258 research outputs found
Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies
Let K \subset R^N be a convex body containing the origin. A measurable set G
\subset R^N with positive Lebesgue measure is said to be uniformly K-dense if,
for any fixed r > 0, the measure of G \cap (x + rK) is constant when x varies
on the boundary of G (here, x + rK denotes a translation of a dilation of K).
We first prove that G must always be strictly convex and at least C1,1-regular;
also, if K is centrally symmetric, K must be strictly convex, C1,1-regular and
such that K = G - G up to homotheties; this implies in turn that G must be
C2,1- regular. Then for N = 2, we prove that G is uniformly K-dense if and only
if K and G are homothetic to the same ellipse. This result was already proven
by Amar, Berrone and Gianni in [3]. However, our proof removes their regularity
assumptions on K and G and, more importantly, it is susceptible to be
generalized to higher dimension since, by the use of Minkowski's inequality and
an affine inequality, avoids the delicate computations of the higher-order
terms in the Taylor expansion near r = 0 for the measure of G\cap(x+rK) (needed
in [3])
Theoretical study of dark resonances in micro-metric thin cells
We investigate theoretically dark resonance spectroscopy for a dilute atomic
vapor confined in a thin (micro-metric) cell. We identify the physical
parameters characterizing the spectra and study their influence. We focus on a
Hanle-type situation, with an optical irradiation under normal incidence and
resonant with the atomic transition. The dark resonance spectrum is predicted
to combine broad wings with a sharp maximum at line-center, that can be singled
out when detecting a derivative of the dark resonance spectrum. This narrow
signal derivative, shown to broaden only sub-linearly with the cell length, is
a signature of the contribution of atoms slow enough to fly between the cell
windows in a time as long as the characteristic ground state optical pumping
time. We suggest that this dark resonance spectroscopy in micro-metric thin
cells could be a suitable tool for probing the effective velocity distribution
in the thin cell arising from the atomic desorption processes, and notably to
identify the limiting factors affecting desorption under a grazing incidence.Comment: 12 pages, 11 figures theoretical articl
Valuations on lattice polytopes
This survey is on classification results for valuations defined on lattice polytopes that intertwine the special linear group over the integers. The basic real valued valuations, the coefficients of the Ehrhart polynomial, are introduced and their characterization by Betke and Kneser is discussed. More recent results include classification theorems for vector and convex body valued valuations. © Springer International Publishing AG 2017
Basic Atomic Physics
Contains reports on five research projects.National Science Foundation Grant PHY 89-19381U.S. Navy - Office of Naval Research Grant N00014-90-J-1322Joint Services Electronics Program Contract DAAL03-89-C-0001National Science Foundation Grant PHY 86-05893U.S. Army Research Office Contract DAAL03-89-K-0082U.S. Navy - Office of Naval Research Grant N00014-89-J-1207U.S. Navy - Office of Naval Research Grant N00014-90-J-164
The Early Days of Research on Carbonic Anhydrase
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73862/1/j.1749-6632.1984.tb12310.x.pd
- …