20,832 research outputs found
Progress on Hardy-type Inequalities
This paper surveys some of our recent progress on Hardy-type inequa\-lities
which consist of a well-known topic in Harmonic Analysis. In the first section,
we recall the original probabilistic motivation dealing with the stability
speed in terms of the -theory. A crucial application of a result by
Fukushima and Uemura (2003) is included. In the second section, the non-linear
case (a general Hardy-type inequality) is handled with a direct and analytic
proof. In the last section, it is illustrated that the basic estimates
presented in the first two sections can still be improved considerably.Comment: 13 pages, 5 figures, Festschrift Masatoshi Fukushima: In Honor of
Masatoshi Fukushima's Sanju. World Scientific, 201
Models of Neutrino Masses and Mixing
Neutrino physics has entered an era of precision measurements. With these
precise measurements, we may be able to distinguish different models that have
been constructed to explain the small neutrino masses and the large mixing
among them. In this talk, I review some of the existing theoretical models and
their predictions for neutrino oscillations.Comment: Talk presented at the 2nd International Colliders to Cosmic Rays
Conference (C2CR07), Lake Tahoe, CA, February 25 - March 1, 2007; 8 pages; 2
figure
General estimate of the first eigenvalue on manifolds
Ten sharp lower estimates of the first non-trivial eigenvalue of Laplacian on
compact Riemannian manifolds are reviewed and compared. An improved variational
formula, a general common estimate, and a new sharp one are added. The best
lower estimates are now updated. The new estimates provide a global picture of
what one can expect by our approach.Comment: 19 page
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