Continuous functions with universally divergent Fourier series on small subsets of the circle

It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality properties.Comment: 6 page

Spin effects in strong-field laser-electron interactions

The electron spin degree of freedom can play a significant role in relativistic scattering processes involving intense laser fields. In this contribution we discuss the influence of the electron spin on (i) Kapitza-Dirac scattering in an x-ray laser field of high intensity, (ii) photo-induced electron-positron pair production in a strong laser wave and (iii) multiphoton electron-positron pair production on an atomic nucleus. We show that in all cases under consideration the electron spin can have a characteristic impact on the process properties and their total probabilities. To this end, spin-resolved calculations based on the Dirac equation in the presence of an intense laser field are performed. The predictions from Dirac theory are also compared with the corresponding results from the Klein-Gordon equation.Comment: 9 pages, 6 figure

The CLT Analogue for Cyclic Urns

A cyclic urn is an urn model for balls of types $0,\ldots,m-1$ where in each draw the ball drawn, say of type $j$, is returned to the urn together with a new ball of type $j+1 \mod m$. The case $m=2$ is the well-known Friedman urn. The composition vector, i.e., the vector of the numbers of balls of each type after $n$ steps is, after normalization, known to be asymptotically normal for $2\le m\le 6$. For $m\ge 7$ the normalized composition vector does not converge. However, there is an almost sure approximation by a periodic random vector. In this paper the asymptotic fluctuations around this periodic random vector are identified. We show that these fluctuations are asymptotically normal for all $m\ge 7$. However, they are of maximal dimension $m-1$ only when $6$ does not divide $m$. For $m$ being a multiple of $6$ the fluctuations are supported by a two-dimensional subspace.Comment: Extended abstract to be replaced later by a full versio

Reducing Global Warming: The Potential of Organic Agriculture

For a successful outcome at COP 15 in Copenhagen in December, viable policy paths for effective climate change mitigation need to be provided. In addition, adaptation is unavoidable. One key point is the integration of agriculture (accounting for 10-12% of global emissions, Smith et al. 2007) in a post-2012 agreement. Its main potential lies in its significant capacity to sequester CO2 in soils, and in its synergies between mitigation and adaptation. This potential is best utilized employing sustainable agricultural practices such as organic agriculture (OA). Conservative estimates of the total mitigation potential of OA amount to 4.5-6.5 Gt CO2eq/yr (of ca. 50 Gt CO2eq total global greenhouse gas emissions). Depending on agricultural management practices, much higher amounts seem however possible. Organic agriculture complements emission reduction efforts with its major sequestration potential, which is based on the intensive humus production (requiring CO2) of the fertile soils. In comparison to conventional agriculture, OA also directly contributes to emission reductions as it emits less N2O from nitrogen application (due to lower nitrogen input), less N2O and CH4 from biomass waste burning (as burning is avoided), and requires less energy, mainly due to zero chemical fertilizer use. Its synergies between mitigation and adaptation also exert a positive influence. This in part due to the increased soil quality, which reduces vulnerability to drought periods, extreme precipitation events and waterlogging. In addition, the high diversity of crops and farming activities in organic agriculture, together with its lower input costs, reduce economic risks. OA has additional benefits beyond its direct relevance for mitigation and adaptation to climate change and climate variability, as it helps to increase food security and water protection. In the following, key points of organic agriculture are briefly listed, together with references for detailed information. The data refer to the annual potential of a global shift of agriculture to organic practices