Norms of basic elementary operators on algebras of regular operators

We show that if E is an atomic Banach lattice with an ordercontinuous norm, A, B ∈ L^r(E) and M_A,_B is the operator on L^r(E) defined by M_A,_B(T) = AT B then ||M_A,_B||r = ||A||_r||B||_r but that there is no real α > 0 such that ||MA,B || ≥ α ||A||r||B ||r.

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

Basic and Employability Skills

This is the editorial opening paper to a special issue of the International Journal of Training and Development focusing on basic skills and employability

Physical and numerical constraints in source modeling for finite difference simulation of room acoustics

In finite difference time domain simulation of room acoustics, source functions are subject to various constraints. These depend on the way sources are injected into the grid and on the chosen parameters of the numerical scheme being used. This paper addresses the issue of selecting and designing sources for finite difference simulation, by first reviewing associated aims and constraints, and evaluating existing source models against these criteria. The process of exciting a model is generalized by introducing a system of three cascaded filters, respectively, characterizing the driving pulse, the source mechanics, and the injection of the resulting source function into the grid. It is shown that hard, soft, and transparent sources can be seen as special cases within this unified approach. Starting from the mechanics of a small pulsating sphere, a parametric source model is formulated by specifying suitable filters. This physically constrained source model is numerically consistent, does not scatter incoming waves, and is free from zero- and low-frequency artifacts. Simulation results are employed for comparison with existing source formulations in terms of meeting the spectral and temporal requirements on the outward propagating wave.

Changing policy and legislation in special and inclusive education: a perspective from Northern Ireland

It is now 15 years since the signing of the 1998 Belfast (or ‘Good Friday’) Peace Agreement which committed all participants to exclusively democratic and peaceful means of resolving differences, and towards a shared and inclusive society defined by the principles of respect for diversity, equality and the interdependence of people. In particular, it committed participants to the protection and vindication of the human rights of all. This is, therefore, a precipitous time to undertake a probing analysis of educational reforms in Northern Ireland associated with provision in the areas of inclusion and special needs education. Consequently, by drawing upon analytical tools and perspectives derived from critical policy analysis, this article, by Ron Smith from the School of Education, Queen’s University Belfast, discusses the policy cycle associated with the proposed legislation entitled Every School a Good School: the way forward for special educational needs and inclusion. It examines how this policy text structures key concepts such as ‘inclusion’, ‘additional educational needs’ and ‘barriers to learning’, and how the proposals attempt to resolve the dilemma of commonality and difference. Conceived under direct rule from Westminster (April 2006), issued for consultation when devolved powers to a Northern Ireland Assembly had been restored, and with the final proposals yet to be made public, this targeted educational strategy tells a fascinating story of the past, present and likely future of special needs education in Northern Ireland. Before offering an account of this work, it is placed within some broader ecological frameworks.

European urban spaces in crisis - the mapping of affective pracitices with Living with Difference: introduction

The introduction outlines the notion of urban space and crisis in Europe while taking into account the more recent protests and riots in different cities, in and beyond Europe. It is argued that the phenomen of protest is happening alongside the economic crisis underscoring an alternative political public civic spirit expressing to a certain degree the renaissance and timely making of, what might be called in the digital age, #œuvre. Its forces and emotional properties capture a political realm that unfolds as a globalized urban transnational public space, still progressing. Further, it introduces the collection of papers for the special themed feature. Five papers look at affective practices through a Continental European lens, which places the meaning of race, migration and intersecting identity angles at the centre of debates of individual encounters in public spaces. The final and sixth paper, written by Brenda Yeoh, looks through a Singapore/East Asia lens, and comments on the common European threats as well as on the historical specificity and implications of distinctive geo-political spaces for affective practices.