Regge models of hadronic elastic scattering at all angles

A Regge-based model for the elastic scattering of hadrons at all angles is developed, which combines the best features of a conventional Regge model with those of a quark interchange model. As t tends to - the meson Regge trajectories approach negative integers, while their residues vary like negative integer powers of t, the sum of the two integers being such that the Dimensional Counting Rule is satisfied. Within this framework nucleon-nucleon differential crosssections, polarizations and spin correlation parameters, and π(^±)p differential cross-sections are studied. It is found that the Regge pole terms dominate for -t < 1 (GeV/c)(^2) ; Regge cuts become important at intermediate t values, but at large angles the meson-Reggeons (with trajectories now approaching integers) re-emerge as the most important contributions. Fits are presented which give a good account of the experimental data at all angles for the pp, pn and pp differential cross-sections, polarizations and spin correlation parameters (where available) and the π(^±)p differential cross-sections

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

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

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

Changes in Pasture Growth Rate Due to Fertiliser and Grazing Management

It is imperative that sheep production systems in southern Australia continue to be refined so producers remain financially viable but at the same time the environment is not degraded. As part of a national thrust for development and promotion of better production systems, one research site has been established in Victoria where pastures and animal production are measured together with water and nutrient movement. Results for pasture growth rates over two years are presented here and will be used to develop best industry practice at completion of the project

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

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