Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory

Equations for determining aircraft motions for accident data

Procedures for determining a comprehensive accident scenario from a limited data set are reported. The analysis techniques accept and process data from either an Air Traffic Control radar tracking system or a foil flight data recorder. Local meteorological information at the time of the accident and aircraft performance data are also utilized. Equations for the desired aircraft motions and forces are given in terms of elements of the measurement set and certain of their time derivatives. The principal assumption made is that aircraft side force and side-slip angle are negligible. An estimation procedure is outlined for use with each data source. For the foil case, a discussion of exploiting measurement redundancy is given. Since either formulation requires estimates of measurement time derivatives, an algorithm for least squares smoothing is provided

Europe-Afrique : des acteurs en quête de scénarios

With the marginalization of Africa in international trade, previous models for operationalizing relations with Europe have become obsolete. There is increasingly a trend towards uncoupling between North Africa, the Republic of South Africa, and Black Africa. North Africa has broken away to the point of regarding itself as a hinterland of Europe. South Africa is likely to become both a crossroads and a transit point in trade between Europe, Africa, and the Pacific region. In Black Africa, the only current scenarios for reconnection with the rest of the world seem to amount to pointing out this subregion's capability to do harm if it were ever abandoned

Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, $e^2$, and the ultra-violet cut-off, $\Lambda$, and for all nuclear charges less than the critical charge without radiation field, $Z_c=e^{-2}2/(2/\pi+\pi/2)$. We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of $e^2$ and $\Lambda$ and for nuclear charges less than $e^{-2}2/\pi$.Comment: 37 page

Nigeria's "manifest destiny" in West Africa: dominance without power

"Ever since independence, messianic references to a natural Nigerian leadership in the affairs of the African continent have been ingrained in the conduct of Nigeria's foreign policy. Internationally, Nigeria's endowments of human and natural resources, deeply asymmetrical interactions with neighboring states and the active engagement of successive regimes in the affairs of the continent have called for the country's treatment as a regional power and a pivotal state for West Africa. However, Nigeria's 'manifest destiny' remains more about influence than power. The country's unsteady projection of structural or relational power starkly contrasts with the deep regional imprint left by trans-frontier networks that focus on Nigeria but operate independently of territorial affiliations. The related regionalization process exacerbates the fluidity and fragility of region-building as much as problems of statehood and governance within Nigeria." (author's abstract

Europe Within the World of Regionalisms

The surge of diversified forms of regionalism and regional integration within the past few decades has stimulated the reappraisal of the conceptual tools traditionally designed to bench-mark and monitor region-building processes across the world. More recently, the Brexit negotiations have become a reminder that the EU remains an unfolding experience. This article argues that the study of African regionalisms constitutes a timely invitation to revisit the experience of the EU and its contribution to the world of regionalisms. After a brief survey of the classic definition of the region, we will discuss the ongoing relevance of European integration and the implications of the analytical distinction between regionalism, regionalisation and regional integration, before drawing from the study of Africa five threads which set the basis for a comparative study of regions and regionalisms beyond the classic emphasis on the EU or the world of regions