12,695 research outputs found
Uniqueness and examples of compact toric Sasaki-Einstein metrics
In [11] it was proved that, given a compact toric Sasaki manifold of positive
basic first Chern class and trivial first Chern class of the contact bundle,
one can find a deformed Sasaki structure on which a Sasaki-Einstein metric
exists. In the present paper we first prove the uniqueness of such Einstein
metrics on compact toric Sasaki manifolds modulo the action of the identity
component of the automorphism group for the transverse holomorphic structure,
and secondly remark that the result of [11] implies the existence of compatible
Einstein metrics on all compact Sasaki manifolds obtained from the toric
diagrams with any height, or equivalently on all compact toric Sasaki manifolds
whose cones have flat canonical bundle. We further show that there exists an
infinite family of inequivalent toric Sasaki-Einstein metrics on for each positive integer .Comment: Statements of the results are modifie
Twisted topological structures related to M-branes II: Twisted Wu and Wu^c structures
Studying the topological aspects of M-branes in M-theory leads to various
structures related to Wu classes. First we interpret Wu classes themselves as
twisted classes and then define twisted notions of Wu structures. These
generalize many known structures, including Pin^- structures, twisted Spin
structures in the sense of Distler-Freed-Moore, Wu-twisted differential
cocycles appearing in the work of Belov-Moore, as well as ones introduced by
the author, such as twisted Membrane and twisted String^c structures. In
addition, we introduce Wu^c structures, which generalize Pin^c structures, as
well as their twisted versions. We show how these structures generalize and
encode the usual structures defined via Stiefel-Whitney classes.Comment: 20 page
Hypersensitivity Lung Disease in the Turkey Raising Industry
journal articleBiomedical Informatic
Ultraslow propagation of matched pulses by four-wave mixing in an atomic vapor
We have observed the ultraslow propagation of matched pulses in nondegenerate
four-wave mixing in a hot atomic vapor. Probe pulses as short as 70 ns can be
delayed by a tunable time of up to 40 ns with little broadening or distortion.
During the propagation, a probe pulse is amplified and generates a conjugate
pulse which is faster and separates from the probe pulse before getting locked
to it at a fixed delay. The precise timing of this process allows us to
determine the key coefficients of the susceptibility tensor. The presence of
gain in this system makes this system very interesting in the context of
all-optical information processing.Comment: 5 pages, 4 figure
Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation
By numerical calculation, the Planck spectrum with zero-point radiation is
shown to satisfy a natural maximum-entropy principle whereas alternative
choices of spectra do not. Specifically, if we consider a set of
conducting-walled boxes, each with a partition placed at a different location
in the box, so that across the collection of boxes the partitions are uniformly
spaced across the volume, then the Planck spectrum correspond to that spectrum
of random radiation (having constant energy kT per normal mode at low
frequencies and zero-point energy (1/2)hw per normal mode at high frequencies)
which gives maximum uniformity across the collection of boxes for the radiation
energy per box. The analysis involves Casimir energies and zero-point radiation
which do not usually appear in thermodynamic analyses. For simplicity, the
analysis is presented for waves in one space dimension.Comment: 11 page
Incremental Distance Transforms (IDT)
A new generic scheme for incremental implementations of distance transforms (DT) is presented: Incremental Distance Transforms (IDT). This scheme is applied on the cityblock, Chamfer, and three recent exact Euclidean DT (E2DT). A benchmark shows that for all five DT, the incremental implementation results in a significant speedup: 3.4×−10×. However, significant differences (i.e., up to 12.5×) among the DT remain present. The FEED transform, one of the recent E2DT, even showed to be faster than both city-block and Chamfer DT. So, through a very efficient incremental processing scheme for DT, a relief is found for E2DT’s computational burden
New Results in Sasaki-Einstein Geometry
This article is a summary of some of the author's work on Sasaki-Einstein
geometry. A rather general conjecture in string theory known as the AdS/CFT
correspondence relates Sasaki-Einstein geometry, in low dimensions, to
superconformal field theory; properties of the latter are therefore reflected
in the former, and vice versa. Despite this physical motivation, many recent
results are of independent geometrical interest, and are described here in
purely mathematical terms: explicit constructions of infinite families of both
quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry;
an extremal problem that determines the Reeb vector field for, and hence also
the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the
existence of Sasaki-Einstein metrics. Some of these results also provide new
insights into Kahler geometry, and in particular new obstructions to the
existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the
conference "Riemannian Topology: Geometric Structures on Manifolds"; minor
typos corrected, reference added; published version; Riemannian Topology and
Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov
2008
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