An exactly solvable self-convolutive recurrence

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function $U(a,b,z)$. By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the $n$th coefficient is expressed as the $(n-1)$th moment of a measure, and also as the trace of the $(n-1)$th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics

THE SPANNING SET AS A MEASURE OF MOVEMENT VARIABILITY

The variability of an individual’s movement pattern is an increasingly important focus of research in sport and exercise biomechanics. Inter-trial variability of a single variable is typically assessed using mean deviation or coefficient of variation, however, recent alternatives to these have been proposed such as the spanning set technique. This paper presents an investigation into the validity of the spanning set measure. Variability scores using the spanning set were compared against more traditional measures of variability (mean deviation, coefficient of variation and variance ratio). Results indicate that the spanning set is biased towards early-phase variability and may inaccurately describe the overall level of movement variability

Pressure Monitoring Using Hybrid fs/ps Rotational CARS

We investigate the feasibility of gas-phase pressure measurements at kHz-rates using fs/ps rotational CARS. Femtosecond pump and Stokes pulses impulsively prepare a rotational Raman coherence, which is then probed by a high-energy 6-ps pulse introduced at a time delay from the Raman preparation. Rotational CARS spectra were recorded in N2 contained in a room-temperature gas cell for pressures from 0.1 to 3 atm and probe delays ranging from 10-330 ps. Using published self-broadened collisional linewidth data for N2, both the spectrally integrated coherence decay rate and the spectrally resolved decay were investigated as means for detecting pressure. Shot-averaged and single-laser-shot spectra were interrogated for pressure and the accuracy and precision as a function of probe delay and cell pressure are discussed. Single-shot measurement accuracies were within 0.1 to 6.5% when compared to a transducer values, while the precision was generally between 1% and 6% of measured pressure for probe delays of 200 ps or more, and better than 2% as the delay approached 300 ps. A byproduct of the pressure measurement is an independent but simultaneous measurement of the gas temperature

Mobagogy- mobile learning for a higher education community

This paper reports on a project in which a learning community of higher educators was formed to investigate how best to use mobile technologies in their own learning and teaching. Activities of this group included investigating best practice approaches by interviewing experts in the field, exploring the literature on mobile learning and then initiating and testing some mobile learning pedagogies in the context of their own higher education subjects. The community met regularly to discuss emerging issues and applications. The paper shares some of the findings gained both from the expert interviews and from the experiences of members of the community, and discusses the challenges and constraints that were experienced. We conclude with recommendations for promoting mobile learning communities in higher education. © 2010 IADIS

Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution

We introduce an alternative definition of the relative height h^\kappa(x) of a one-dimensional fluctuating interface indexed by a continuously varying real paramater 0 \leq \kappa \leq 1. It interpolates between the height relative to the initial value (i.e. in x=0) when \kappa = 0 and the height relative to the spatially averaged height for \kappa = 1. We compute exactly the distribution P^\kappa(h_m,L) of the maximum h_m of these relative heights for systems of finite size L and periodic boundary conditions. One finds that it takes the scaling form P^\kappa(h_m,L) = L^{-1/2} f^\kappa (h_m L^{-1/2}) where the scaling function f^\kappa(x) interpolates between the Rayleigh distribution for \kappa=0 and the Airy distribution for \kappa=1, the latter being the probability distribution of the area under a Brownian excursion over the unit interval. For arbitrary \kappa, one finds that it is related to, albeit different from, the distribution of the area restricted to the interval [0, \kappa] under a Brownian excursion over the unit interval.Comment: 25 pages, 4 figure

Area distribution and the average shape of a L\'evy bridge

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the area A = \sum_{m=1}^n x_B(m) under such a L\'evy bridge and show that, for large n, it has the scaling form P_B(A,n) \sim n^{-1-1/\alpha} F_\alpha(A/n^{1+1/\alpha}), with the asymptotic behavior F_\alpha(Y) \sim Y^{-2(1+\alpha)} for large Y. For \alpha=1, we obtain an explicit expression of F_1(Y) in terms of elementary functions. We also compute the average profile < \tilde x_B (m) > at time m of a L\'evy bridge with fixed area A. For large n and large m and A, one finds the scaling form = n^{1/\alpha} H_\alpha({m}/{n},{A}/{n^{1+1/\alpha}}), where at variance with Brownian bridge, H_\alpha(X,Y) is a non trivial function of the rescaled time m/n and rescaled area Y = A/n^{1+1/\alpha}. Our analytical results are verified by numerical simulations.Comment: 21 pages, 4 Figure

Does contact with a podiatrist prevent the occurrence of a lower extremity amputation in people with diabetes? A systematic review and meta-analysis

Objective To determine the effect of contact with a podiatrist on the occurrence of Lower Extremity Amputation (LEA) in people with diabetes.Design and data sources We conducted a systematic review of available literature on the effect of contact with a podiatrist on the risk of LEA in people with diabetes. Eligible studies, published in English, were identified through searches of PubMed, CINAHL, EMBASE and Cochrane databases. The key terms, ‘podiatry’, ‘amputation’ and ‘diabetes’, were searched as Medical Subject Heading terms. Reference lists of selected papers were hand-searched for additional articles. No date restrictions were imposed.Study selection Published randomised and analytical observational studies of the effect of contact with a podiatrist on the risk of LEA in people with diabetes were included. Cross-sectional studies, review articles, chart reviews and case series were excluded. Two reviewers independently assessed titles, abstracts and full articles to identify eligible studies and extracted data related to the study design, characteristics of participants, interventions, outcomes, control for confounding factors and risk estimates.Analysis Meta-analysis was performed separately for randomised and non-randomised studies. Relative risks (RRs) with 95% CIs were estimated with fixed and random effects models as appropriate.Results Six studies met the inclusion criteria and five provided data included in meta-analysis. The identified studies were heterogenous in design and included people with diabetes at both low and high risk of amputation. Contact with a podiatrist did not significantly affect the RR of LEA in a meta-analysis of available data from randomised controlled trials (RCTs); (1.41, 95% CI 0.20 to 9.78, 2 RCTs) or from cohort studies; (0.73, 95% CI 0.39 to 1.33, 3 Cohort studies with four substudies in one cohort). Conclusions There are very limited data available on the effect of contact with a podiatrist on the risk of LEA in people with diabetes

Exploring teacher pedagogy, stages of concern and accessibility as determinants of technology adoption

© 2017 Association for Information Technology in Teacher Education. This research examines how the pedagogical orientations of teachers affect technology adoption in the classroom. At the same time, the authors account for the stage of concern that teachers are experiencing regarding the use of the technology, their access to the technology and the level of schooling at which they teach.The authors’ investigation of these factors occurs in the context of a contemporary technology, the interactive whiteboard (IWB), in Australian schools. A structural equation model was estimated using a reflective measure of technology usage with antecedents in the form of pedagogical-oriented beliefs and best–worst scaling derived scores for a teacher’s stage of concern regarding IWBs. Teachers with constructivist-oriented pedagogical beliefs were significantly more likely to use IWBs than transmission-oriented teachers. However, the strongest determinant of usage was whether the technology is immediately accessible or not

Precise Asymptotics for a Random Walker's Maximum

We consider a discrete time random walk in one dimension. At each time step the walker jumps by a random distance, independent from step to step, drawn from an arbitrary symmetric density function. We show that the expected positive maximum E[M_n] of the walk up to n steps behaves asymptotically for large n as, E[M_n]/\sigma=\sqrt{2n/\pi}+ \gamma +O(n^{-1/2}), where \sigma^2 is the variance of the step lengths. While the leading \sqrt{n} behavior is universal and easy to derive, the leading correction term turns out to be a nontrivial constant \gamma. For the special case of uniform distribution over [-1,1], Coffmann et. al. recently computed \gamma=-0.516068...by exactly enumerating a lengthy double series. Here we present a closed exact formula for \gamma valid for arbitrary symmetric distributions. We also demonstrate how \gamma appears in the thermodynamic limit as the leading behavior of the difference variable E[M_n]-E[|x_n|] where x_n is the position of the walker after n steps. An application of these results to the equilibrium thermodynamics of a Rouse polymer chain is pointed out. We also generalize our results to L\'evy walks.Comment: new references added, typos corrected, published versio

Effective mass and quantum lifetime in a Si/Si0.87Ge0.13/Si two-dimensional hole gas

Measurements of Shubnikov de Haas oscillations in the temperature range 0.3–2 K have been used to determine an effective mass of 0.23 m0 in a Si/Si0.87Ge0.13/Si two-dimensional hole gas. This value is in agreement with theoretical predictions and with that obtained from cyclotron resonance measurements. The ratio of the transport time to the quantum lifetime is found to be 0.8. It is concluded that the 4 K hole mobility of 11 000 cm2 V−1 s−1 at a carrier sheet density of 2.2×1011 cm−2 is limited by interface roughness and short-range interface charge scattering