Negative immersions for one-relator groups

We prove a freeness theorem for low-rank subgroups of one-relator groups. Let F be a free group, and let w ∈ F be a nonprimitive element. The primitivity rank of w, π(w), is the smallest rank of a subgroup of F containing w as an imprimitive element. Then any subgroup of the one-relator group G = F/⟨⟨w⟩⟩ generated by fewer than π(w) elements is free. In particular, if π(w) > 2, then G does not contain any Baumslag–Solitar groups. The hypothesis that π(w) > 2 implies that the presentation complex X of the one-relator group G has negative immersions: if a compact, connected complex Y immerses into X and X(Y) ≥ 0, then Y Nielsen reduces to a graph. The freeness theorem is a consequence of a dependence theorem for free groups, which implies several classical facts about free and one-relator groups, including Magnus’ Freiheitssatz and theorems of Lyndon, Baumslag, Stallings, and Duncan–Howie. The dependence theorem strengthens Wise’s w-cycles conjecture, proved independently by the authors and Helfer–Wise, which implies that the one-relator complex X has nonpositive immersions when π(w) > 1

One-relator groups with torsion are coherent

We show that any one-relator group G = F/⟪w⟫ with torsion is coherent – i.e., that every finitely generated subgroup of G is finitely presented – answering a 1974 question of Baumslag in this case

A mathematical model of coal-fired fluidised bed boilers

A mathematical model of a large coal-fired fluidized bed boiler for power generation is synthesised. The effect of variations in the main parameters of the model on variables such as the background carbon concentrations in the bed, and the transient response of heat evolution are studied. The mechanisms of solids mixing within the bed, combustion and the flow of heat to the boiler tubes are shown to result in a characteristic dynamic response, knowledge of which is essential for the proper control and regulation of a practical system

Whites' perceptions of biracial individuals' race shift when biracials speak out against bias

Previous research suggests that a person’s racial identity shapes the way others respond when that person speaks out against racial prejudice. In the present research, we consider instead how speaking out against racial prejudice shapes people’s impressions of a confronter’s racial identity, such as experiences with discrimination, stereotype enactment, and even phenotype. Two experiments found that White perceivers evaluated a Black/White biracial person who spoke out against (versus remained silent to) racial prejudice as more stigmatized and Black-identified, and as having more stereotypically Black (vs. White) preferences and Black (vs. White) ancestry when they confronted. The faces of biracial confronters (vs. non-confronters) were also recalled as more phenotypically Black (vs. White; Study 2). This evidence suggests that speaking out against bias colors Whites’ impressions of a biracial target across both subjective and objective measures of racial identity. Implications for interracial interactions and interpersonal perception are discussed

The Changing Role of the Attorney with Respect to the Corporation

Supreme Court Justice Potter Stewart once stated that the propriety of a lawyer serving as a member of the Board of Directors of his corporate client remains, even today, a vexing problem of professional responsibility.” Historically, accountants have been assumed, as well as required, to be independent of any enterprise in which they express an opinion regarding the enterprise\u27s financial statements. Independence had been interpreted to mean that accountants may not serve on the board of directors or invest in any enterprise which they, or their firm, audit, or for whom either expresses an opinion on the enterprise\u27s financial statements. By contrast, attorneys have been counsel to an enterprise, have served as officers and directors, and have invested in the enterprise. The purposes of this article are to: (1) compare and contrast the difference between the accounting and the legal profession\u27s self-regulation of board membership; (2) analyze the trend towards requiring more independence of attorneys as it relates to simultaneously providing legal advice to a client and serving on the client\u27s board of directors; and (3) predict the future trends regarding attorneys serving as directors of clients

Metal-bending brake facilitates lightweight, close-tolerance fabrication

A lightweight, metal bending brake ensures very accurate bends. Features of the brake that adapt it for making complex reverse bends to close tolerances are a pronounced relief or cutaway of the underside of the bodyplate combined with modification in the leaf design and its suspension

Selection indexes for beef cattle

International audienc

A 10B-based neutron detector with stacked Multiwire Proportional Counters and macrostructured cathodes

We present the results of the measurements of the detection efficiency for a 4.7 \r{A} neutron beam incident upon a detector incorporating a stack of up to five MultiWire Proportional Counters (MWPC) with Boron-coated cathodes. The cathodes were made of Aluminum and had a surface exhibiting millimeter-deep V-shaped grooves of 45{\deg}, upon which the thin Boron film was deposited by DC magnetron sputtering. The incident neutrons interacting with the converter layer deposited on the sidewalls of the grooves have a higher capture probability, owing to the larger effective absorption film thickness. This leads to a higher overall detection efficiency for the grooved cathode when compared to a cathode with a flat surface. Both the experimental results and the predictions of the GEANT4 model suggests that a 5-counter detector stack with coated grooved cathodes has the same efficiency as a 7-counter stack with flat cathodes. The reduction in the number of counters in the stack without altering the detection efficiency will prove highly beneficial for large-area position-sensitive detectors for neutron scattering applications, for which the cost-effective manufacturing of the detector and associated readout electronics is an important objective. The proposed detector concept could be a technological option for one of the new chopper spectrometers and other instruments planned to be built at the future European Spallation Source in Sweden. These results with macrostructured cathodes generally apply not just to MWPCs but to other gaseous detectors as well.Comment: 14 pages, 9 figure