CONTRA: improving the performance of dynamic investigations in natural abundance organic solids by mirror-symmetric constant-time CODEX

We present a minor but essential modification to the CODEX 1D-MAS exchange experiment. The new CONTRA method, which requires minor changes of the original sequence only, has advantages over the previously introduced S-CODEX, since it is less sensitive to artefacts caused by finite pulse lengths. The performance of this variant, including the finite pulse effect, was confirmed by SIMPSON calculations and demonstrated on a number of dynamic systems.     

Project Planning and Prioritization in the Social Services–an OR Contribution

This paper describes a study carried out for the Social Services Department of a UK County Council towards the development of a system for the evaluation and prioritization of project-based work. There are three major components of the study; an activity analysis to investigate how managers in the department spend their time, with a view to establishing a time budget for the project work; a pilot study to introduce a simple system for project planning and workload balancing with a specialist team; and the development of a multiple criteria model for the evaluation and prioritization of projects. We envisaged a Decision Support System which integrated all of these elements; however, this was never developed; instead, the resultant benefits were of a very different nature. We reflect on the reasons for this and the implications for the success of the study.     

The chaotic-representation property for a class of normal martingales

Suppose $Z=(Z_t)_{t\ge0}$ is a normal martingale which satisfies the structure equation $$d[Z]_t = (\alpha(t)+\beta(t)Z_{t-}) dZ_t + dt$$ . By adapting and extending techniques due to Parthasarathy and to Kurtz, it is shown that, if α is locally bounded and β has values in the interval [-2,0], the process Z is unique in law, possesses the chaotic-representation property and is strongly Markovian (in an appropriate sense). If also β is bounded away from the endpoints 0 and 2 on every compact subinterval of [0,∞] then Z is shown to have locally bounded trajectories, a variation on a result of Russo and Vallois.     

Quantum Random Walks with General Particle States

A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This unifies and extends previous work on repeated-interactions models, including that of Attal and Pautrat (Ann Henri Poincaré 7:59–104 2006) and Belton (J Lond Math Soc 81:412–434, 2010; Commun Math Phys 300:317–329, 2010). When the random-walk generator acts by ampliation and either multiplication or conjugation by a unitary operator, it is shown that the quantum stochastic cocycle which arises in the limit is driven by a unitary process.