The characteristic Cauchy problem for Dirac fields on curved backgrounds

On arbitrary spacetimes, we study the characteristic Cauchy problem for Dirac fields on a light-cone. We prove the existence and uniqueness of solutions in the future of the light-cone inside a geodesically convex neighbourhood of the vertex. This is done for data in $L^2$ and we give an explicit definition of the space of data on the light-cone producing a solution in $H^1$. The method is based on energy estimates following L. H\"ormander (J.F.A. 1990). The data for the characteristic Cauchy problem are only a half of the field, the other half is recovered from the characteristic data by integration of the constraints, consisting of the restriction of the Dirac equation to the cone. A precise analysis of the dynamics of light rays near the vertex of the cone is done in order to understand the integrability of the constraints; for this, the Geroch-Held-Penrose formalism is used.Comment: 39 pages. An error in lemma 3.1 in the first version has been corrected. Moreover, the treatment of the constraints (restriction of the equations to the null cone) has been considerably extended and is now given in full details. To appear in Journal of Hyperbolic Differential Equation

Jens Bartelson: Sovereignty as Symbolic Form (= Critical Issues in Global Politics,vol. 6), London:: Routledge Publishing 2014, 134 S.

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Disentangling the Regionalization of Law Enforcement in Southern Africa

Dieser Artikel trägt zu der sich stets erweiternden Literatur im Bereich der neuen Regionalismen in zweifacher Hinsicht bei: Zunächst wird die überregionale Polizeikooperation als bisher vernachlässigte Fachrichtung in der Regionalisierungsforschung herausgestellt. Am Beispiel der Southern African Regional Police Chiefs Cooperation Organization (SARPCCO) wird die Regionalisierung der Polizeiarbeit im südlichen Afrika erklärt, die im Zuge einer verstärkt wahrgenommen Globalisierung von Kriminalität in den 990er Jahren entstanden ist. Anschließend werden die Portale der Globalisierung als methodisches Hilfsmittel zur Untersuchung von Regionalisierungsprozessen miteinbezogen. Damit lassen sich konkrete Akteure, Orte und Räume identiizieren und Rückschlüsse auf die Gestaltung von Regionalisierung auf mehreren Ebenen ziehen, was der vertieften Analyse der SARPCCO zuträglich ist.This article contributes to the growing literature on new regionalism(s) in two ways: It irst exposes regional police cooperation as a neglected subject area in the study of regionalism/regionalization. The case of the emergence of the Southern African Regional Police Chiefs Cooperation Organization (SARPCCO) is used to contextualize the regionalization of policing in relation to a perceived globalization of crime since the 990s. The article then introduces the framework portals of globalization as a methodological tool to study processes of regionalization. The framework is used to deepen the analysis of SARPCCO by helping to more concretely identify the actors, places, and spaces in and through which regionalization, as a multi-actor and multilevel process, takes place

Hadamard Powers and Kernel Perceptrons

We study a relation between Hadamard powers and polynomial kernel perceptrons. The rank of Hadamard powers for the special case of a Boolean matrix and for the generic case of a real matrix is computed explicitly. These results are interpreted in terms of the classification capacities of perceptrons.Comment: 12 page

Existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the De Sitter-Kerr-Newman metric

We show the existence of exponentially growing finite energy solutions for the charged Klein-Gordon equation on the De Sitter-Kerr-Newman metric for small charge and mass of the field and small angular momentum of the black hole. The mechanism behind is that the zero resonance that exists for zero charge, mass and angular momentum moves into the upper half plane

A new direct technique for visualizing and measuring gas–liquid mass transfer around bubbles moving in a straight millimetric square channel

The present paper focuses on the local characterization of gas–liquid mass transfer in a straight millimetric square channel, as constituting the preliminary step required for performing gas–liquid reactions in such devices. For this purpose, a new colourimetric technique using an oxygen sensitive dye was developed. It was based on the reduction of a colourimetric indicator in presence of oxygen, this reduction being catalysed by sodium hydroxide and glucose. In this study, resazurin was selected as the colourimetric indicator as it offered various reduced forms, the colours of which ranged from colourless (without oxygen) to pink (when oxygen was present). Thus the mass transfer around bubbles flowing in a straight millimetric square channel could be visualized in space and time. Some pictures were recorded by a monochromatic CCD high speed camera and, after post-processing, the shape, size and velocity of the bubbles, and the grey-level maps around them were measured. A calculation method was also developed to determine the transferred oxygen fluxes around the bubbles and the associated liquid-side mass transfer coefficients. The results compared satisfactorily with global measurements made using oxygen microsensors (Roudet et al., 2011. Hydrodynamics and mass transfer in inertial gas–liquid flow regimes through straigth and meandering millimetric square channels. Chem. Eng. Sci. 66, 2974–2990). This study constitutes a striking example of how interesting a tool this new colourimetric method could be for investigating gas–liquid mass transfer in transparent fluids with a view to quick millireactor design

Scattering theory for Dirac fields inside a Reissner-Nordstr\"om-type black hole

We show asymptotic completeness for the massive charged Dirac equation between the black hole and Cauchy horizons of a sub-extremal ((Anti-) De Sitter) Reissner-Nordstr\"om black hole.Comment: 18 pages, 1 figur