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