Hall conditions for edge-weighted bipartite graphs

A weighted variant of Hall's condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite graphs whose edges may be replicated so as to yield semiregular multigraphs or, equivalently, semiregular edge-weightings. Such bipartite graphs will be called semiregularizable. Some infinite families of semiregularizable trees are described and all semiregularizable trees on at most 11 vertices are listed. Matrix analogues of some of the results are mentioned and are shown to imply some of the known characterizations of regularizable graphs.

Exeter-Hall Science and Evangelical Rhetoric in Mid-Victorian Britain

In the early and mid-Victorian period public pronouncements by evangelicals were often described as the antithesis of rational speech. The voice of science, on the other hand, was routinely equated with the voice of reason. This disparity was particularly clear in satirical and critical commentary about the platform rhetoric associated with London’s Exeter Hall, a key meeting place for evangelicals and a metonym for evangelical expressions of Christian belief. It was against this backdrop that the fledgling Young Men’s Christian Association inaugurated a popular series of lectures in 1845. Held in Exeter Hall from 1848, the series ran until 1865 and proved to be immensely popular. By investigating the ways in which the promotion of science was combined with religious exhortation in the YMCA lectures, this paper examines how evangelicals positioned themselves with respect to the growing cultural authority of science. The paper also argues that these efforts were indelibly marked by the Hall and the communicative medium in which they were made. As such, the paper sheds light on the significance of platform culture within and beyond evangelicalism and on the importance of venue and audience in understanding science and religion relations in an age of lecturing.

Low-frequency electromagnetic waves in a Hall-magnetohydrodynamic plasma with charged dust macroparticles

A linear theory for intermediate-frequency [much smaller (larger) than the electron gyrofrequency (dust plasma and dust gyrofrequencies)], long wavelength (in comparison with the ion gyroradius and the electron skin depth) electromagnetic waves in a multicomponent, homogeneous electron-ion-dust magnetoplasma is presented. For this purpose, the generalized Hall-magnetohydrodynamic (GH-MHD) equations are derived for the case with immobile charged dust macroparticles. The GH-MHD equations in a quasineutral plasma consist of the ion continuity equation, the generalized ion momentum equation, and Faraday's law with the Hall term. The GH-MHD equations are Fourier transformed and combined to obtain a general dispersion relation. The latter is analyzed to understand the influence of immobile charged dust grains on various electromagnetic wave modes in a magnetized dusty plasma. (C) 2005 American Institute of Physics.

New generalized dispersion relation for low-frequency electromagnetic waves in Hall-magnetohydrodynamic dusty plasma

A generalized linear theory for electromagnetic waves in a homogeneous dusty magnetoplasma is presented. The waves described are characterized by a frequency which is much smaller (larger) than the electron gyrofrequency (dust plasma and dust gyrofrequencies), and a long wavelength (in comparison with the ion gyroradius and the electron skin depth). The generalized Hall- magnetohydrodynamic (GH-MHD) equations are derived by assuming massive charged dust macroparticles to be immobile, and Fourier transformed to obtain a general dispersion relation. The latter is analyzed to understand the influence of immobile charged dust grains on various electromagnetic wave modes in a magnetized dusty plasma.