10% of the total magnetic scattering, as expected for J_{eff} = 1/2 moments frozen on a time scale that exceeds \hbar/\delta E=3.8 ps. The diffuse scattering is consistent with short range XY antiferromagnetism with a correlation length of 16 \AA. The momentum (Q) dependence of the inelastic intensity indicates relaxing XY-like antiferromagnetic clusters at energies below ~ 5.5 meV, and collinear antiferromagnetic fluctuations above this energy. The relevant XY configurations form a continuous manifold of symmetry-related states. Contrary to well-known models that produce this continuous manifold, order-by-disorder does not select an ordered state in NaCaCo2F7 despite evidence for weak (~12 %) exchange disorder. Instead, NaCaCo2F7 freezes into short range ordered clusters that span this manifold.Comment: 9 pages, 9 figures. This updated version features modified figures and some new discussio

The Virtues of Nonsimulation Games

The use of games as teaching devices is receiving attention from an increasing number of educators. Data from tests conducted with one such educational game-WFF ’N PROOF strongly indicate that this and similar games are useful, not only in teaching a particular subject (in this case symbolic logic), but also in increasing the general problem-solving ability of the student. WFF ’N PROOF is actually not one game but a series of 21 games of increasing difficulty. The first games in the series are quite simple and can be enjoyed by first graders. The final games are challenging and stimulating even for a university teacher of logic

The Virtues of Nonsimulation Games

The use of games as teaching devices is receiving attention from an increasing number of educators. Data from tests conducted with one such educational game-WFF ’N PROOF strongly indicate that this and similar games are useful, not only in teaching a particular subject (in this case symbolic logic), but also in increasing the general problem-solving ability of the student. WFF ’N PROOF is actually not one game but a series of 21 games of increasing difficulty. The first games in the series are quite simple and can be enjoyed by first graders. The final games are challenging and stimulating even for a university teacher of logic

UV Imaging Polarimetry of the Seyfert 2 Galaxy Mrk 3

We present UV imaging polarimetry data of the Seyfert 2 galaxy Mrk 3 taken by the Hubble Space Telescope. The polarized flux is found to be extended to ~1 kpc from the nucleus, and the position angles of polarization are centrosymmetric, confirming that the polarization is caused by scattering. We determine the location of the hidden nucleus as the center of this centrosymmetric pattern. From the polarization images taken in two broad bands, we have obtained the color distribution of the polarized flux. Some regions have blue polarized flux, consistent with optically-thin dust scattering, but some bright knots have a color similar to that of Seyfert 1 nucleus. Also, the recent Chandra X-ray observation suggests that the ratio of scattered UV flux to scattered X-ray flux is rather similar to the intrinsic UV/X-ray ratio in a Seyfert 1 nucleus, if the observed extended X-ray continuum is scattered light. While the scattered X-ray would be essentially from electron scattering, the UV slope and UV/X-ray ratio both being similar to Seyfert 1's would lead to two possibilities as to the nature of the UV scatterers. One is that the UV may also be scattered by electrons, in which case the scattering gas is somehow dust-free. The other is that the UV is scattered by dust grains, but the wavelength-independent UV scattering with low efficiency indicated by the UV slope and UV/X-ray ratio would suggest that the grains reside in UV-opaque clouds, or the dust might be mainly composed of large grains and lacks small-grain population.Comment: 15 pages, 8 figures (plus 2 color versions of grayscale figures), To appear in ApJ; minor corrections for the proofs of the manuscrip

Real-space investigation of short-range magnetic correlations in fluoride pyrochlores NaCaCo2_2F7_7 and NaSrCo2_2F7_7 with magnetic pair distribution function analysis

We present time-of-flight neutron total scattering and polarized neutron scattering measurements of the magnetically frustrated compounds NaCaCo$_2$F$_7$ and NaSrCo$_2$F$_7$, which belong to a class of recently discovered pyrochlore compounds based on transition metals and fluorine. The magnetic pair distribution function (mPDF) technique is used to analyze and model the total scattering data in real space. We find that a previously-proposed model of short-range XY-like correlations with a length scale of 10-15 \AA, combined with nearest-neighbor collinear antiferromagnetic correlations, accurately describes the mPDF data at low temperature, confirming the magnetic ground state in these materials. This model is further verified by the polarized neutron scattering data. From an analysis of the temperature dependence of the mPDF and polarized neutron scattering data, we find that short-range correlations persist on the nearest-neighbor length scale up to 200 K, approximately two orders of magnitude higher than the spin freezing temperatures of these compounds. These results highlight the opportunity presented by these new pyrochlore compounds to study the effects of geometric frustration at relatively high temperatures, while also advancing the mPDF technique and providing a novel opportunity to investigate a genuinely short-range-ordered magnetic ground state directly in real space