The uniqueness of solutions to discrete, victor, two-point boundary value problems

Difference equations which may arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations are investigated and conditions are formulated under which solutions to the discrete problem are unique. Some existence, uniqueness implies existence, and convergence theorems for solutions to the discrete problem are also presented.

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Physical activity and sedentary behavior: A population-based study of barriers, enjoyment, and preference

The associations of physical activity and sedentary behavior with barriers, enjoyment, and preferences were examined in a population-based mail survey of 1,332 adults. Respondents reporting high enjoyment and preference for physical activity were more likely to report high levels of activity. Those reporting cost, the weather, and personal barriers to physical activity were less likely to be physically active. Preference for sedentary behavior was associated with the decreased likelihood of being physically active, and the weather as a barrier to physical activity was associated with the increased likelihood of sedentary behavior. These constructs can be used to examine individual and environmental influences on physical activity and sedentary behavior in specific populations and could inform the development of targeted interventions.

Injury related risk behavior - a study of Australian skydivers

Risk taking behaviour has been identified as an important host-related determinant of injury in young adults. The aim of this study is to clarify the relationship between the two key elements of risk taking behaviour - ie, risk assessment and risk acceptance - in participants of a high risk sporting activity. Skydivers registered with the Australian Parachute Federation were sampled at several jump meetings held at three 'drop-zones' in North Eastern Australia. A cross sectional survey of 215 skydivers ascertained each subject's risk assessment of each of nine hypothetical sky diving scenes and whether or not they would jump in the described conditions. Variables which independently predicted an individual's risk assessment were age group (p < 0.05), gender (p < 0.05) and scene details (p < 0.001). Risk assessment was found to be a statistically significant predictor of the decision to jump, with a 22% decrease in the odds of jumping with every unit increase in risk assessment (OR = 0.78: 95% Cl; 0.76, 0.80). Gender was also found to be a statistically significant predictor of the decision to jump, with males being 19% more likely to jump than females, after controlling for age, experience, currency and risk assessment (OR = 1.19: 95% CI; 1.04, 1.38). The importance of these results is that, by quantifying the relationship between two key elements of risk taking behaviour and several important host factor determinants, they facilitate more informed discussion about the possible role of risk taking behaviour in the causation of injury.