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

Determination of complex dielectric functions of ion implanted and implanted‐annealed amorphous silicon by spectroscopic ellipsometry

Measuring with a spectroscopic ellipsometer (SE) in the 1.8–4.5 eV photon energy region we determined the complex dielectric function (ϵ = ϵ1 + iϵ2) of different kinds of amorphous silicon prepared by self‐implantation and thermal relaxation (500 °C, 3 h). These measurements show that the complex dielectric function (and thus the complex refractive index) of implanted a‐Si (i‐a‐Si) differs from that of relaxed (annealed) a‐Si (r‐a‐Si). Moreover, its ϵ differs from the ϵ of evaporated a‐Si (e‐a‐Si) found in the handbooks as ϵ for a‐Si. If we use this ϵ to evaluate SE measurements of ion implanted silicon then the fit is very poor. We deduced the optical band gap of these materials using the Davis–Mott plot based on the relation: (ϵ2E2)1/3 ∼ (E− Eg). The results are: 0.85 eV (i‐a‐Si), 1.12 eV (e‐a‐Si), 1.30 eV (r‐a‐Si). We attribute the optical change to annihilation of point defects

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

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

Mouse spleen lymphoblasts generated in vitro: Recovery in high yield and purity after floatation in dense bovine plasma albumin solutions*

[No abstract available

The Axial Anomaly in D=3+1 Light-Cone QED

We consider $(3+1)$-dimensional, Dirac electrons of arbitrary mass, propagating in the presence of electric and magnetic fields which are both parallel to the $x^3$ axis. The magnetic field is constant in space and time whereas the electric field depends arbitrarily upon the light-cone time parameter $x^+ = (x^0 + x^3)/\sqrt{2}$. We present an explicit solution to the Heisenberg equations for the electron field operator in this background. The electric field results in the creation of electron-positron pairs. We compute the expectation values of the vector and axial vector currents in the presence of a state which is free vacuum at $x^+ = 0$. Both current conservation and the standard result for the axial vector anomaly are verified for the first time ever in $(3+1)$-dimensional light-cone QED. An interesting feature of our operator solution is the fact that it depends in an essential way upon operators from the characteristic at $x^- = -L$, in addition to the usual dependence upon operators at $x^+ = 0$. This dependence survives even in the limit of infinite $L$. Ignoring the $x^-$ operators leads to a progressive loss of unitarity, to the violation of current conservation, to the loss of renormalizability, and to an incorrect result for the axial vector anomaly.Comment: 31 pages, LaTeX 2 epsilon, no figures, some typoes corrected for publicatio

S-DIMM+ height characterization of day-time seeing using solar granulation

To evaluate site quality and to develop multi-conjugative adaptive optics systems for future large solar telescopes, characterization of contributions to seeing from heights up to at least 12 km above the telescope is needed. We describe a method for evaluating contributions to seeing from different layers along the line-of-sight to the Sun. The method is based on Shack Hartmann wavefront sensor data recorded over a large field-of-view with solar granulation and uses only measurements of differential image displacements from individual exposures, such that the measurements are not degraded by residual tip-tilt errors. We conclude that the proposed method allows good measurements when Fried's parameter r_0 is larger than about 7.5 cm for the ground layer and that these measurements should provide valuable information for site selection and multi-conjugate development for the future European Solar Telescope. A major limitation is the large field of view presently used for wavefront sensing, leading to uncomfortably large uncertainties in r_0 at 30 km distance.Comment: Accepted by AA 22/01/2010 (12 pages, 11 figures

Morphological Evolution and the Ages of Early-Type Galaxies in Clusters

Morphological and spectroscopic studies of high redshift clusters indicate that a significant fraction of present-day early-type galaxies was transformed from star forming galaxies at z<1. On the other hand, the slow luminosity evolution of early-type galaxies and the low scatter in their color-magnitude relation indicate a high formation redshift of their stars. In this paper we construct models which reconcile these apparently contradictory lines of evidence, and we quantify the effects of morphological evolution on the observed photometric properties of early-type galaxies in distant clusters. We show that in the case of strong morphological evolution the apparent luminosity and color evolution of early-type galaxies are similar to that of a single age stellar population formed at z=infinity, irrespective of the true star formation history of the galaxies. Furthermore, the scatter in age, and hence the scatter in color and luminosity, is approximately constant with redshift. These results are consequences of the ``progenitor bias'': the progenitors of the youngest low redshift early-type galaxies drop out of the sample at high redshift. We construct models which reproduce the observed evolution of the number fraction of early-type galaxies in rich clusters and their color and luminosity evolution simultaneously. Our modelling indicates that approx. 50% of early-type galaxies were transformed from other galaxy types at z<1, and their progenitor galaxies may have had roughly constant star formation rates prior to morphological transformation. After correcting the observed evolution of the mean M/L_B ratio for the maximum progenitor bias we find that the mean luminosity weighted formation redshift of stars in early-type galaxies z_*=2.0^{+0.3}_{-0.2} for Omega_m=0.3 and Omega_Lambda=0.7. [ABRIDGED]Comment: Accepted for publication in The Astrophysical Journal. 13 pages, 6 figure