752 research outputs found
Generic metrics and the mass endomorphism on spin three-manifolds
Let be a closed Riemannian spin manifold. The constant term in the
expansion of the Green function for the Dirac operator at a fixed point is called the mass endomorphism in associated to the metric due to
an analogy to the mass in the Yamabe problem. We show that the mass
endomorphism of a generic metric on a three-dimensional spin manifold is
nonzero. This implies a strict inequality which can be used to avoid
bubbling-off phenomena in conformal spin geometry.Comment: 8 page
Manifolds with small Dirac eigenvalues are nilmanifolds
Consider the class of n-dimensional Riemannian spin manifolds with bounded
sectional curvatures and diameter, and almost non-negative scalar curvature.
Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of
the Dirac operator on such a manifold has small eigenvalues, then the
manifold is diffeomorphic to a nilmanifold and has trivial spin structure.
Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a
non-trivial spin structure, then there exists a uniform lower bound on the r-th
eigenvalue of the square of the Dirac operator. If a manifold with almost
nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume
is not too small, then we show that the metric is close to a Ricci-flat metric
on M with a parallel spinor. In dimension 4 this implies that M is either a
torus or a K3-surface
Dirac-harmonic maps from index theory
We prove existence results for Dirac-harmonic maps using index theoretical
tools. They are mainly interesting if the source manifold has dimension 1 or 2
modulo 8. Our solutions are uncoupled in the sense that the underlying map
between the source and target manifolds is a harmonic map.Comment: 26 pages, no figur
Die Regierungsreform im Bund : in kleinen Schritten und auf einem engen Pfad, Inkrementalismus und PfadabhÀngigkeit
Die Bestrebungen fĂŒr eine Regierungsreform in der Schweiz lassen sich weit zurĂŒckverfolgen, sie fĂŒhrten aber zu keinen weitreichenden Ănde-rungen betreffend das Regierungsorgan. HauptsĂ€chliche Folgen waren Verwaltungsreformen.
Schrittweise oder inkrementalistische Ănderungen sind feststellbar. Sie betreffen die sogenannte Organisationsgewalt, die Bundeskanzlei, die FĂŒhrungsstĂ€be, vor allem aber die StaatssekretĂ€rinnen und Staatssekre-tĂ€re.
Die Leitplanken und die Zusatzbotschaft aus dem Jahr 2010 des Bun-desrates fĂŒr eine Regierungsreform richten sich nach den Ergebnissen des Beitrages nach inkrementalistischen Entwicklungen aus. Mit der VerlĂ€ngerung der Amtsdauer der BundesprĂ€sidentin oder des Bundes-prĂ€sidenten könnte zudem ein neuer Entwicklungspfad begrĂŒndet wer-den. Dem aktuellen Reformanstoss werden auf Grund der verwendeten ErklĂ€rungsansĂ€tze erhöhte Chancen zugemessen.
Les efforts pour une réforme du gouvernement en Suisse remontent loin, mais ils n'ont pas abouti à des modifications de longue portée concernant l'organe gouvernemental. Les résultats principaux étaient des réformes de l'administration.
Des modifications graduelles ou incrĂ©mentales sont dĂ©tectables. Elles concernent le pouvoir d'organisation, la Chancellerie fĂ©dĂ©rale, les Ă©tats-majors, mais surtout les secrĂ©taires d'Ătat.
Les axes principaux et le message additionnel pour une réforme du gouvernement sont orientés vers les développements incrémentales constatés selon les recherches effectuées. L'allongement de la durée de fonction du président de la Confédération pourrait en plus constituer un nouveau chemin du développement. L'impulsion actuelle pour une réforme a des chances élevées d'aboutir selon les essais d'explication
The Dirac operator on untrapped surfaces
We establish a sharp extrinsic lower bound for the first eigenvalue of the
Dirac operator of an untrapped surface in initial data sets without apparent
horizon in terms of the norm of its mean curvature vector. The equality case
leads to rigidity results for the constraint equations with spherical boundary
as well as uniqueness results for constant mean curvature surfaces in Minkowski
space.Comment: 16 page
Quantum Link Models with Many Rishon Flavors and with Many Colors
Quantum link models are a novel formulation of gauge theories in terms of
discrete degrees of freedom. These degrees of freedom are described by quantum
operators acting in a finite-dimensional Hilbert space. We show that for
certain representations of the operator algebra, the usual Yang-Mills action is
recovered in the continuum limit. The quantum operators can be expressed as
bilinears of fermionic creation and annihilation operators called rishons.
Using the rishon representation the quantum link Hamiltonian can be expressed
entirely in terms of color-neutral operators. This allows us to study the large
N_c limit of this model. In the 't Hooft limit we find an area law for the
Wilson loop and a mass gap. Furthermore, the strong coupling expansion is a
topological expansion in which graphs with handles and boundaries are
suppressed.Comment: Lattice2001(theorydevelop), poster by O. Baer and talk by B.
Schlittgen, 6 page
Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms
We give a spinorial characterization of isometrically immersed surfaces of
arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For
Lorentzian surfaces, this generalizes a recent work of the first author in
to other Lorentzian space forms. We also characterize
immersions of Riemannian surfaces in these spaces. From this we can deduce
analogous results for timelike immersions of Lorentzian surfaces in space forms
of corresponding signature, as well as for spacelike and timelike immersions of
surfaces of signature (0,2), hence achieving a complete spinorial description
for this class of pseudo-Riemannian immersions.Comment: 9 page
Benchmarking CPUs and GPUs on embedded platforms for software receiver usage
Smartphones containing multi-core central processing units (CPUs) and powerful many-core graphics processing units (GPUs) bring supercomputing technology into your pocket (or into our embedded devices). This can be exploited to produce power-efficient, customized receivers with flexible correlation schemes and more advanced positioning techniques. For example, promising techniques such as the Direct Position Estimation paradigm or usage of tracking solutions based on particle filtering, seem to be very appealing in challenging environments but are likewise computationally quite demanding. This article sheds some light onto recent embedded processor developments, benchmarks Fast Fourier Transform (FFT) and correlation algorithms on representative embedded platforms and relates the results to the use in GNSS software radios. The use of embedded CPUs for signal tracking seems to be straight forward, but more research is required to fully achieve the nominal peak performance of an embedded GPU for FFT computation. Also the electrical power consumption is measured in certain load levels.Peer ReviewedPostprint (published version
Calabi-Yau cones from contact reduction
We consider a generalization of Einstein-Sasaki manifolds, which we
characterize in terms both of spinors and differential forms, that in the real
analytic case corresponds to contact manifolds whose symplectic cone is
Calabi-Yau. We construct solvable examples in seven dimensions. Then, we
consider circle actions that preserve the structure, and determine conditions
for the contact reduction to carry an induced structure of the same type. We
apply this construction to obtain a new hypo-contact structure on S^2\times
T^3.Comment: 30 pages; v2: typos corrected, presentation improved, one reference
added. To appear in Ann. Glob. Analysis and Geometr
Spectral Bounds for Dirac Operators on Open Manifolds
We extend several classical eigenvalue estimates for Dirac operators on
compact manifolds to noncompact, even incomplete manifolds. This includes
Friedrich's estimate for manifolds with positive scalar curvature as well as
the author's estimate on surfaces.Comment: pdflatex, 14 pages, 3 figure
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