2,901 research outputs found
Analytic Torsion on Hyperbolic Manifolds and the Semiclassical Approximation for Chern-Simons Theory
The invariant integration method for Chern-Simons theory for gauge group
SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation.
The semiclassical limit for the partition function associated with a connected
sum of hyperbolic 3-manifolds is presented. We discuss briefly L^2 - analytical
and topological torsions of a manifold with boundary.Comment: 12 pages, LaTeX fil
S5 0716+714 : GeV variability study
The GeV observations by Fermi-LAT give us the opportunity to characterize the
high-energy emission (100 MeV - 300 GeV) variability properties of the BL Lac
object S5 0716+714. In this study, we performed flux and spectral analysis of
more than 3 year long (August 2008 to April 2012) Fermi-LAT data of the source.
During this period, the source exhibits two different modes of flux variability
with characteristic timescales of ~75 and ~140 days, respectively. We also
notice that the flux variations are characterized by a weak spectral hardening.
The GeV spectrum of the source shows a clear deviation from a simple power law,
and is better explained by a broken power law. Similar to other bright Fermi
blazars, the break energy does not vary with the source flux during the
different activity states. We discuss several possible scenarios to explain the
observed spectral break.Comment: 21 pages, 10 figures, Accepted for publication in Advances in Space
Research journa
New holomorphically closed subalgebras of -algebras of hyperbolic groups
We construct dense, unconditional subalgebras of the reduced group
-algebra of a word-hyperbolic group, which are closed under holomorphic
functional calculus and possess many bounded traces. Applications to the cyclic
cohomology of group -algebras and to delocalized -invariants of
negatively curved manifolds are given
Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
This paper is devoted to a deeper understanding of the heat flow and to the
refinement of calculus tools on metric measure spaces (X,d,m). Our main results
are:
- A general study of the relations between the Hopf-Lax semigroup and
Hamilton-Jacobi equation in metric spaces (X,d).
- The equivalence of the heat flow in L^2(X,m) generated by a suitable
Dirichlet energy and the Wasserstein gradient flow of the relative entropy
functional in the space of probability measures P(X).
- The proof of density in energy of Lipschitz functions in the Sobolev space
W^{1,2}(X,d,m).
- A fine and very general analysis of the differentiability properties of a
large class of Kantorovich potentials, in connection with the optimal transport
problem.
Our results apply in particular to spaces satisfying Ricci curvature bounds
in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the
doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4,
Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop.
4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6
simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients,
still equivalent to all other ones, has been propose
A network-based ranking system for American college football
American college football faces a conflict created by the desire to stage
national championship games between the best teams of a season when there is no
conventional playoff system to decide which those teams are. Instead, ranking
of teams is based on their record of wins and losses during the season, but
each team plays only a small fraction of eligible opponents, making the system
underdetermined or contradictory or both. It is an interesting challenge to
create a ranking system that at once is mathematically well-founded, gives
results in general accord with received wisdom concerning the relative
strengths of the teams, and is based upon intuitive principles, allowing it to
be accepted readily by fans and experts alike. Here we introduce a
one-parameter ranking method that satisfies all of these requirements and is
based on a network representation of college football schedules.Comment: 15 pages, 3 figure
In vivo potassium MRI of the human heart
PURPOSE: Potassium ions (K(+)) play a critical role in cardiac electrophysiology, and changes in their concentration reflect pathophysiological processes related to cardiovascular diseases. Here, we investigated the feasibility of in vivo (39)K MRI of the human heart. To achieve this, we developed, evaluated, and applied a (39)K/(1)H RF coil, which is tailored for (39)K MRI of human heart at 7.0T. METHODS: The performance of the (39)K/(1)H RF coil was evaluated by electromagnetic field and specific absorption ratio simulations using 2 (male/female) human voxel models. The RF coil was evaluated at the bench and applied in an in vivo proof-of-principle study involving 7 healthy volunteers. The experiments were performed using a 7.0T whole-body MR system in conjunction with a 3D density-adapted projection reconstruction imaging technique. RESULTS: For in vivo (39)K MRI of the human heart, a nominal spatial resolution of 14.5 à 14.5 à 14.5 mm(3) within a total scan time of 30 min was achieved. The average SNR within the heart was 9.6 ± 2.4. CONCLUSION: This work validates the design of a (39)K/(1)H RF coil for cardiac MR at 7.0T and demonstrates for the first time in vivo the feasibility of (39)K MRI of the human heart
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