About the mass of certain second order elliptic operators

Let $(M,g)$ be a closed Riemannian manifold of dimension $n \geq 3$ and let $f\in C^{\infty}(M)$, such that the operator $P_f:= \Delta_g+f$ is positive. If $g$ is flat near some point $p$ and $f$ vanishes around $p$, we can define the mass of $P_f$ as the constant term in the expansion of the Green function of $P_f$ at $p$. In this paper, we establish many results on the mass of such operators. In particular, if f:= \frac{n-2}{4(n-1)} \scal_g, i.e. if $P_f$ is the Yamabe operator, we show the following result: assume that there exists a closed simply connected non-spin manifold $M$ such that the mass is non-negative for every metric $g$ as above on $M$, then the mass is non-negative for every such metric on every closed manifold of the same dimension as $M$.Comment: 39 page

Transparency in monetary policy

For some time now the buzzword 'transparency' has been bandied about in the media almost daily. For example, calls were made for greater transparency in the financial system in connection with developments in the Asian financial markets. But the call for greater transparency goes far beyond the financial markets. It is now regarded as a necessary part of "good governance" demanded of all economic policy makers. As the World Bank's chief economist Joseph Stiglitz put it: 'No one would dare say that they were against transparency (....): It would be like saying you were against motherhood or apple pie.' This paper focuses on transparency in monetary policy, in particular with respect to the European System of Central Bank

Ressourcenschutz in der umweltfreundlichen öffentlichen Beschaffung

Die Vertiefungsanalyse „Ressourcenschutz in der umweltfreundlichen öffentlichen Beschaffung“ von Andreas Hermann (2018) untersucht die rechtlichen Ansatzpunkte, mit denen die Politik den Ressourcenschutz in der umweltfreundlichen Beschaffung in Deutschland stärken kann. Untersucht werden die Beschaffungsfelder „Bau und Unterhalt von Straßen“, „Bauen und Wohnen“ sowie „IT-Produkte“. Dazu werden die umweltbezogenen Beschaffungskriterien zum Ressourcenschutz analysiert, die die EU selbst veröffentlicht hat sowie die nationalen Kriterien in Deutschland und den Niederlanden. Der Überblick zeigt, dass es sich bei den untersuchten Umweltkriterien zum Ressourcenschutz um nicht rechtsverbindliche „Empfehlungen“ an die öffentlichen Beschaffungsstellen handelt. Soll die Nutzung in der Praxis forciert werden, ist in ProgRess III zu prüfen, ob und welche Kriterien auch verpflichtend im deutschen Beschaffungsrecht vorgeschrieben werden. Bei der Beschaffung von IT-Produkten werden derzeit nur umweltfreundliche Beschaffungskriterien für die Verbesserung der Produktlebensdauer (z. B. Design für Haltbarkeit, Reparierbarkeit und Nachrüstung) empfohlen. Denn Kriterien und Nachweismöglichkeiten für den umweltschonenden Abbau und die Weiterverarbeitung der mineralischen Rohstoffe, die in den IT-Produkten enthalten sind, existieren nicht. Um auch den umweltschonenden Abbau von Rohstoffen in der Beschaffung zu berücksichtigen, sollte die Politik und Forschung die Standardisierung von Umweltkriterien vorantreiben

Towards Comparative and Aggregate Vulnerability: An Analysis of Welfare Distributions in Rural Provinces in Thailand and Vietnam

Several measures of vulnerability to poverty have been suggested in the literature. In practise, only little is known about the robustness of vulnerability comparisons based on these often quite specific measures. The theory of stochastic orders can be applied to shed some light on such issues. In the DFG research project "Impact of Shocks on the Vulnerability to Poverty: Consequences for Development of Emerging Southeast Asian Economies" (DFG FOR 756), an extensive panel survey was carried out in six rural provinces of Thailand and Vietnam in 2007. We establish cumulative distribution functions for income and consumption at the provincial level and search for stochastic dominance relations between these distributions. Our comparisons allow for initial, but quite robust conclusions on welfare and provide benchmarks for assessing the vulnerability to poverty in the research regions. --welfare distribution,stochastic ordering,vulnerability

High-pressure phase of brucite stable at Earth’s mantle transition zone and lower mantle conditions

We investigate the high-pressure phase diagram of the hydrous mineral brucite, Mg(OH)2, using structure search algorithms and ab initio simulations. We predict a new high-pressure phase stable at pressure and temperature conditions found in cold subducting slabs in Earth’s mantle transition zone and lower mantle. This implies that brucite can play a much more important role in water transport and storage in Earth’s interior than hitherto thought. The predicted high-pressure phase, stable in calculations between 20-35 GPa and up to 800 K, features MgO6 octahedral units arranged in the anatase-TiO2 structure. This suggests that brucite will transform from a layered to a compact three-dimensional network structure before eventual decomposition into periclase and ice. We show that the new phase has unique spectroscopic fingerprints that should allow for straightforward detection in experiments. The new phase also has distinct elastic properties that might make its direct detection in the deep Earth with geophysical methods possible.See readme file

Mass endomorphism, surgery and perturbations

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments

Dirac eigenspinors for generic metrics

We consider a Riemannian spin manifold (M,g) with a fixed spin structure. The zero sets of solutions of generalized Dirac equations on M play an important role in some questions arising in conformal spin geometry and in mathematical physics. In this setting the mass endomorphism has been defined as the constant term in an expansion of Green's function for the Dirac operator. One is interested in obtaining metrics, for which it is not zero. In this thesis we study the dependence of the zero sets of eigenspinors of the Dirac operator on the Riemannian metric. We prove that on closed spin manifolds of dimension 2 or 3 for a generic Riemannian metric the non-harmonic eigenspinors have no zeros. Furthermore we prove that on closed spin manifolds of dimension 3 the mass endomorphism is not zero for a generic Riemannian metric.Comment: PhD thesis, 96 page

Recycling probability and dynamical properties of germinal center reactions

We introduce a new model for the dynamics of centroblasts and centrocytes in a germinal center. The model reduces the germinal center reaction to the elements considered as essential and embeds proliferation of centroblasts, point mutations of the corresponding antibody types represented in a shape space, differentiation to centrocytes, selection with respect to initial antigens, differentiation of positively selected centrocytes to plasma or memory cells and recycling of centrocytes to centroblasts. We use exclusively parameters with a direct biological interpretation such that, once determined by experimental data, the model gains predictive power. Based on the experiment of Han et al. (1995b) we predict that a high rate of recycling of centrocytes to centroblasts is necessary for the germinal center reaction to work reliably. Furthermore, we find a delayed start of the production of plasma and memory cells with respect to the start of point mutations, which turns out to be necessary for the optimization process during the germinal center reaction. The dependence of the germinal center reaction on the recycling probability is analyzed.Comment: 30 pages, 8 figure