Variational formulation of problems involving fractional order differential operators

In this work, we consider boundary value problems involving either Caputo or Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to nonsymmetric boundary value problems, which are investigated from a variational point of view. The variational problem for the Riemann-Liouville case is coercive on the space Hα/2 0 (0, 1) but the solutions are less regular, whereas that for the Caputo case involves different test and trial spaces. The numerical analysis of these problems requires the so-called shift theorems which show that the solutions of the variational problem are more regular. The regularity pickup enables one to establish convergence rates of the finite element approximations. The analytical theory is then applied to the Sturm-Liouville problem involving a fractional derivative in the leading term. Finally, extensive numerical results are presented to illustrate the error estimates for the source problem and eigenvalue problem

Space-Time Petrov–Galerkin FEM for Fractional Diffusion Problems

We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order α ∈ (0, 1) in time and zero initial data. We derive a proper weak formulation involving different solution and test spaces and show the inf-sup condition for the bilinear form and thus its well-posedness. Further, we develop a novel finite element formulation, show the well-posedness of the discrete problem, and derive error bounds in both energy and L 2 norms for the finite element solution. In the proof of the discrete inf-sup condition, a certain nonstandard L 2 stability property of the L 2 projection operator plays a key role. We provide extensive numerical examples to verify the convergence analysis

Vulnerable warriors: the atmospheric marketing of military and policing equipment before and after 9/11

In this article, we analyse changes in the circulation of advertisements of policing products at security expos between 1995 and 2013. While the initial aim of the research was to evidence shifts in terrorist frames in the marketing of policing equipment before and after 9/11, our findings instead suggested that what we are seeing is the rise of marketing to police as “vulnerable warriors”, law enforcement officers in need of military weapons both for their offensive capabilities and for the protection they can offer to a police force that is always under threat

The use of yttrium in medical imaging and therapy : historical background and future perspectives

Yttrium is a chemically versatile rare earth element that finds use in a range of applications including lasers and superconductors. In medicine, yttrium-based materials are used in medical lasers and biomedical implants. This is extended through the array of available yttrium isotopes to enable roles for 90Y complexes as radiopharmaceuticals and 86Y tracers for positron emission tomography (PET) imaging. The naturally abundant isotope 89Y is proving to be suitable for nuclear magnetic resonance investigations, where initial reports in the emerging field of hyperpolarised magnetic resonance imaging (MRI) are promising. In this review we explore the coordination and radiochemical properties of yttrium, and its role in drugs for radiotherapy, PET imaging agents and perspectives for applications in hyperpolarised MRI. This journal i

Hybrid polymer electrolyte membrane fuel cell-lithium-ion battery powertrain testing platform - hybrid fuel cell electric vehicle emulator

Abstract not availableP. Bujlo, C. J. Xie, D. Shen, O. Ulleberg, S. Pasupathi, G. Pasciak and B. G. Polle