Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations

Localization of linear integral equation eigenvalues with applications to linear ordinary differential equation

On the linear independence of spikes and sines

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This problem is equivalent to studying the spectral norm of a random submatrix drawn from the discrete Fourier transform matrix. The proof involves depends on an extrapolation argument of Bourgain and Tzafriri.Comment: 16 pages, 4 figures. Revision with new proof of major theorem

Spurious Parasites in a Dog

A spurious parasite, according to Maruice C. Hall (1), is anything which is not a true parasite, at least in the host in which it is found. For example intestinal parasite ova of chickens can often be demonstrated in the feces of farm dogs who have been eating entrails of infested birds

A bound for the spectral radius of a matrix

Bound for spectral radius of matrix derived by constructing integral equation with degenerate kerne

A prospective study of mental health status in morbidly obese patients.

Aim: To determine if co-morbidities have an effect on mood in a cohort of morbidly obese patients

Boundary Crossing: Networked Policing and Emergent “Communities of Practice” in Safeguarding Children

Child safeguarding has come to the forefront of public debate in the UK in the aftermath of a series of highly publicised incidents of child sexual exploitation and abuse. These have exposed the inadequacies and failings of inter-organisational relations between police and key partners. While the discourse of policing partnerships is now accepted wisdom, progress has been distinctly hesitant. This paper contributes to understanding both the challenges and opportunities presented through working across organisational boundaries in the context of safeguarding children. It draws on a study of relations within one of the largest Safeguarding Children partnerships in England, developing insights from Etienne Wenger regarding the potential of ‘communities of practice’ that innovate on the basis of everyday learning through ‘boundary work’. We demonstrate how such networked approaches expose the differential power relations and sites of conflict between organisations but also provide possibilities to challenge introspective cultures and foster organisational learning. We argue that crucial in cultivating effective ‘communities of practice’ are: shared commitment and purpose; relations of trust; balanced exchange of information and resources; mutual respect for difference; and an open and mature dialogue over possible conflicts. Boundary crossing can open opportunities to foster increased reflexivity among policing professionals, prompting critical self-reflection on values, ongoing reassessment of assumptions and questioning of terminology. Yet, there is an inherent tension in that the learning and innovative potential afforded by emergent ‘communities of practice’ derives from the coexistence and interplay between both the depth of knowledge within practices and active boundaries across practices