Brauer-Thrall for totally reflexive modules over local rings of higher dimension

Let $R$ be a commutative Noetherian local ring. Assume that $R$ has a pair $\{x,y\}$ of exact zerodivisors such that $\dim R/(x,y)\ge2$ and all totally reflexive $R/(x)$-modules are free. We show that the first and second Brauer--Thrall type theorems hold for the category of totally reflexive $R$-modules. More precisely, we prove that, for infinitely many integers $n$, there exists an indecomposable totally reflexive $R$-module of multiplicity $n$. Moreover, if the residue field of $R$ is infinite, we prove that there exist infinitely many isomorphism classes of indecomposable totally reflexive $R$-modules of multiplicity $n$.Comment: to appear in Algebras and Representation Theor

Ultrasonic Flaw Classification — An Expert System Approach

An expert system, FLEX, for classifying isolated flaws as either crack-like or volumetric has been under development at the Center for NDE, Iowa State University. Previously, we have described the overall design of the system [1], which is composed of two cooperating systems FEAP and FLAP. The feature processing (FEAP) system is designed to extract fundamental features in the ultrasonic signals that are indicative of cracks or volumetric flaws. The flaw processing (FLAP) system then uses the existence (or non-existence) of these features to classify the flaw. FLAP is structured as a classical rule-based expert system and has also been described previously [2]. Here, we will present the major elements of FEAP and the design philosophy that has gone into its construction. A more detailed account of FEAP is given in the thesis of Christensen [3].</p

Melting of a 2D Quantum Electron Solid in High Magnetic Field

The melting temperature ($T_m$) of a solid is generally determined by the pressure applied to it, or indirectly by its density ($n$) through the equation of state. This remains true even for helium solids\cite{wilk:67}, where quantum effects often lead to unusual properties\cite{ekim:04}. In this letter we present experimental evidence to show that for a two dimensional (2D) solid formed by electrons in a semiconductor sample under a strong perpendicular magnetic field\cite{shay:97} ($B$), the $T_m$ is not controlled by $n$, but effectively by the \textit{quantum correlation} between the electrons through the Landau level filling factor $\nu$=$nh/eB$. Such melting behavior, different from that of all other known solids (including a classical 2D electron solid at zero magnetic field\cite{grim:79}), attests to the quantum nature of the magnetic field induced electron solid. Moreover, we found the $T_m$ to increase with the strength of the sample-dependent disorder that pins the electron solid.Comment: Some typos corrected and 2 references added. Final version with minor editoriol revisions published in Nature Physic

A rapidly spinning supermassive black hole at the centre of NGC 1365

Broad X-ray emission lines from neutral and partially ionized iron observed in active galaxies have been interpreted as fluorescence produced by the reflection of hard X-rays off the inner edge of an accretion disk. In this model, line broadening and distortion result from rapid rotation and relativistic effects near the black hole, the line shape being sensitive to its spin. Alternative models in which the distortions result from absorption by intervening structures provide an equally good description of the data, and there has been no general agreement on which is correct. Recent claims that the black hole (2 × 10^6 solar masses) at the centre of the galaxy NGC 1365 is rotating at close to its maximum possible speed rest on the assumption of relativistic reflection. Here we report X-ray observations of NGC 1365 that reveal the relativistic disk features through broadened Fe-line emission and an associated Compton scattering excess of 10–30 kiloelectronvolts. Using temporal and spectral analyses, we disentangle continuum changes due to time-variable absorption from reflection, which we find arises from a region within 2.5 gravitational radii of the rapidly spinning black hole. Absorption-dominated models that do not include relativistic disk reflection can be ruled out both statistically and on physical grounds

NuSTAR and XMM-Newton observations of NGC 1365: Extreme absorption variability and a constant inner accretion disk

We present a spectral analysis of four coordinated NuSTAR+XMM-Newton observations of the Seyfert galaxy NGC 1365. These exhibit an extreme level of spectral variability, which is primarily due to variable line-of-sight absorption, revealing relatively unobscured states in this source for the first time. Despite the diverse range of absorption states, each of the observations displays the same characteristic signatures of relativistic reflection from the inner accretion disk. Through time-resolved spectroscopy we find that the strength of the relativistic iron line and the Compton reflection hump relative to the intrinsic continuum are well correlated, as expected if they are two aspects of the same broadband reflection spectrum. We apply self-consistent disk reflection models to these time-resolved spectra in order to constrain the inner disk parameters, allowing for variable, partially covering absorption to account for the vastly different absorption states observed. Each of the four observations is treated independently to test the consistency of the results obtained for the black hole spin and the disk inclination, which should not vary on observable timescales. We find both the spin and the inclination determined from the reflection spectrum to be consistent, confirming NGC 1365 hosts a rapidly rotating black hole; in all cases the dimensionless spin parameter is constrained to be a* > 0.97 (at 90% statistical confidence or better)

Emergent global patterns of ecosystem structure and function from a mechanistic general ecosystem model

Anthropogenic activities are causing widespread degradation of ecosystems worldwide, threatening the ecosystem services upon which all human life depends. Improved understanding of this degradation is urgently needed to improve avoidance and mitigation measures. One tool to assist these efforts is predictive models of ecosystem structure and function that are mechanistic: based on fundamental ecological principles. Here we present the first mechanistic General Ecosystem Model (GEM) of ecosystem structure and function that is both global and applies in all terrestrial and marine environments. Functional forms and parameter values were derived from the theoretical and empirical literature where possible. Simulations of the fate of all organisms with body masses between 10 µg and 150,000 kg (a range of 14 orders of magnitude) across the globe led to emergent properties at individual (e.g., growth rate), community (e.g., biomass turnover rates), ecosystem (e.g., trophic pyramids), and macroecological scales (e.g., global patterns of trophic structure) that are in general agreement with current data and theory. These properties emerged from our encoding of the biology of, and interactions among, individual organisms without any direct constraints on the properties themselves. Our results indicate that ecologists have gathered sufficient information to begin to build realistic, global, and mechanistic models of ecosystems, capable of predicting a diverse range of ecosystem properties and their response to human pressures

A Large Specific Deterrent Effect of Arrest for Patronizing a Prostitute

BACKGROUND: Prior research suggests that arrest, compared with no police detection, of some types of offenders does not decrease the chances they will reoffend. METHODOLOGY/PRINCIPAL FINDINGS: We assessed the specific deterrent effect of arrest for patronizing a street prostitute in Colorado Springs by comparing the incidence of arrest for clients of prostitutes first detected through public health surveillance with the incidence of rearrest for clients first detected by police arrest. Although these sets of clients were demographically and behaviorally similar, arrest reduced the likelihood of a subsequent arrest by approximately 70%. In other areas of the United States, arrest did not appear to displace a client's patronizing. CONCLUSIONS/SIGNIFICANCE: Our results suggest that apprehending clients decreases their patronizing behavior substantially