Relatively computably enumerable reals

A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and Y does not compute X. A real X is relatively simple and above if there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset Z of the complement of X such that Z is c.e.(Y). We prove that every nonempty Pi^0_1 class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above.Comment: 5 pages. Significant changes from earlier versio

Classification of Generalized Symmetries for the Vacuum Einstein Equations

A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. To begin, we analyze symmetries that can be built from the metric, curvature, and covariant derivatives of the curvature to any order; these are called natural symmetries and are globally defined on any spacetime manifold. We next classify first-order generalized symmetries, that is, symmetries that depend on the metric and its first derivatives. Finally, using results from the classification of natural symmetries, we reduce the classification of all higher-order generalized symmetries to the first-order case. In each case we find that the generalized symmetries are infinitesimal generalized diffeomorphisms and constant metric scalings. There are no non-trivial conservation laws associated with these symmetries. A novel feature of our analysis is the use of a fundamental set of spinorial coordinates on the infinite jet space of Ricci-flat metrics, which are derived from Penrose's ``exact set of fields'' for the vacuum equations.Comment: 57 pages, plain Te

X-ray Sources and their Optical Counterparts in the Globular Cluster M4

We report on the Chandra X-ray Observatory ACIS-S3 imaging observation of the Galactic globular cluster M4 (NGC 6121). We detect 12 X-ray sources inside the core and 19 more within the cluster half-mass radius. The limiting luminosity of this observation is Lx~10e29 erg/sec for sources associated with the cluster, the deepest X-ray observation of a globular cluster to date. We identify 6 X-ray sources with known objects and use ROSAT observations to show that the brightest X-ray source is variable. Archival data from the Hubble Space Telescope allow us to identify optical counterparts to 16 X-ray sources. Based on the X-ray and optical properties of the identifications and the information from the literature, we classify two (possibly three) sources as cataclysmic variables, one X-ray source as a millisecond pulsar and 12 sources as chromospherically active binaries. Comparison of M4 with 47 Tuc and NGC 6397 suggests a scaling of the number of active binaries in these clusters with the cluster (core) mass.Comment: 11 pages, 6 figures, accepted for publication in ApJ. Figure 1 and 5 are of reduced qualit

Thermodynamics and Kinetic Theory of Relativistic Gases in 2-D Cosmological Models

A kinetic theory of relativistic gases in a two-dimensional space is developed in order to obtain the equilibrium distribution function and the expressions for the fields of energy per particle, pressure, entropy per particle and heat capacities in equilibrium. Furthermore, by using the method of Chapman and Enskog for a kinetic model of the Boltzmann equation the non-equilibrium energy-momentum tensor and the entropy production rate are determined for a universe described by a two-dimensional Robertson-Walker metric. The solutions of the gravitational field equations that consider the non-equilibrium energy-momentum tensor - associated with the coefficient of bulk viscosity - show that opposed to the four-dimensional case, the cosmic scale factor attains a maximum value at a finite time decreasing to a "big crunch" and that there exists a solution of the gravitational field equations corresponding to a "false vacuum". The evolution of the fields of pressure, energy density and entropy production rate with the time is also discussed.Comment: 23 pages, accepted in PR

What do young athletes implicitly understand about psychological skills?

One reason sport psychologists teach psychological skills is to enhance performance in sport; but the value of psychological skills for young athletes is questionable because of the qualitative and quantitative differences between children and adults in their understanding of abstract concepts such as mental skills. To teach these skills effectively to young athletes, sport psychologists need to appreciate what young athletes implicitly understand about such skills because maturational (e.g., cognitive, social) and environmental (e.g., coaches) factors can influence the progressive development of children and youth. In the present qualitative study, we explored young athletes’ (aged 10–15 years) understanding of four basic psychological skills: goal setting, mental imagery, self-talk, and relaxation. Young athletes (n = 118: 75 males and 43 females) completed an open-ended questionnaire to report their understanding of these four basic psychological skills. Compared with the older youth athletes, the younger youth athletes were less able to explain the meaning of each psychological skill. Goal setting and mental imagery were better understood than self-talk and relaxation. Based on these findings, sport psychologists should consider adapting interventions and psychoeducational programs to match young athletes’ age and developmental level

Evolution of the pairing pseudogap in the spectral function with interplane anisotropy

We study the pairing pseudogap in the spectral function as a function of interplane coupling. The analytical expressions for the self-energy in the critical regime are obtained for any degree of anisotropy. The frequency dependence of the self-energy is found to be qualitatively different in two and three dimensions, and the crossover from two to three dimensional behavior is discussed. In particular, by considering the anisotropy of the Fermi velocity and gap along the Fermi surface, we can qualitatively explain recent photoemission experiments on high temperature superconductors concerning the temperature dependent Fermi arcs seen in the pseudogap phase.Comment: 20 pages, revtex, 5 encapsulated postscript figures include

An adaptive inelastic magnetic mirror for Bose-Einstein condensates

We report the reflection and focussing of a Bose-Einstein condensate by a new pulsed magnetic mirror. The mirror is adaptive, inelastic, and of extremely high optical quality. The deviations from specularity are less than 0.5 mrad rms, making this the best atomic mirror demonstrated to date. We have also used the mirror to realize the analog of a beam-expander, producing an ultra-cold collimated fountain of matter wavesComment: 4 pages, 4 figure

Magneto-optical trap for metastable helium at 389 nm

We have constructed a magneto-optical trap (MOT) for metastable triplet helium atoms utilizing the 2 3S1 -> 3 3P2 line at 389 nm as the trapping and cooling transition. The far-red-detuned MOT (detuning Delta = -41 MHz) typically contains few times 10^7 atoms at a relatively high (~10^9 cm^-3) density, which is a consequence of the large momentum transfer per photon at 389 nm and a small two-body loss rate coefficient (2 * 10^-10 cm^3/s < beta < 1.0 * 10^-9 cm^3/s). The two-body loss rate is more than five times smaller than in a MOT on the commonly used 2 3S1 -> 2 3P2 line at 1083 nm. Furthermore, we measure a temperature of 0.46(1) mK, a factor 2.5 lower as compared to the 1083 nm case. Decreasing the detuning to Delta= -9 MHz results in a cloud temperature as low as 0.25(1) mK, at small number of trapped atoms. The 389 nm MOT exhibits small losses due to two-photon ionization, which have been investigated as well.Comment: 11 page

A strongly first order electroweak phase transition from strong symmetry-breaking interactions

We argue that a strongly first order electroweak phase transition is natural in the presence of strong symmetry-breaking interactions, such as technicolor. We demonstrate this using an effective linear scalar theory of the symmetry-breaking sector.Comment: LaTex, 15 pages, 3 figures in EPS format. Phys. Rev. D approved Typographically Correct version, minor grammatical change

Late Holocene isotope hydrology of Lake Qinghai, NE Tibetan Plateau: effective moisture variability and atmospheric circulation changes

A sub-centennial-resolution record of lacustrine carbonate oxygen isotopes (δ&lt;sup&gt;18&lt;/sup&gt;O&lt;sub&gt;C&lt;/sub&gt;) from the closed-basin Lake Qinghai on the NE Tibetan Plateau shows pronounced variability over the past 1500 years. Changes in δ&lt;sup&gt;18&lt;/sup&gt;O&lt;sub&gt;C&lt;/sub&gt; in hydrologically closed lakes are often interpreted in terms of changing effective moisture. Under this interpretation our record would imply increasing effective moisture during the Little Ice Age (LIA) compared to the Medieval Warm Period (MWP). However, independent evidence from other archives strongly suggests the Asian summer monsoon was stronger during the MWP and weakened during the LIA. Controls other than effective moisture (the balance of water inputs over evaporative loss) must therefore have contributed to the δ&lt;sup&gt;18&lt;/sup&gt;O&lt;sub&gt;C&lt;/sub&gt; values. We propose the LIA signal in Lake Qinghai resulted from a reduction in evaporation caused by colder air temperatures, coupled with a decrease in oxygen isotope composition of input waters as a result of an increase in the relative importance of westerly-derived precipitation. Our results caution against simplistic interpretations of carbonate oxygen isotope records from hydrologically closed lakes and suggest all possible controlling factors must be taken into account in order to avoid misleading palaeoclimatic reconstructions