On the Speed of Spread for Fractional Reaction-Diffusion Equations

The fractional reaction diffusion equation u_t + Au = g(u) is discussed, where A is a fractional differential operator on the real line with order \alpha between 0 and 2, the C^1 function g vanishes at 0 and 1, and either g is non-negative on (0,1) or g < 0 near 0. In the case of non-negative g, it is shown that solutions with initial support on the positive half axis spread into the left half axis with unbounded speed if g satisfies some weak growth condition near 0 in the case \alpha > 1, or if g is merely positive on a sufficiently large interval near 1 in the case \alpha < 1. On the other hand, it shown that solutions spread with finite speed if g'(0) < 0. The proofs use comparison arguments and a new family of traveling wave solutions for this class of problems

Asymptotic stability of traveling wave solutions for perturbations with algebraic decay

For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation of the traveling wave profile decays at an algebraic rate, then the solution is shown to converge to a shifted wave profile at a corresponding temporal algebraic rate, and optimal intermediate results that combine temporal and spatial decay are obtained. The proofs are based on a general interpolation principle which says that algebraic decay results of this form always follow if exponential temporal decay holds for perturbation with exponential spatial decay and the wave profile is stable for general perturbations.Comment: 14 page

The Comparison of Dual-Tasking and Functional Fitness in Older Females

Context: America’s aging population is growing faster than ever, resulting in increasing challenges for healthcare providers and caregivers. Over 33% of adults aged 65 and older fall annually, and falls are the number one cause of injury-related death in this age group. Assessing fall risk is difficult due to its multifactorial nature, but functional fitness serves as a proxy measure. Women are at a particularly high risk for fall-related injury due to lower bone mineral density and higher fall frequency when compared to males. Fear of falling is also a serious contributor to fall risk, and it affects up to 89% of older adults. Objective: This study investigated the effects of functional fitness on walking speed under dual-tasking conditions. We hypothesized that women who were less functionally fit would experience greater declines in dual-task walking speed. Design: This experiment had a cross-sectional design. Setting: Tests were conducted at a retirement community in northwest Arkansas. Participants: Participants were females over the age of 65 y, with a mean age of 79.6 y. They were recruited on a volunteer basis and divided in two groups of 13 based on functional fitness levels. Interventions: Functional fitness was determined using the 8-foot up-and-go, a measure of agility and dynamic balance. For walking speed assessments, subjects walked a 10-meter distance with 3 meters extra on each end to account for acceleration and deceleration. Speed was measured with a laser timer. Dual-task assessment required subjects to count backwards by threes from a predetermined number. Four protocols with two trials each were used: single-task walking at habitual and maximal speeds, and dual-task walking at habitual and maximal speeds. Main Outcome Measures: The independent variable was functional fitness level (moderate or high). The dependent variables were dual-task walking time and Dual-Task Cost, calculated by subtracting single-task from dual-task walking time. A one-way ANOVA determined differences between dual-task decrement of the habitual and maximal walking speed trials. Statistical significance was set at α=.05. Results: Average 8-foot up-and-go time for the high functioning group was 5.74 seconds. The average time for the moderate functioning group was 8.33 seconds. Dual-task time difference between the two groups for habitual walking was statistically insignificant (p =.789). For maximal speed, dual-task time difference was statistically significant (p =.04). The moderate group exhibited smaller Dual-Task Costs than the high group for both habitual (difference of 1.3 ± 1.5 s) and maximal (difference of 0.3 ± 0.3 s) conditions. These Dual-Task Cost differences were insignificant for usual speed (p = .11) and maximal speed (p = .38) Discussion: The results did not support the hypothesis of Dual-Task Costs being related to functional fitness level. However, there was a significant difference in maximal dual-task speed between the groups. This shows that maximal dual-task walking speed is more closely linked to functional fitness than is habitual dual-task speed

Monetary Policy and Unemployment in Open Economies

After an expansionary monetary policy shock employment increases and unemployment falls. In standard New Keynesian models the fall in aggregate unemployment does not affect employed workers at all. However, Luchinger, Meier and Stutzer (2010) found that the risk of unemployment negatively affects utility of employed workers: An increases in aggregate unemployment decreases workers' subjective well-being, which can be explained by an increased risk of becoming unemployed. I take account of this effect in an otherwise standard New Keynesian open economy model with unemployment as in Gali (2010) and find two important results with respect to expansionary monetary policy shocks: First, the usual wealth effect in New Keynesian models of a declining labor force, which is at odds with the data as high-lighted by Christiano, Trabandt and Walentin (2010), is shut down. Second, the welfare effects of such shocks improve considerably, modifying the standard results of the open economy literature that set off with Obstfeld and Rogoff's (1995) redux model.Open economy macroeconomics, monetary policy, unemployment

Global rebalancing in a three-country model

This paper extends the model of Engler et al. (2007) on the adjustment of the US current account to a three-country world economy. This allows an analysis of the differential impact of a reversal of the US current account on Europe and Asia. In particular, the outcomes under different exchange rate policies are analysed. The main finding is that large factor re-allocations from non-tradables to tradables will be necessary in the US. The direction of factor re-allocation in Asia depends on whether the Bretton-Woods-II regime of unilaterally fixed or manipulated exchange rates in Asia is continued. If this is the case, the tradables sector and the current account surplus will continue to grow even when the US deficit closes. The flip side of this result is that Europe will face a huge real appreciation and an enormous current account deficit. With floating exchange rates worldwide, the impact on Europe will be limited while Asia´s tradables sector will shrink. --Global imbalances,US current account deficit,dollar adjustment,sectoral adjustment

Redistribution in Switzerland: Social Cohesion or Simple Smoothing of Lifetime Incomes?

Using the example of Switzerland, this paper examines the extent to which the state and the social security institutions change the income distribution. Two sets of questions are examined: (1) Who benefits from the public services, and who bears the public costs? (2) To what extent does an annual redistribution involve redistribution (a) across households with different lifetime income, and (b) across different phases of life within the same households? Budget incidence analyses and pseudo panel procedures allow to compare annual and lifetime household incomes that arise before and after transfers. The results suggest that public interventions induce substantial redistribution, which is due primarily, however, to income-smoothing transfers within households and not to redistribution across households.Budget Incidence Analysis, Redistribution, Lifetime Income Smoothing, Pseudo Panel Procedure