1,379 research outputs found
Full blow-up range for co-rotaional wave maps to surfaces of revolution
We construct blow-up solutions of the energy critical wave map equation on
with polynomial blow-up rate ( for
blow-up at ) in the case when is a surface of revolution.
Here we extend the blow-up range found by C\^arstea () based on
the work by Krieger, Schlag and Tataru to . This work relies on and
generalizes the recent result of Krieger and the author where the target
manifold is chosen as the standard sphere
Optimal polynomial blow up range for critical wave maps
We prove that the critical Wave Maps equation with target and origin
admits energy class blow up solutions of the form
where is the
ground state harmonic map and for any . This
extends the work [13], where such solutions were constructed under the
assumption . In light of a result of Struwe [22], our result is
optimal for polynomial blow up rates
A Universal Constraint on the Infrared Behavior of the Ghost Propagator in QCD
With proposing a unified description of the fields variation at the level of
generating functional, we obtain a new identity for the quark-gluon interaction
vertex based on gauge symmetry, which is similar to the Slavnov-Taylor
Identities(STIs) based on the Becchi-Rouet-Stora-Tyutin transformation. With
these identities, we find that in Landau gauge, the dressing function of the
ghost propagator approaches to a constant as its momentum goes to zero, which
provides a strong constraint on the infrared behaviour of ghost propagator.Comment: 4 pages, no figur
Volatility, valuation ratios, and bubbles: an empirical measure of market sentiment
We define a sentiment indicator based on option prices, valuation ratios, and interest rates. The indicator can be interpreted as a lower bound on the expected growth in fundamentals that a rational investor would have to perceive to be happy to hold the market. The bound was unusually high in the late 1990s, reflecting dividend growth expectations that in our view were unreasonably optimistic. Our approach exploits two key ingredients. First, we derive a new valuation ratio decomposition that is related to the Campbell–Shiller loglinearization but that resembles the Gordon growth model more closely and has certain other advantages. Second, we introduce a volatility index that provides a lower bound on the market's expected log return
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