Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

“And now to the rest of the trash…” Representations of begging Roma and an ideal society in two Nordic newspapers

Since begging East European Roma became a common view in the streets of larger Nordic cities, vivid discussions about their presence and activities have been carried out in the mass media. This thesis examines the public debates in Finland and Norway through a discursive analysis and comparison of press content from the two countries. The aim of the study is firstly to identify the prominent discourses which construct certain images of the beggars, as well as the elements and internal logics that these discourses are constructed around. But in addition to scrutinizing representations of the Roma, also an opposite perspective is applied. In accordance with the theoretical concept of ‘othering’, debates about ‘them’ are assumed to simultaneously reveal something significant about ‘us’. The second research question is thus what kind of images of the ideal Finnish and Norwegian societies are reflected in the data, and which societal values are salient in these images. The analysis comprises 79 texts printed in the main Finnish and Norwegian quality newspapers; Helsingin Sanomat and Aftenposten. The data consists of news articles, editorials, columns and letters to the editor from a three-month period in the summer of 2010. The analysis was carried out within the theoretical and methodological framework of critical discourse analysis as outlined by Norman Fairclough. A customized nine-step coding scheme was developed in order to reach the most central dimensions of the texts. Seven main discourses were identified; the Deprivation-solidarity, Human rights, Order, Crime, Space and majority reactions, Authority control, and Authority critique discourse. These were grouped into two competing normative stances on what an ideal society looks like; the exclusionary and the inclusionary stance. While the exclusionary stance places the begging Roma within a frame of crime, illegitimate use of public space and threat to the social order, the other advocates an attitude of solidarity and humanitarian values. The analysis points to a dominance of the former, although it is challenged by the latter. The Roma are “individualized” by quoting and/or presenting them by name in a fair part of the Finnish news articles. In Norway, the opposite is true; there the beggars are dominantly presented as anonymous and passive. Overall, the begging Roma are subjected to a double bind as they are faced with simultaneous expectations of activity and passivity. Theories relating to moral panics and ‘the good enemy’ provide for a deepened understanding of the intensity of the debates. Keywords: East European Roma, begging, media, newspapers, Helsingin Sanomat, Aftenposten, critical discourse analysis, Norman Fairclough, othering, ideal society, moral panics, good enemy, double bind, Finland, Norway