5,280 research outputs found
Alternating groups and moduli space lifting Invariants
Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S
Behavior of self-propelled acetone droplets in a Leidenfrost state on liquid substrates
It is demonstrated that non-coalescent droplets of acetone can be formed on
liquid substrates. The fluid flows around and in an acetone droplet hovering on
water are recorded to shed light on the mechanisms which might lead to
non-coalescence. For sufficiently low impact velocities, droplets undergo a
damped oscillation on the surface of the liquid substrate but at higher
velocities clean bounce-off occurs. Comparisons of experimentally observed
static configurations of floating droplets to predictions from a theoretical
model for a small non-wetting rigid sphere resting on a liquid substrate are
made and a tentative strategy for determining the thickness of the vapor layer
under a small droplet on a liquid is proposed. This strategy is based on the
notion of effective surface tension. The droplets show self-propulsion in
straight line trajectories in a manner which can be ascribed to a Marangoni
effect. Surprisingly, self-propelled droplets can become immersed beneath the
undisturbed water surface. This phenomenon is reasoned to be drag-inducing and
might provide a basis for refining observations in previous work
Optical propagation measurements at Emerson Lake, 1968
Optical propagation measurements in inhomogeneous atmosphere at Emerson Lake, California for optical propagation theory validity testin
Two-body effects in the decay rate of atomic levels
Recoil corrections to the atomic decay rate are considered in the order of
Zm/M . The expressions are treated exactly without any expansion over Z alpha.
The expressions obtained are valid both for muonic atoms (for which they
contribute on the level of a few percent in high Z ions) and for electronic
atoms. Explicit results for Lyman-alpha transitions for low-Z of the order
(Zm/M)(Z alpha)^2 are also presented.Comment: 5 pages, 1 table, email: [email protected]
A Side of Mercury Not Seen By Mariner 10
More than 60,000 images of Mercury were taken at ~29 deg elevation during two
sunrises, at 820 nm, and through a 1.35 m diameter off-axis aperture on the
SOAR telescope. The sharpest resolve 0.2" (140 km) and cover 190-300 deg
longitude -- a swath unseen by the Mariner 10 spacecraft -- at complementary
phase angles to previous ground-based optical imagery. Our view is comparable
to that of the Moon through weak binoculars. Evident are the large crater
Mozart shadowed on the terminator, fresh rayed craters, and other albedo
features keyed to topography and radar reflectivity, including the putative
huge ``Basin S'' on the limb. Classical bright feature Liguria resolves across
the northwest boundary of the Caloris basin into a bright splotch centered on a
sharp, 20 km diameter radar crater, and is the brightest feature within a
prominent darker ``cap'' (Hermean feature Solitudo Phoenicis) that covers the
northern hemisphere between longitudes 140-250 deg. The cap may result from
space weathering that darkens via a magnetically enhanced flux of the solar
wind, or that reddens low latitudes via high solar insolation.Comment: 7 pages, 4 PDF figures, pdfLaTeX, typos corrected, Fig. 2 modified
slightly to add crater diameters not given in published versio
Nonlocal spectral properties of disordered alloys
A general method is proposed for calculating a fully k-dependent, continuous,
and causal spectral function A(k,E) within the recently introduced nonlocal
version of the coherent-potential approximation (NLCPA). The method involves
the combination of both periodic and anti-periodic solutions to the associated
cluster problem and also leads to correct bulk quantities for small cluster
sizes. We illustrate the method by investigating the Fermi surface of a
two-dimensional alloy. Dramatically, we find a smeared electronic topological
transition not predicted by the conventional CPA.Comment: 17 pages, 5 figures, Submitted to: J. Phys.: Condens. Matter
Editorial receipt 25 May 200
Stimulated Raman spin coherence and spin-flip induced hole burning in charged GaAs quantum dots
High-resolution spectral hole burning (SHB) in coherent nondegenerate
differential transmission spectroscopy discloses spin-trion dynamics in an
ensemble of negatively charged quantum dots. In the Voigt geometry, stimulated
Raman spin coherence gives rise to Stokes and anti-Stokes sidebands on top of
the trion spectral hole. The prominent feature of an extremely narrow spike at
zero detuning arises from spin population pulsation dynamics. These SHB
features confirm coherent electron spin dynamics in charged dots, and the
linewidths reveal spin spectral diffusion processes.Comment: 5 pages, 5 figure
An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images
Adaptive optics (AO) systems have significantly improved astronomical imaging
capabilities over the last decade, and are revolutionizing the kinds of science
possible with 4-5m class ground-based telescopes. A thorough understanding of
AO system performance at the telescope can enable new frontiers of science as
observations push AO systems to their performance limits. We look at recent
advances with wave front reconstruction (WFR) on the Advanced Electro-Optical
System (AEOS) 3.6 m telescope to show how progress made in improving WFR can be
measured directly in improved science images. We describe how a "waffle mode"
wave front error (which is not sensed by a Fried geometry Shack-Hartmann wave
front sensor) affects the AO point-spread function (PSF). We model details of
AEOS AO to simulate a PSF which matches the actual AO PSF in the I-band, and
show that while the older observed AEOS PSF contained several times more waffle
error than expected, improved WFR techniques noticeably improve AEOS AO
performance. We estimate the impact of these improved WFRs on H-band imaging at
AEOS, chosen based on the optimization of the Lyot Project near-infrared
coronagraph at this bandpass.Comment: 15 pages, 11 figures, 1 table; to appear in PASP, August 200
Mimicking Behaviors in Separated Domains
Devising a strategy to make a system mimic behaviors from another system is a problem that naturally arises in many areas of Computer Science. In this work, we interpret this problem in the context of intelligent agents, from the perspective of LTLf , a formalism commonly used in AI for expressing finite-trace properties. Our model consists of two separated dynamic domains, DA and DB , and an LTLf specification that formalizes the notion of mimicking by mapping properties on behaviors (traces) of DA into properties on behaviors of DB . The goal is to synthesize a strategy that step-by-step maps every behavior of DA into a behavior of DB so that the specification is met. We consider several forms of mapping specifications, ranging from simple ones to full LTLf , and for each, we study synthesis algorithms and computational properties
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