22,435 research outputs found

    Monotonicity results and bounds for the inverse hyperbolic sine

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    In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine. From these, we derive some inequalities for bounding the inverse hyperbolic sine.Comment: 3 page

    Epitaxial graphene on SiC(0001): More than just honeycombs

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    The potential of graphene to impact the development of the next generation of electronics has renewed interest in its growth and structure. The graphitization of hexagonal SiC surfaces provides a viable alternative for the synthesis of graphene, with wafer-size epitaxial graphene on SiC(0001) now possible. Despite this recent progress, the exact nature of the graphene-SiC interface and whether the graphene even has a semiconducting gap remain controversial. Using scanning tunneling microscopy with functionalized tips and density functional theory calculations, here we show that the interface is a warped carbon sheet consisting of three-fold hexagon-pentagon-heptagon complexes periodically inserted into the honeycomb lattice. These defects relieve the strain between the graphene layer and the SiC substrate, while still retaining the three-fold coordination for each carbon atom. Moreover, these defects break the six-fold symmetry of the honeycomb, thereby naturally inducing a gap: the calculated band structure of the interface is semiconducting and there are two localized states near K below the Fermi level, explaining the photoemission and carbon core-level data. Nonlinear dispersion and a 33 meV gap are found at the Dirac point for the next layer of graphene, providing insights into the debate over the origin of the gap in epitaxial graphene on SiC(0001). These results indicate that the interface of the epitaxial graphene on SiC(0001) is more than a dead buffer layer, but actively impacts the physical and electronic properties of the subsequent graphene layers

    Gamma-ray burst contributions to constraining the evolution of dark energy

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    We explore the gamma-ray bursts' (GRBs') contributions in constraining the dark energy equation of state (EOS) at high (1.8<z<71.8 < z < 7) and at middle redshifts (0.5<z<1.80.5 < z < 1.8) and estimate how many GRBs are needed to get substantial constraints at high redshifts. We estimate the constraints with mock GRBs and mock type Ia supernovae (SNe Ia) for comparisons. When constraining the dark energy EOS in a certain redshift range, we allow the dark energy EOS parameter to vary only in that redshift bin and fix EOS parameters elsewhere to -1. We find that it is difficult to constrain the dark energy EOS beyond the redshifts of SNe Ia with GRBs unless some new luminosity relations for GRBs with smaller scatters are discovered. However, at middle redshifts, GRBs have comparable contributions with SNe Ia in constraining the dark energy EOS.Comment: 3 pages, 5 figures. Published in Astronomy and Astrophysics. Corrected referenc

    A comparison of robust Mendelian randomization methods using summary data.

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    The number of Mendelian randomization (MR) analyses including large numbers of genetic variants is rapidly increasing. This is due to the proliferation of genome-wide association studies, and the desire to obtain more precise estimates of causal effects. Since it is unlikely that all genetic variants will be valid instrumental variables, several robust methods have been proposed. We compare nine robust methods for MR based on summary data that can be implemented using standard statistical software. Methods were compared in three ways: by reviewing their theoretical properties, in an extensive simulation study, and in an empirical example. In the simulation study, the best method, judged by mean squared error was the contamination mixture method. This method had well-controlled Type 1 error rates with up to 50% invalid instruments across a range of scenarios. Other methods performed well according to different metrics. Outlier-robust methods had the narrowest confidence intervals in the empirical example. With isolated exceptions, all methods performed badly when over 50% of the variants were invalid instruments. Our recommendation for investigators is to perform a variety of robust methods that operate in different ways and rely on different assumptions for valid inferences to assess the reliability of MR analyses

    Parametric Fokker-Planck equation

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    We derive the Fokker-Planck equation on the parametric space. It is the Wasserstein gradient flow of relative entropy on the statistical manifold. We pull back the PDE to a finite dimensional ODE on parameter space. Some analytical example and numerical examples are presented

    Transport properties and anisotropy in rare earth doped CaFe2As2 single crystals with Tc above 40 K

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    In this paper we report the superconductivity above 40 K in the electron doping single crystal Ca1-xRexFe2As2 (Re = La, Ce, Pr). The x-ray diffraction patterns indicate high crystalline quality and c-axis orientation. the resistivity anomaly in the parent compound CaFe2As2 is completely suppressed by partial replacement of Ca by rare earth and a superconducting transition reaches as high as 43 K, which is higher than the value in electron doping FeAs-122 compounds by substituting Fe ions with transition metal, even surpasses the highest values observed in hole doping systems with a transition temperature up to 38 K. The upper critical field has been determined with the magnetic field along ab-plane and c-axis, yielding the anisotropy of 2~3. Hall-effect measurements indicate that the conduction in this material is dominated by electron like charge carriers. Our results explicitly demonstrate the feasibility of inducing superconductivity in Ca122 compounds via electron doping using aliovalent rare earth substitution into the alkaline earth site, which should add more ingredients to the underlying physics of the iron-based superconductors.Comment: 21 pages, 7 figure

    Remark on Charm Quark Fragmentation to D∗∗D^{**} Mesons

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    The observed D∗∗D^{**} mesons have cqˉc\bar q flavor quantum numbers and spin-parity of the light degrees of freedom sℓπℓ=3/2+s_\ell^{\pi_{\ell}} = 3/2^+. In the mc→∞m_c \rightarrow \infty limit the spin of the charm quark is conserved and the c→D∗∗c \rightarrow D^{**} fragmentation process is characterized by the probability for the charm quark to fragment to a D∗∗D^{**} meson with a given helicity for the light degrees of freedom. We consider the calculated b→Bc∗∗b \rightarrow B_c^{**} fragmentation functions in the limit mc/mb→0m_c/m_b \rightarrow 0 as a qualitative model for the c→D∗∗c \rightarrow D^{**} fragmentation functions. We find that in this model charm quark fragmentation to sℓπℓ=3/2+s_\ell^{\pi_{\ell}} = 3/2^+ light degrees of freedom with helicities ±1/2\pm 1/2 is favored over fragmentation to sℓπℓ=3/2+s_\ell^{\pi_{\ell}} = 3/2^+ light degrees of freedom with helicities ±3/2\pm 3/2.Comment: 6 pages, CALT-68-192

    Constraints on Cosmological Models and Reconstructing the Acceleration History of the Universe with Gamma-Ray Burst Distance Indicators

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    Gamma-ray bursts (GRBs) have been regarded as standard candles at very high redshift for cosmology research. We have proposed a new method to calibrate GRB distance indicators with Type Ia supernova (SNe Ia) data in a completely cosmology-independent way to avoid the circularity problem that had limited the direct use of GRBs to probe cosmology [N. Liang, W. K. Xiao, Y. Liu, and S. N. Zhang, Astrophys. J. 685, 354 (2008).]. In this paper, a simple method is provided to combine GRB data into the joint observational data analysis to constrain cosmological models; in this method those SNe Ia data points used for calibrating the GRB data are not used to avoid any correlation between them. We find that the Λ\LambdaCDM model is consistent with the joint data in the 1-σ\sigma confidence region, using the GRB data at high redshift calibrated with the interpolating method, the Constitution set of SNe Ia, the cosmic microwave background radiation from Wilkinson Microwave Anisotropy Probe five year observation, the baryonic acoustic oscillation from the spectroscopic Sloan Digital Sky Survey Data Release 7 galaxy sample, the x-ray baryon mass fraction in clusters of galaxies, and the observational Hubble parameter versus redshift data. Comparing to the joint constraints with GRBs and without GRBs, we find that the contribution of GRBs to the joint cosmological constraints is a slight shift in the confidence regions of cosmological parameters to better enclose the Λ\LambdaCDM model. Finally, we reconstruct the acceleration history of the Universe up to z>6z>6 with the distance moduli of SNe Ia and GRBs and find some features that deviate from the Λ\LambdaCDM model and seem to favor oscillatory cosmology models; however further investigations are needed to better understand the situation.Comment: 14 pages, 9 figures, 2 tables; v3: the revised version, fig. 6 and some discussions added, accepted for for publication in Phys. Rev. D; v4: the published version (Phys. Rev. D 81, 083518, 2010
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