Robin conditions on the Euclidean ball

Techniques are presented for calculating directly the scalar functional determinant on the Euclidean d-ball. General formulae are given for Dirichlet and Robin boundary conditions. The method involves a large mass asymptotic limit which is carried out in detail for d=2 and d=4 incidentally producing some specific summations and identities. Extensive use is made of the Watson-Kober summation formula.Comment: 36p,JyTex, misprints corrected and a section on the massive case adde

Protection characteristics of a Faraday cage compromised by lightning burnthrough.

A lightning flash consists of multiple, high-amplitude but short duration return strokes. Between the return strokes is a lower amplitude, continuing current which flows for longer duration. If the walls of a Faraday cage are made of thin enough metal, the continuing current can melt a hole through the metal in a process called burnthrough. A subsequent return stroke can couple energy through this newly-formed hole. This LDRD is a study of the protection provided by a Faraday cage when it has been compromised by burnthrough. We initially repeated some previous experiments and expanded on them in terms of scope and diagnostics to form a knowledge baseline of the coupling phenomena. We then used a combination of experiment, analysis and numerical modeling to study four coupling mechanisms: indirect electric field coupling, indirect magnetic field coupling, conduction through plasma and breakdown through the hole. We discovered voltages higher than those encountered in the previous set of experiments (on the order of several hundreds of volts)

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket

Fossil energy in economic growth: A study of the energy direction of technical change, 1950-2012

Climate change mitigation challenges national economies to increase productivity while reducing fossil energy consumption. Fossil energy-saving technical change has been assumed to accomplish this, yet empirical evidence is scarce. This paper investigates the long-run relationship between the rate and direction of technical change with respect to fossil energy and labor in the world economy. Growth rates of labor productivity and the fossil energy-labor ratio are examined for more than 95 of world output between 1950 and 2012. The average elasticity of the energy-labor ratio with respect to labor productivity is close to one, implying highly energy-using technical change, but no trade-o between factor productivity growth rates. This stylized fact suggests the importance of a cheap, abundant energy supply for robust global growth, and a more important role for renewable energy. Integrated assessment models do not incorporate this restriction which may result in poorly speci ed baseline scenarios

Feasibility and effects of adapted cardiac rehabilitation after stroke: a prospective trial

Abstract Background Despite the cardiovascular etiology of stroke, exercise and risk factor modification programs akin to cardiac rehabilitation (CR) are not available. This study aimed to establish the feasibility of adapting a CR model for individuals with mild to moderate stroke disability. A secondary objective was to determine the program's effects on aerobic and walking capacity, and stroke risk factors. Methods A repeated measures design was used with a 3-month baseline period and 6-month adapted CR intervention (n = 43, mean ± SD age 65 ± 12 years, 30 ± 28 months post stroke). Feasibility was determined by the number of participants who completed the study, occurrence of adverse events and frequency, duration and intensity of exercise performed. To determine effectiveness of the program, outcomes measured included aerobic capacity (VO2peak, ventilatory threshold), 6-Minute Walk Test (6MWT) distance, and risk factors. Descriptive statistics characterized the classes attended and number and intensity of exercise sessions. Paired t-tests, one-factor repeated measures analyses of variance contrasts and chi-square analyses were used to compare changes over time. Results Two participants withdrew during the baseline period. Of the remaining 41 participants who commenced the program, 38 (93%) completed all aspects. No serious adverse effects occurred. Post-intervention, VO2peak improved relative to the stable baseline period (P = 0.046) and the increase in ventilatory threshold approached significance (P = 0.062). Conclusions CR is feasible after stroke and may be adapted to accommodate for those with a range of post-stroke disability. It is effective in increasing aerobic capacity. CR may be an untapped opportunity for stroke survivors to access programs of exercise and risk factor modification to lower future event risk. Trial registration ClinicalTrials.gov registration number: NCT0106749