The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Presbyterian Religion, Historiography and Ulster Scots Identity, c. 1800 to 1914

The links between Presbyterians in Scotland and the north of Ireland are obvious but have been largely ignored by historians of the nineteenth century. This article addresses this gap by showing how Ulster Presbyterians considered their relationship with their Scottish co-religionists and how they used the interplay of religious and ethnic considerations this entailed to articulate an Ulster Scots identity. For Presbyterians in Ireland, their Scottish origins and identity represented a collection of ideas that could be deployed at certain times for specific reasons – theological orthodoxy, civil and religious liberty, and certain character traits such as hard work, courage, and soberness. Ideas about the Scottish identity of Presbyterianism were reawakened for a more general audience in the first half of the nineteenth century, during the campaign for religious reform and revival within the Irish church, and were expressed through a distinctive denominational historiography inaugurated by James Seaton Reid. The formulation of a coherent narrative of Presbyterian religion and the improvement of Ulster laid the religious foundations of a distinct Ulster Scots identity and its utilization by unionist opponents of Home Rule between 1885 and 1914.

'Like waking up in a Franz Kafka novel': Service users' experiences of the child protection system when domestic violence and acrimonious separations are involved

The challenges that arise in respect of child abuse reports made in the context of domestic violence and/or acrimonious separation have been the subject of recent academic discussion. This paper adds a service user perspective to the debate and reports on the findings from a study conducted in the Republic of Ireland. In addition to the previously established evidence about such cases, it demonstrates the level of powerlessness and frustration experienced by families who found it difficult to have their needs heard or met. It also illustrates the very detrimental emotional impact on children and parents who frequently encountered indifference as well as insensitive and gendered responses from child protection staff. The findings indicate that mainstream statutory child protection services do not have the capacity to deal with these complex cases, and advocates the adoption of alternative approaches. Importantly, the study demonstrates the necessity to pay attention to the views of service users in developing an appropriate response.

Covenanter Politics: Evangelicalism, Political Liberalism and Ulster Presbyterians, 1798-1914

Historians of Ireland have devoted considerable attention to the Presbyterian origins of modern Irish republicanism in the 1790s and their overwhelming support for the Union with Great Britain in the 1880s. On the one hand, it has been argued that conservative politics came to dominate nineteenth-century Presbyterianism in the form of Henry Cooke who combined conservative evangelical religion with support for the established order. On the other hand, historians have long acknowledged the continued importance of liberal and radical impulses amongst Presbyterians. Few historians of the nineteenth century have attempted to bring these two stories together and to describe the relationship between the religion and politics of Presbyterians along the lines suggested by scholars of Presbyterian radicalism in the last quarter of the eighteenth century. This article argues that a distinctive form of Presbyterian evangelicalism developed in the nineteenth century that sought to bring the denomination back to the theological and spiritual priorities of seventeenth-century Scottish and Irish Presbyterianism. By doing so, it encouraged many Presbyterians to get involved in movements for reform and liberal politics. Supporters of ‘Covenanter Politics’ utilised their denominational principles and traditions as the basis for political involvement and as a rhetoric of opposition to Anglican privilege and Catholic tyranny. These could be the prime cause of Presbyterian opposition to the infringement of their rights, such as the marriage controversy and the Disruption of the Church of Scotland in the early 1840s, and they could also be employed as a language of opposition in response to broader social and political developments, such as the demands for land reform stimulated by the agricultural depression that accompanied the Famine. Despite their opposition to ascendancy, however, the Covenanter Politics of Presbyterian Liberals predisposed them towards pan-protestant unionism against the threat of ‘Rome Rule’.