Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System

We consider holomorphic deformations of Fuchsian systems parameterized by the pole loci. It is well known that, in the case when the residue matrices are non-resonant, such a deformation is isomonodromic if and only if the residue matrices satisfy the Schlesinger system with respect to the parameter. Without the non-resonance condition this result fails: there exist non-Schlesinger isomonodromic deformations. In the present article we introduce the class of the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal deformation is also an isomonodromic one. In general, the class of the isomonodromic deformations is much richer than the class of the isoprincipal deformations, but in the non-resonant case these classes coincide. We prove that a deformation is isoprincipal if and only if the residue matrices satisfy the Schlesinger system. This theorem holds in the general case, without any assumptions on the spectra of the residue matrices of the deformation. An explicit example illustrating isomonodromic deformations, which are neither isoprincipal nor meromorphic with respect to the parameter, is also given

Electric Field Effect Analysis of Thin PbTe films on high-epsilon SrTiO3 Substrate

Thin PbTe films (thickness 500 - 600 angstrom), deposited on SrTiO3, have been investigated by electric field effect (EFE). The high resistivity of such thin films warrants a high sensitivity of the EFE method. The SrTiO3 substrate serves as the dielectric layer in the Gate-Dielectric-PbTe structure. Due to the large dielectric constant of SrTiO3, particularly at low temperatures, the electric displacement D in the film reaches the high value of about 10^8 V/cm, and the EFE introduced charge into the PbTe film amounts to ~ 8 microC/cm2. The high D permits to measure the EFE resistance and Hall constant over a wide region of D, revealing the characteristic features of their D-dependence. An appropriate theoretical model has been formulated, showing that, for such films, one can measure the dependence of the Fermi level on D. In fact, we demonstrate that shifting the Fermi level across the gap by varying D, the density-of-states of the in-gape states can be mapped out. Our results show, that the PbTe layers studied, possess a mobility gap exceeding the gap of bulk PbTe.Comment: 27 pages, 12 figure

Copyright and cultural work: an exploration

This article first discusses the contemporary debate on cultural “creativity” and the economy. Second, it considers the current state of UK copyright law and how it relates to cultural work. Third, based on empirical research on British dancers and musicians, an analysis of precarious cultural work is presented. A major focus is how those who follow their art by way of “portfolio” work handle their rights in ways that diverge significantly from the current simplistic assumptions of law and cultural policy. Our conclusions underline the distance between present top-down conceptions of what drives production in the cultural field and the actual practice of dancers and musicians

Non-Schlesinger Deformations of Ordinary Differential Equations with Rational Coefficients

We consider deformations of $2\times2$ and $3\times3$ matrix linear ODEs with rational coefficients with respect to singular points of Fuchsian type which don't satisfy the well-known system of Schlesinger equations (or its natural generalization). Some general statements concerning reducibility of such deformations for $2\times2$ ODEs are proved. An explicit example of the general non-Schlesinger deformation of $2\times2$-matrix ODE of the Fuchsian type with 4 singular points is constructed and application of such deformations to the construction of special solutions of the corresponding Schlesinger systems is discussed. Some examples of isomonodromy and non-isomonodromy deformations of $3\times3$ matrix ODEs are considered. The latter arise as the compatibility conditions with linear ODEs with non-singlevalued coefficients.Comment: 15 pages, to appear in J. Phys.

Substantiating a political public sphere in the Scottish press : a comparative analysis

This article uses content analysis to characterize the performance of the media in a national public sphere, by setting apart those qualities that typify internal press coverage of a political event. The article looks at the coverage of the 1999 devolved Scottish election from the day before the election until the day after. It uses a word count to measure the election material in Scottish newspapers the Herald, the Press and Journal and the Scotsman, and United Kingdom newspapers the Guardian, the Independent and The Times, and categorizes that material according to discourse type, day and page selection. The article finds a number of qualities that typify the Scottish sample in particular, and might be broadly indicative of a political public sphere in action. Firstly, and not unexpectedly, it finds that the Scottish newspapers carry significantly more election coverage. Just as tellingly, though, the article finds that the Scottish papers offer a greater proportion of advice and background information, in the form of opinion columns and feature articles. It also finds that the Scottish papers place a greater concentration of both informative and evaluative material in the period before the vote, consistent with their making a contribution to informed political action. Lastly, the article finds that the Scottish sample situates coverage nearer the front of the paper and places a greater proportion on recto pages. The article therefore argues that the Scottish papers display features that distinguish them from the UK papers, and are broadly consistent with their forming part of a deliberative public sphere, and suggests that these qualities might be explored as a means of judging future media performance