Bijective Proofs of Gould's and Rothe's Identities

We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the $q$-Chu-Vandermonde formula.Comment: 4 page

A unified approach to complementarity in optimization

AbstractAn underlying general structure of complementary pivot theory is presented with applications to various problems in optimization theory. The applications include linear complementarity, fixed point theory, unconstrained and constrained convex optimization without derivatives, nonlinear complementarity, and saddle point problems

Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas

Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler's pentagonal number theorem, we study multiple extensions of the latter formula. In a different direction we derive a common extension of this multivariate series identity and two formulas of Lucas. Finally we give a combinatorial proof of Lucas' formulas.Comment: 11 pages, to appear in Discrete Mathematics. See also http://math.univ-lyon1.fr/~gu

Calculation of NMR Properties of Solitons in Superfluid 3He-A

Superfluid 3He-A has domain-wall-like structures, which are called solitons. We calculate numerically the structure of a splay soliton. We study the effect of solitons on the nuclear-magnetic-resonance spectrum by calculating the frequency shifts and the amplitudes of the soliton peaks for both longitudinal and transverse oscillations of magnetization. The effect of dissipation caused by normal-superfluid conversion and spin diffusion is calculated. The calculations are in good agreement with experiments, except a problem in the transverse resonance frequency of the splay soliton or in magnetic-field dependence of reduced resonance frequencies.Comment: 15 pages, 10 figures, updated to the published versio

KELT-3b: A Hot Jupiter Transiting A V=9.8 Late-F Star

We report the discovery of KELT-3b, a moderately inflated transiting hot Jupiter with a mass of 1.477(-0.067)(+0.066) M-J, radius of 1.345 +/- 0.072 R-J, and an orbital period of 2.7033904 +/- 0.000010 days. The host star, KELT-3, is a V = 9.8 late F star with M-* = 1.278(-0.061)(+0.063) M-circle dot, R-* = 1.472(-0.067)(+0.065) R-circle dot, T-eff = 6306(-49)(+50) K, log(g) = 4.209(-0.031)(+0.033), and [Fe/H] = 0.044(-0.082)(+0.080), and has a likely proper motion companion. KELT-3b is the third transiting exoplanet discovered by the KELT survey, and is orbiting one of the 20 brightest known transiting planet host stars, making it a promising candidate for detailed characterization studies. Although we infer that KELT-3 is significantly evolved, a preliminary analysis of the stellar and orbital evolution of the system suggests that the planet has likely always received a level of incident flux above the empirically identified threshold for radius inflation suggested by Demory & Seager

‘One door closes, a next door opens up somewhere’: The learning of one Olympic synchronised swimmer

Although training in sport is necessary to reach Olympic status, a conditioned body is not the only outcome. Athletes also learn how to be Olympians. This learning involves taking on certain ways of acting, thinking and valuing. Such learning has implications beyond competition, as athletes eventually retire from elite sport and devote their time to other activities. This paper examines processes of learning and transition using the case of Amelia, a former Olympic synchronised swimmer. Through two in-depth interviews, empirical material was generated which focused on the learning that took place during this athlete’s career and after, during her transition to paid employment. A cultural view of learning was used as the theoretical frame to understand the athlete’s experiences. Our reading suggests that the athlete learned in various ways to be productive. Some of these ways of being were useful after retirement; others were less compatible. In fact, Amelia used a two-year period after retirement to reconstruct herself. Key to her eventual successful transition was to distance herself from the sport and to critically reflect upon her sporting experiences. We thus recommend that those involved with high-performance athletes foster a more balanced perspective that acknowledges and promotes ways of being beyond athletic involvement

Further investigation of a relic neutralino as a possible origin of an annual-modulation effect in WIMP direct search

We analyze the annual-modulation effect, measured by the DAMA Collaboration with the new implementation of a further two-years running, in the context of a possible interpretation in terms of relic neutralinos. We impose over the set of supersymmetric configurations, selected by the annual-modulation data, the constraints derived from WIMP indirect measurements, and discuss the features of the ensuing relic neutralinos. We critically discuss the sources of the main theoretical uncertainties in the analysis of event rates for direct and indirect WIMP searches.Comment: 29 pages, 12 figures, typeset with ReVTeX. In order to reduce size, the version on the archive has low resolution figures. A full version of the paper can be found at http://www.to.infn.it/~fornengo/papers

Avalanche Dynamics in Evolution, Growth, and Depinning Models

The dynamics of complex systems in nature often occurs in terms of punctuations, or avalanches, rather than following a smooth, gradual path. A comprehensive theory of avalanche dynamics in models of growth, interface depinning, and evolution is presented. Specifically, we include the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models into a unified treatment encompassing a large class of far from equilibrium processes. The formation of fractal structures, the appearance of $1/f$ noise, diffusion with anomalous Hurst exponents, Levy flights, and punctuated equilibria can all be related to the same underlying avalanche dynamics. This dynamics can be represented as a fractal in $d$ spatial plus one temporal dimension. We develop a scaling theory that relates many of the critical exponents in this broad category of extremal models, representing different universality classes, to two basic exponents characterizing the fractal attractor. The exact equations and the derived set of scaling relations are consistent with numerical simulations of the above mentioned models.Comment: 27 pages in revtex, no figures included. Figures or hard copy of the manuscript supplied on reques

KELT-6b: A P ~ 7.9 Day Hot Saturn Transiting A Metal-Poor Star With A Long-Period Companion

We report the discovery of KELT-6b, a mildly inflated Saturn-mass planet transiting a metal-poor host. The initial transit signal was identified in KELT-North survey data, and the planetary nature of the occulter was established using a combination of follow-up photometry, high-resolution imaging, high-resolution spectroscopy, and precise radial velocity measurements. The fiducial model from a global analysis including constraints from isochrones indicates that the V = 10.38 host star (BD+31 2447) is a mildly evolved, late-F star with T eff = 6102 ± 43 K, log g_\star =4.07_{-0.07}^{+0.04}, and [Fe/H] = -0.28 ± 0.04, with an inferred mass M sstarf = 1.09 ± 0.04 M ☉ and radius R_\star =1.58_{-0.09}^{+0.16} \,R_\odot. The planetary companion has mass MP = 0.43 ± 0.05 M Jup, radius R_{P}=1.19_{-0.08}^{+0.13} \,R_Jup, surface gravity log g_{P}=2.86_{-0.08}^{+0.06}, and density \rho _{P}=0.31_{-0.08}^{+0.07}\,g\,cm^{-3}. The planet is on an orbit with semimajor axis a = 0.079 ± 0.001 AU and eccentricity e=0.22_{-0.10}^{+0.12}, which is roughly consistent with circular, and has ephemeris of T c(BJDTDB) = 2456347.79679 ± 0.00036 and P = 7.845631 ± 0.000046 days. Equally plausible fits that employ empirical constraints on the host-star parameters rather than isochrones yield a larger planet mass and radius by ~4}-7}. KELT-6b has surface gravity and incident flux similar to HD 209458b, but orbits a host that is more metal poor than HD 209458 by ~0.3 dex. Thus, the KELT-6 system offers an opportunity to perform a comparative measurement of two similar planets in similar environments around stars of very different metallicities. The precise radial velocity data also reveal an acceleration indicative of a longer-period third body in the system, although the companion is not detected in Keck adaptive optics images.KELT is a joint project of The Ohio State University, Vanderbilt University, and Lehigh University