On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

'Hey little rich boy, take a good look at me': punk, class and British oi!

This article looks at the controversial music genre Oi! in relation to youth cultural identity in late 1970s and early 1980s Britain. By examining the six compilation albums released to promote Oi! as a distinct strand of punk, it seeks to challenge prevailing dismissals of the genre as inherently racist or bound to the politics of the far right. Rather, Oi! – like punk more generally – was a contested cultural form. It was, moreover, centred primarily on questions of class and locality. To this end, Oi! sought to realize the working-class rebellion of punk’s early aesthetic; to give substance to its street-level pretentions and offer a genuine ‘song from the streets’.

British working-class household composition, labour supply, and commercial leisure participation during the 1930s

The early twentieth century constituted the heyday of the ‘breadwinner–homemaker’ household, characterized by a high degree of intra-household functional specialization between paid and domestic work according to age, gender, and marital status. This article examines the links between formal workforce participation and access to resources for individualized discretionary spending in British working-class households during the late 1930s, via an analysis of household leisure expenditures. Leisure spending is particularly salient to intra-household resource allocation, as it constitutes one of the most highly prioritized areas of individualized expenditure, especially for young, single people. Using a database compiled from surviving returns to the Ministry of Labour's national 1937/8 working-class expenditure survey, we examine leisure participation rates for over 600 households, using a detailed set of commercial leisure activities together with other relevant variables. We find that the employment status of family members other than the male breadwinner was a key factor influencing their access to commercial leisure. Our analysis thus supports the view that the breadwinner–homemaker household was characterized by strong power imbalances that concentrated resources—especially for individualized expenditures—in the hands of those family members who engaged in paid labour.

An operationally simple sonogashira reaction for an undergraduate organic chemistry laboratory class

An operationally simple, reliable, and cheap Sonogashira reaction suitable for an undergraduate laboratory class that can be completed within a day-long (8 h) laboratory session has been developed. Cross-coupling is carried out between 2-methyl-3-butyn-2-ol and various aryl iodides using catalytic amounts of bis-(triphenylphosphine)palladium(II) dichloride, with copper(I) iodide as a cocatalyst, in triethylamine at room temperature, so a range of products can be prepared within a single group and results compared. The coupling itself is usually complete within 1.5 h and is easily monitored by TLC, leaving up to 6 h for purification and characterization. Purification is by “mini flash column chromatography” through a plug of silica encased in the barrel of a plastic syringe, so the procedure is amenable to large class sizes.

Home in British working-class fiction

Offering new readings of working-class writing that focus on the home as a key emotional and material site in writing by working-class authors from the Edwardian period through to the mid-1990s. With close readings of The Ragged Trousered Philanthropists, works by D. H. Lawrence, Ethel Carnie Holdsworth, Ellen Wilkinson, Lewis Grassic Gibbon, Walter Brierley, Alan Sillitoe, John Braine, Nell Dunn, Sam Selvon, Sid Chaplin, Buchi Emecheta, Pat Barker, Jeanette Winterson, James Kelman and many others. The book demonstrates the importance of ideas of home and its narrative representation to the making and expression of class feeling and identity.

Demonstrating distinction at ‘the lowest edge of the black-coated class’: the family expenditures of Edwardian railway clerks

Families at the bottom end of the Edwardian white-collar income spectrum demonstrated middle-class status through observable consumption, at the cost of squeezing other expenditures, including ‘necessities’. This had negative economic impacts, lowering living standards due to inefficiently high budget shares for positional goods. Drawing on the work of Pierre Bourdieu, we examine how railway clerks sought to demonstrate ‘distinction’ from manual workers through certain conspicuous expenditures and how this strategy was progressively undermined by falling real incomes over the Edwardian period.

Perfective marking in L2 Mandarin: agreement with inherent lexical aspect or the derived Sentential Aspectual class?

This study evaluates the differing claims of the Aspect Hypothesis (Anderson & Shirai 1996) and the Sentential Aspect Hypothesis (Sharma & Deo 2009) for perfective marking by L1 English learners of Mandarin. The AH predicts a narrow focus on inherent lexical aspect (the verb and predicate) in determining the use of the perfective marker le, whilst the SAH suggests that – subject to L1 influence – perfective marking agrees with the final derived aspectual class of the sentence. To test these claims data were collected using a controlled le-insertion task, combined with oral corpus data. The results show that learners’ perfective marking patterns with the sentential aspectual class and not inherent lexical aspect (where these differ), and that overall the sentential aspectual class better predicts learners’ assignment of perfective marking than lexical aspect.

Authenticity and performance of class in British factual TV series

The chapter characterises British ‘Reality TV’ as a hybrid of factual and fictional television genres, as signaled by the more accurate genre designation ‘structured reality’ television. From the 1990s onwards, in order to develop programmes that are attractive to audiences and inexpensive to produce, programme makers have focused on hybrids of dramatic and documentary modes. This chapter argues that many recent Reality TV programmes privilege soap opera’s emphasis on character, storyline and performance. This affects the ways that class authenticity is understood, undermining factual programmes’ usual claim to legitimacy based on reference to a pre-existing reality, and transforming hierarchies that separate highly-valued from low-valued types of programme.

Using problem-based learning in a chemistry practical class for pharmacy students and engaging them with feedback

Objective: To introduce a new approach to problem based learning (PBL) used in the context of medicinal chemistry practical class teaching pharmacy students. Design: The described chemistry practical is based on independent studies by small groups of undergraduate students (4-5), who design their own practical work taking relevant professional standards into account. Students are carefully guided by feedback and acquire a set of skills important to their future profession as healthcare professionals. This model has been tailored to the application of PBL in a chemistry practical class setting for a large student cohort (150 students). Assessment: The achievement of learning outcomes is based on the submission of relevant documentation including a certificate of analysis, in addition to peer assessment. Some of the learning outcomes are also assessed in the final written examination at the end of the academic year. Conclusion: The described design of a novel PBL chemistry laboratory course for pharmacy students has been found to be successful. Self-reflective learning and engagement with feedback were encouraged, and students enjoyed the challenging learning experience. Skills that are highly essential for the students’ future careers as healthcare professionals are promoted.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Cupreines and cupreidines: an established class of bifunctional cinchona organocatalysts

Cinchona alkaloids with a free 6'-OH functionality are being increasingly used within asymmetric organocatalysis. This fascinating class of bifunctional catalyst offers a genuine alternative to the more commonly used thiourea systems and because of the different spacing between the functional groups, can control enantioselectivity where other organocatalysts have failed. In the main, this review covers the highlights from the last five years and attempts to show the diversity of reactions that these systems can control. It is hoped that chemists developing asymmetric methodologies will see the value in adding these easily accessible, but underused organocatalysts to their screens.