On a generalization of Pólya’s theorem

We consider generalizations of Pólya’s theorem to the case of entire functions taking algebraic values at natural or integer points.     

Mixing methodologies to enhance the implementation of healthcare operational research

Healthcare Operational Research (OR) has had limited success in achieving a sufficient level of stakeholder acceptance to lead to implementation of results. This research study is aimed at combining OR methodologies to achieve greater acceptance of results for organizational change. Patient flow delays in the Paediatric intensive care unit (PICU) at Children's Hospital of Wisconsin were identified using case studies. Patient flow was modelled using hard OR (simulation) using case study findings, with active stakeholder participation, and enhanced with outcomes research. Outcomes research allowed achieving greater clinical relevance of OR findings. Results from hard OR, particularly for politically sensitive issues, were persuasive but inadequate to result in change. Soft OR (cognitive mapping) was used to identify new issues and enhance results. Consequently, the planned PICU expansion was deferred, and resources focused on improving staffing strategies identified independently from both hard and soft OR. These findings suggest that: (1) Outcomes research can play a unique role to enhance results in healthcare OR. (2) After obtaining a holistic understanding of the system using hard and soft OR, stakeholders are willing to implement results from each independently, supporting the development of a common form of knowledge, which is consistent with Mixed-Mode Modelling. (3) Hard OR, enhanced with outcomes research, with active stakeholder participation, and combined with soft OR, results in greater acceptance and sustained organizational change.     

Acute Triangulations of Flat Mobius Strips

In this paper we investigate the acute triangulations of flat Mobius strips. We find out that we can always triangulate a flat Mobius strip with at most nine acute triangles, and sometimes (but not always) that many triangles are really needed.     

Dimensional variation in production of high-aspect-ratio micro-pillars array by micro powder injection molding

Micro powder injection molding (μPIM) is one of the potential processes for the mass production of metallic microstructures and micro components. Here, μPIM is the miniaturization of conventional PIM, which involves four processing steps: mixing, injection molding, debinding and sintering. This paper looks into the feasibility and effectiveness of μPIM as a key mass production process for the fabrication of metallic micro components. For it to be an effective re-production process, it is imperative to examine how well parts can be duplicated/fabricated from a master mold. In this work, the dimensional variation of high-aspect-ratio micro-pillars arrays, in particular the dimensional shrinkage, global warpage, and surface roughness at each stage of the μPIM process for a range of molding pressures, are quantified and compared in detail. The sensitivity of the dimensional variation of the microstructures to the packing pressure is reported. The mechanism behind the dimensional variation is analyzed. PACS 81.20.Ev; 81.20.Hy; 81.70.Fy; 07.60.Ly; 81.05.-t     

Structure transition of single-texture CoSi2 nanolayer grown by refractory-interlayer-mediated epitaxy method

In this investigation, the crystalline structure of a nanometric CoSi₂ layer, formed in heat treated Co/W_xTa_(1−x)/Si(1 0 0) systems, has been studied by XRD analysis. Careful measurements of the diffraction intensities revealed that temporary formation of a metastable diamond cubic structure of CoSi₂ phase, rather than its usual CaF₂ structure, was occurred. It has been shown that formation of this metastable structure depends on the kind of the applied interlayer in addition to the annealing temperature. Among the studied systems with x = 0, 0.25, 0.5, 0.75 and 1, the second and the last systems resulted in growing a (1 0 0) single-texture CoSi₂ layer with the preferred usual CaF₂ structure, a strained lattice parameter, and the best thermal stability (900-1000 °C).     

The essential Lagrangian-Grassmannian and the homotopy type of the Fredholm Lagrangian-Grassmannian

Let H be a separable infinite dimensional Hilbert space endowed with a symplectic structure and let L₀⊂H be a Lagrangian subspace. Using the results of [A. Abbondandolo, P. Majer, Infinite dimensional Grassmannians, math.AT/0307192], we show that the Fredholm Lagrangian-Grassmannian FL₀(Λ) has the homotopy type of Gc(L₀), the Grassmannian of all Lagrangian subspaces of H that are compact perturbations of L₀. It is well known that the latter has the homotopy type of the quotient U(∞)/O(∞). As a corollary, we recover a result by B. Booss-Bavnbek and K. Furutani (see [B. Booss-Bavnbek, K. Furutani, Symplectic functional analysis and spectral invariants, Contemp. Math. 242 (1999) 53-83; K. Furutani, Fredholm-Lagrangian-Grassmannian and the Maslov index, J. Geom. Phys. 51 (2004) 269-331]) that the L₀-Maslov index is an isomorphism between the fundamental group of FL₀(Λ) and the integers.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.