The horofunction boundary of the Hilbert geometry

We investigate the horofunction boundary of the Hilbert geometry defined on an arbitrary finite-dimensional bounded convex domain D. We determine its set of Busemann points, which are those points that are the limits of `almost-geodesics'. In addition, we show that any sequence of points converging to a point in the horofunction boundary also converges in the usual sense to a point in the Euclidean boundary of D. We prove that all horofunctions are Busemann points if and only if the set of extreme sets of the polar of D is closed in the Painleve-Kuratowski topology.Comment: 24 pages, 2 figures; minor changes, examples adde

Some Guidance on Conducting and Reporting Qualitative Studies

This paper sets out to address the problem of the imbalance between the number of quantitative and qualitative articles published in highly ranked research journals, by providing guidelines for the design, implementation and reporting of qualitative research. Clarification is provided of key terms (such as quantitative and qualitative) and the interrelationships between them. The relative risks and benefits of using guidelines for qualitative research are considered, and the importance of using any such guidelines flexibly is highlighted. The proposed guidelines are based on a synthesis of existing guidelines and syntheses of guidelines from a range of fields

Perron-Frobenius theorem for nonnegative multilinear forms and extensions

We prove an analog of Perron-Frobenius theorem for multilinear forms with nonnegative coefficients, and more generally, for polynomial maps with nonnegative coefficients. We determine the geometric convergence rate of the power algorithm to the unique normalized eigenvector.Comment: 13 page

Asymptotic behaviour of random Markov chains with tridiagonal generators

Continuous-time discrete-state random Markov chains generated by a random linear differential equation with a random tridiagonal matrix are shown to have a random attractor consisting of singleton subsets, essentially a random path, in the simplex of probability vectors. The proof uses comparison theorems for Carath\'eodory random differential equations and the fact that the linear cocycle generated by the Markov chain is a uniformly contractive mapping of the positive cone into itself with respect to the the Hilbert projective metric. It does not involve probabilistic properties of the sample path and is thus equally valid in the nonautonomous deterministic context of Markov chains with, say, periodically varying transitions probabilities, in which case the attractor is a periodic path.Comment: 11 pages, 15 bibliography references, added bibliography, minor change

Ten myths about character, virtue and virtue education – plus three well-founded misgivings

Initiatives to cultivate character and virtue in moral education at school continue to provoke sceptical responses. Most of those echo familiar misgivings about the notions of character, virtue and education in virtue – as unclear, redundant, old-fashioned, religious, paternalistic, anti-democratic, conservative, individualistic, relative and situation dependent. I expose those misgivings as ‘myths’, while at the same time acknowledging three better-founded historical, methodological and practical concerns about the notions in question

Mazurka

https://digitalcommons.library.umaine.edu/mmb-ps/1139/thumbnail.jp

High-frequency oscillatory ventilation in pediatric acute hypoxemic respiratory failure: disease-specific morbidity survival analysis.

BackgroundMultiple ventilatory strategies for acute hypoxemic respiratory failure (AHRF) in children have been advocated, including high-frequency oscillatory ventilation (HFOV). Despite the frequent deployment of HFOV, randomized controlled trials remain elusive and currently there are no pediatric trials looking at its use. Our longitudinal study analyzed the predictive clinical outcome of HFOV in pediatric AHRF given disease-specific morbidity.MethodsA retrospective 8-year review on pediatric intensive care unit admissions with AHRF ventilated by HFOV was performed. Primary outcomes included survival, morbidity, length of stay (LOS), and factors associated with survival or mortality.ResultsA total of 102 patients underwent HFOV with a 66 % overall survival rate. Survivors had a greater LOS than nonsurvivors (p = 0.001). Mortality odds ratio (OR) for patients without bronchiolitis was 8.19 (CI = 1.02, 65.43), and without pneumonia it was 3.07 (CI = 1.12, 8.39). A lower oxygenation index (OI) after HFOV commencement and at subsequent time points analyzed predicted survival. After 24 h, mortality was associated with an OI > 35 [OR = 31.11 (CI = 3.25, 297.98)]. Sepsis-related mortality was associated with a higher baseline FiO(2) (0.88 vs. 0.65), higher OI (42 vs. 22), and augmented metabolic acidosis (pH of 7.25 vs. 7.32) evaluated 4 h on HFOV (p < 0.05).ConclusionHigh-frequency oscillatory ventilation may be safely utilized. It has a 66 % overall survival rate in pediatric AHRF of various etiologies. Patients with morbidity limited to the respiratory system and optimized oxygenation indices are most likely to survive on HFOV

Research on ICT in K-12 schools e A review of experimental and survey-based studies in computers & education 2011 to 2015

International audienceWhat is the role of a journal? Is it to follow the research or lead it? For the former, it is to serve as an archival record of the scholarship in a field. It can serve to permit the research community to engage with each other via the written record. But, for the latter, it can serve the research community by pointing out gaps in the research based on the archival record. This review is intended to do just that

Stability and convergence in discrete convex monotone dynamical systems

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is weaker than Lyapunov stability. Among others we show that the set of tangentially stable fixed points is isomorphic to a convex inf-semilattice, and a criterion is given for the existence of a unique tangentially stable fixed point. We also show that periods of tangentially stable periodic points are orders of permutations on $n$ letters, where $n$ is the dimension of the underlying space, and a sufficient condition for global convergence to periodic orbits is presented.Comment: 36 pages, 1 fugur