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Let f and g be two distinct Hecke–Maass cusp forms of weight zero for the full modular group $SL(2,\mathbb {Z})$ with Laplacian eigenvalues $\frac {1}{4}+t_{1}^{2}$ and $\frac {1}{4}+t_{2}^{2}$, and denote by $\lambda _{f}(n)$ and $\lambda _{g}(n)$ the n-th normalized Fourier coefficients attached to f and g, respectively. In the present article, we establish a quantitative result regarding the sign changes of the sequence $\{\lambda _{f}(n)\lambda _{g}(n)\}_{n\geqslant 1}$ in the interval $(x,2x]$, supported at a certain primitive integral binary quadratic form with fixed negative discriminant $D<0$, for sufficiently large x.
In the eighteenth century, the publishing of music was the chief method by which a composer could disseminate their work, enabled by the support of other individuals, of which printers, publishers and music-sellers were the most important. One musician who had a particularly close involvement with the trade in printed music was the Doncaster-based organist, Edward Miller (1735–1807). At least fifteen of his music and pedagogical publications were issued between 1756 and 1800 by London music publishers, including three by Longman and Broderip, one of the foremost and largest English music-sellers of the late eighteenth century, and two by the firm's successor Broderip and Wilkinson (see Table 7.1). Miller's music was distributed widely across England, as admirably demonstrated by the impressive subscription list to his monumental work, The Psalms of David, for the Use of Parish Churches (1790). This work advocated the use of simple tunes and the training of church choirs to improve congregational singing, and features a list of over 2600 subscribers, making it the most successful musical publication by subscriber numbers to be published in eighteenth-century Britain. While Miller's career and profes- sional music network has received attention elsewhere, this chapter focuses on the 108 music traders who subscribed to the book: booksellers, music-sellers, stationers, engravers and printers. In doing so, this chapter explores the community of music traders across the country and the importance of their role in the dissemination and circulation of printed music in late eighteenth-century England.
Although few documents have survived to throw any light on social conditions in the Isle of Man in the fourteenth and fifteenth centuries, there are archaeological and circumstantial clues on which to draw, and since it seems likely that conditions changed very little before the political upheavals of the mid-seventeenth century, there is sufficient evidence to sketch a picture of what daily life was like. In the eighteenth and early nineteenth centuries there is a wealth of documentary evidence to chart the changing conditions across the social strata, not least for the expanding merchant and professional classes, which mirror social changes in north-west England, although the peculiar circumstances of the prosperity brought by the running trade and the challenges of its collapse make the Island's eighteenth-century story distinctive.
Most families, from the most successful quarterland farmers down to the majority poor, had to rely on their own resources in times of individual or collective hardship. There was no secular provision for those in need. It was expected that families would support their own, and where this failed it was the church, through the parishes, which maintained an increasingly effective framework of social care. By contrast, the Stanleys and Atholls used the Island for the most part as a source of income, and only occasionally, as for example during the governorship of the enlightened William Sacheverell, were policies introduced to benefit the majority. Without the help of the church and individual philanthropy, conditions for many would have been desperate. Yet the support of the church came within a framework of moral and social control, designed both to preserve family structures and to promote adherence to a strict moral code, enforced by ecclesiastical legislation and the rule of the church courts.
Here we examine the wide-ranging and contrasting purposes to which Döblin put his knowledge of world cultures in various works: evoking an authentic historical reality in Die drei Sprünge des Wang-lun (1916; The Three Leaps of Wang Lun, 1991) and playing on European preconceptions of “savage” cultures in Wadzeks Kampf mit der Dampfturbine (1918; Wadzek's Fight against the Steam Turbine, 2020), drawing on information about ancient cultures for comic purposes in Babylonische Wandrung (A Babylonian Emigration, 1934) and in order to construct a heroic legend in Manas (1927), imagining the future interplay of cultural legacies in Berge Meere und Giganten (1924; Mountains Oceans Giants, 2021) and exploring the epoch-making clash between European and non- European cultures in his South American epic, Amazonas (1937–38; The Land without Death, 2022).
Settings and Contexts
An aspect of Döblin's fiction that tends to arouse instant suspicion in readers who are not familiar with his writings is the fact that he chose to set certain of his works in China, or India, or South America without ever having set foot in those regions of the world himself. Such scepticism cannot straightforwardly be countered by pointing out that he was equally capable of writing about conditions in Europe in the seventeenth century in Wallenstein or in the twenty-seventh century in Berge Meere und Giganten (Mountains Oceans Giants) without having been there, either; and for present-day readers, invoking Samuel Taylor Coleridge's notion of a “willing suspension of disbelief” is unlikely to dispel the expectation that authors who write about distant countries without first having visited them are bound to be projecting the preconceptions of their own culture onto the customs and beliefs of another.
The pessimism about the future of cathedral music expressed by senior musicians in the early years of the war turned out to be unjustified, at least in part. As men were gradually demobilized, organists and lay clerks returned to their posts, including John Dykes Bower to St Paul’s, Gerald Knight to Canterbury, William McKie to Westminster Abbey, and Boris Ord to King’s. Of course, not all lay clerks wanted to return to the choirstalls, and recruitment would prove an increasing problem for choirs outside the capital, since remuneration generally remained pitifully small, and both accommodation and suitable day-time work were in short supply. The cathedrals themselves faced severe financial problems, not least on the fabric front; even if they had not suffered war damage, inability to carry out much routine maintenance during that time, inevitably created a post-war backlog of work. Music could hardly be a priority in the circumstances. Chorister recruitment remained a lesser issue, although the declining viability of small dedicated choir schools increasingly confronted the authorities, a problem to which they would find varying solutions as the century advanced.
The post-war years were dedicated to the restoration of traditional routines, even if it was now generally admitted that, outside London, the final knell for weekday choral Matins was being sounded – Chester, Durham, Worcester and York were among a handful still singing Matins on some weekdays (usually no more than two) in the 1950s.
Mental health problems among children in England are rising, with significant wait times and barriers preventing many from accessing timely support. Watch Me Play! (WMP) is a caregiver–child interaction intervention designed to enhance child development and promote mental health resilience through child-led play.
Aims
To assess the feasibility of delivering WMP remotely to parents and carers of children aged 0–8 years referred to UK early years and children’s services.
Method
A non-randomised, single-group feasibility design with a mixed-methods process evaluation aimed to recruit 40 families. The study evaluated recruitment, retention, adherence, fidelity and acceptability. Outcomes were collected at baseline and 3 months; we conducted qualitative interviews to examine barriers and facilitators, and we used health economic data estimated intervention costs.
Results
WMP was well-regarded and acceptable to families and service providers. Recruitment involved seven sites and 21 families, with 67% retention at 3 months. Self-reported adherence was 80%. Facilitators included the simplicity of the approach and quick access to support. Barriers included limited staff capacity and practitioner perceptions of readiness in families with complex needs. Hybrid delivery (online and face-to-face sessions) was feasible and acceptable. The average intervention cost was £209 per family.
Conclusions
Findings indicate core feasibility parameters – including acceptability, fidelity, data-collection procedures and delivery across diverse contexts – were met. WMP is a low-cost intervention suited for early years services. Although a full-scale effectiveness trial is not yet warranted, a future randomised feasibility trial is recommended to investigate the acceptability of randomisation and recruitment across a broader range of services.