An integral method for solving nonlinear eigenvalue problems

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least $k$ column vectors, where $k$ is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show that the original nonlinear eigenvalue problem reduces to a linear eigenvalue problem of dimension $k$. No initial approximations of eigenvalues and eigenvectors are needed. The method is particularly suitable for moderately large eigenvalue problems where $k$ is much smaller than the matrix dimension. We also give an extension of the method to the case where $k$ is larger than the matrix dimension. The quadrature errors caused by the trapezoid sum are discussed for the case of analytic closed contours. Using well known techniques it is shown that the error decays exponentially with an exponent given by the product of the number of quadrature points and the minimal distance of the eigenvalues to the contour

Diffusive limit for a quantum linear Boltzmann dynamics

In this article, I study the diffusive behavior for a quantum test particle interacting with a dilute background gas. The model I begin with is a reduced picture for the test particle dynamics given by a quantum linear Boltzmann equation in which the gas particle scattering is assumed to occur through a hard-sphere interaction. The state of the particle is represented by a density matrix that evolves according to a translation-covariant Lindblad equation. The main result is a proof that the particle's position distribution converges to a Gaussian under diffusive rescaling.Comment: 51 pages. I have restructured Sections 2-4 from the previous version and corrected an error in the proof of Proposition 7.

The Teachers’ voice in Saxony-Anhalt: perspectives on transition from primary to secondary school

Preparation and provision for transition between primary and secondary school get mixed reviews across all subjects. The literature suggests that modern languages is an area deserving particular attention. There are examples of good practice in transition but the general picture is, at best, patchy. Researchers (eg Blondin et al., 1998; Hill et al., 1998; Rosenbusch, 1995) confirm that this is not a country-specific issue but one which crosses borders of countries and continents. The purpose of this article is to report on how schools in Saxony-Anhalt, Germany, have dealt with the challenge of transition. The outcomes of semi-structured interviews with 25 secondary schools teachers suggest that many of the problems in Saxony-Anhalt are the same as for other countries, not least in relation to communication between secondary and primary schools and the exchange of information on individual pupils. Our German neighbours offer models of good practice in relation to Continuing Professional Development, clearly defined and understood teaching content and methods and the avoidance of any need for pupils to start their modern language learning experience afresh on arrival at secondary school

Divided communities and contested landscapes: Mobility, development and shifting identities in migrant destination sites in Papua New Guinea

Internal conflicts at the local and national levels in several South Pacific countries have revealed the fragility of national unity and the difficulties nations face in governing and managing their own economic development. In Papua New Guinea, the focus of this paper, an uncertain economic future for many rural and urban communities, and rising inequalities in income opportunities and access to resources, have coincided with greater intolerance of migrants at sites of high in-migration by customary landowners and provincial and local authorities. This paper draws on fieldwork undertaken in the major oil palm growing regions of Papua New Guinea where migrants from densely populated regions of the country have settled on state land alienated from customary landowners. We examine how struggles over land, resource control and development are polarising migrant and landowner identities resulting in increasing tensions and episodic communal violence. A settler identity is emerging based on a narrative of nation building and national development, while an ethno-regional identity amongst customary landowners is undermining the citizen rights of migrants and challenging the role and authority of the state in land matters

Science Development

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68479/2/10.1177_107554708500600404.pd

Determinants of international students' academic performance: A comparison between Chinese and other international students

With the increasing number of international students travelling to well-developed countries for higher education, there has been a growing interest in exploring the factors that influence their academic performance during their overseas studies. This study aims to give an insight into international students' learning experience by investigating the differences between Chinese and non-Chinese cultural groups and leads to the identification of the key predictors of their academic achievement via multiple regression analysis. The results suggest that the perceived importance of learning success to family, English writing ability, and social communication with their compatriots are significant predictors for all international students. As the predominant group, Chinese students display some distinctive characteristics. A less active learning strategy is observed among Chinese students relative to others, but no evidence has found that this negatively affects their academic achievement. © 2010 Nuffic

Dynamics of tree diversity in undisturbed and logged subtropical rainforest in Australia

In subtropical rainforest in eastern Australia, changes in the diversity of trees were compared under natural conditions and eight silvicultural regimes over 35 years. In the treated plots basal area remaining after logging ranged from 12 to 58 m2 per ha. In three control plots richness differed little over this period. In the eight treated plots richness per plot generally declined after intervention and then gradually increased to greater than original diversity. After logging there was a reduction in richness per plot and an increase in species richness per stem in all but the lightest selective treatments. The change in species diversity was related to the intensity of the logging, however the time taken for species richness to return to pre-logging levels was similar in all silvicultural treatments and was not effected by the intensity of treatment. These results suggest that light selective logging in these forests mainly affects dominant species. The return to high diversity after only a short time under all silvicultural regimes suggests that sustainability and the manipulation of species composition for desired management outcomes is possible

Le magmatisme de la région de Kwyjibo, Province\ud du Grenville (Canada) : intérêt pour les\ud minéralisations de type fer-oxydes associées

The granitic plutons located north of the Kwyjibo property in Quebec’s Grenville Province are of\ud Mesoproterozoic age and belong to the granitic Canatiche Complex . The rocks in these plutons are calc-alkalic, K-rich,\ud and meta- to peraluminous. They belong to the magnetite series and their trace element characteristics link them to\ud intraplate granites. They were emplaced in an anorogenic, subvolcanic environment, but they subsequently underwent\ud significant ductile deformation. The magnetite, copper, and fluorite showings on the Kwyjibo property are polyphased\ud and premetamorphic; their formation began with the emplacement of hydraulic, magnetite-bearing breccias, followed by\ud impregnations and veins of chalcopyrite, pyrite, and fluorite, and ended with a late phase of mineralization, during\ud which uraninite, rare earths, and hematite were emplaced along brittle structures. The plutons belong to two families:\ud biotite-amphibole granites and leucogranites. The biotite-amphibole granites are rich in iron and represent a potential\ud heat and metal source for the first, iron oxide phase of mineralization. The leucogranites show a primary enrichment in\ud REE (rare-earth elements), F, and U, carried mainly in Y-, U-, and REE-bearing niobotitanates. They are metamict and\ud underwent a postmagmatic alteration that remobilized the uranium and the rare earths. The leucogranites could also be\ud a source of rare earths and uranium for the latest mineralizing events