Deciding logics of linear Kripke frames with scattered end pieces

We show that logics based on linear Kripke frames – with or without constant domains – that have a scattered end piece are not recursively enumerable.This is done by reduction to validity in all finite classical models

How unprovable is Rabin's decidability theorem?

We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical core of typical proofs of Rabin's theorem, is equivalent over the moderately strong second-order arithmetic theory $\mathsf{ACA}_0$ to a determinacy principle implied by the positional determinacy of all parity games and implying the determinacy of all Gale-Stewart games given by boolean combinations of ${\bf \Sigma^0_2}$ sets. It follows that complementation for tree automata is provable from $\Pi^1_3$- but not $\Delta^1_3$-comprehension. We then use results due to MedSalem-Tanaka, M\"ollerfeld and Heinatsch-M\"ollerfeld to prove that over $\Pi^1_2$-comprehension, the complementation theorem for tree automata, decidability of the MSO theory of the infinite binary tree, positional determinacy of parity games and determinacy of $\mathrm{Bool}({\bf \Sigma^0_2})$ Gale-Stewart games are all equivalent. Moreover, these statements are equivalent to the $\Pi^1_3$-reflection principle for $\Pi^1_2$-comprehension. It follows in particular that Rabin's decidability theorem is not provable in $\Delta^1_3$-comprehension.Comment: 21 page

Microfabricated high-finesse optical cavity with open access and small volume

We present a microfabricated optical cavity, which combines a very small mode volume with high finesse. In contrast to other micro-resonators, such as microspheres, the structure we have built gives atoms and molecules direct access to the high-intensity part of the field mode, enabling them to interact strongly with photons in the cavity for the purposes of detection and quantum-coherent manipulation. Light couples directly in and out of the resonator through an optical fiber, avoiding the need for sensitive coupling optics. This renders the cavity particularly attractive as a component of a lab-on-a-chip, and as a node in a quantum network

Proton spin relaxation in dilute methane gas: A symmetrized theory and its experimental verification

Nuclear spin relaxation in low density methane gas is investigated theoretically and experimentally. A theory is developed in which full account is taken of the tetrahedral symmetry of the molecule. For a nuclear Larmor frequency of 30 MHz, the time evolution of the nonequilibrium magnetization is measured as a function of density between approximately 0.005 and 17 amagats at temperatures of 110, 150, and 295 K. In all cases, exponential relaxation is observed. By using the theory in conjunction with the known spin rotation constants and rotational energy levels of CH4, the measured values of the relaxation rate R1 have been fit very well at each temperature, both for the maximum value of R1 which contains no adjustable parameters and for the density dependence of R1 which contains a single parameter taken to be the collision cross section for molecular reorientation. The centrifugal distortion splittings of the rotational levels are shown to have an important influence on the observed values of R1 at 30 MHz and. more generally on the dependence of the time evolution of the nonequilibrium magnetization on density and frequency. On the basis of the theory, a new type of \u27relaxation rate spectroscopy\u27 is proposed. Non-exponential relaxation is predicted to occur at low densities when the nuclear Larmor frequency is tuned to a centrifugal distortion splitting

A Hard Medium Survey with ASCA. IV: the Radio-Loud Type 2 QSO AXJ0843+294 2

We discuss the X-ray, optical and radio properties of AX J0843+2942, a high luminosity Type 2 AGN found in the ASCA Hard Serendipitous Survey. The X-ray spectrum is best described by an absorbed power-law model with photon index of Gamma = 1.72 (+0.3 -0.6) and intrinsic absorbing column density of NH = 1.44 (+0.33 -0.52) x 10E23 cm-2. The intrinsic luminosity in the 0.5-10 keV energy band is ~ 3x10E45 erg s-1, well within the range of quasar luminosities. AX J0843+2942, positionally coincident with the core of a triple and strong (S_1.4 GHz ~ 1 Jy; P_1.4 GHz ~ 9 x 10E33 erg s-1 Hz-1) radio source, is spectroscopically identified with a Narrow Line object (intrinsic FWHM of all the permitted emission lines <= 1200 km s-1) at z=0.398, having line features and ratios typical of Seyfert-2 like objects. The high X-ray luminosity, coupled with the high intrinsic absorption, the optical spectral properties and the radio power, allow us to propose AX J0843+2942 as a Radio-Loud "Type 2 QSO". A discussion of the SED of this object is presented here together with a comparison with the SED of Ultra Luminous Infrared Galaxies, other "Type 2 QSO" candidates from the literature, and "normal" Radio-Quiet and Radio-Loud QSOs.Comment: 10 pages, 7 figures, Latex manuscript, Accepted for publication in Ast ronomy and Astrophysic

Methyl and T-Butyl Group Reorientation in Planar Aromatic Solids: Low-Frequency Nuclear Magnetic Resonance Relaxometry and X-Ray Diffraction

We have synthesized 3-t-butylchrysene and measured the Larmor frequency omega/2pi (= 8.50, 22.5, and 53.0 MHz) and temperature T (110-310 K) dependence of the proton spin-lattice relaxation rate R in the polycrystalline solid [low-frequency solid state nuclear magnetic resonance (NMR) relaxometry]. We have also determined the molecular and crystal structure in a single crystal of 3-t-butylchrysene using x-ray diffraction, which indicates the presence of a unique t-butyl group environment. The spin-1/2 protons relax as a result of the spin-spin dipolar interactions being modulated by the superimposed reorientation of the t-butyl groups and their constituent methyl groups. The reorientation is successfully modeled by the simplest motion; that of random hopping describable by Poisson statistics. The x-ray data indicate near mirror-plane symmetry that places one methyl group nearly in the aromatic plane and the other two almost equally above and below the plane. The NMR relaxometry data indicate that the nearly in-plane methyl group and the entire t-butyl group reorient with a barrier of 24.2 +/- 0.9 kJ mol(-1), and the two out-of-plane methyl groups reorient with a barrier of 14.2 +/- 0.6 kJ mol(-1). Following a brief review of methyl group rotation in simple ethyl-, and isopropyl-substituted one- and two-ring aromatic van der Waals molecular solids, the barriers for the out-of-plane methyl groups and the t-butyl group in 3-t-butylchrysene are compared with those barriers in three related molecular solids whose crystal structure is known: 4-methyl-2,6-di-t-butylphenol, 1,4-di-t-butylbenzene, and polymorph A of 2,6-di-t-butyl- naphthalene. A trend is observed in the reorientational barriers for the t-butyl and the out-of-plane methyl groups across this series of four compounds: as the t-butyl barriers decrease, the out-of-plane methyl barriers increase

Double proximity effect in hybrid planar Superconductor-(Normal metal/Ferromagnet)-Superconductor structures

We have investigated the differential resistance of hybrid planar Al-(Cu/Fe)-Al submicron bridges at low temperatures and in weak magnetic fields. The structure consists of Cu/Fe-bilayer forming a bridge between two superconducting Al-electrodes. In superconducting state of Al-electrodes, we have observed a double-peak peculiarity in differential resistance of the S-(N/F)-S structures at a bias voltage corresponding to the minigap. We claim that this effect (the doubling of the minigap) is due to an electron spin polarization in the normal metal which is induced by the ferromagnet. We have demonstrated that the double-peak peculiarity is converted to a single peak at a coercive applied field corresponding to zero magnetization of the Fe-layer