104,099 research outputs found

    A Counterexample to a Conjecture about Positive Scalar Curvature

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    Conjecture 1 of Stanley Chang: "Positive scalar curvature of totally nonspin manifolds" asserts that a closed smooth manifold M with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain homological condition is satisfied. We present a counterexample to this conjecture, based on the counterexample to the unstable Gromov-Lawson-Rosenberg conjecture given in Schick: "A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture".Comment: v1: 4 pages, AMS-LaTeX; v2: small changes in presentation, typos corrected, v3: comment added, to appear in Proc AM

    Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equations approach

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    This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general conditionally heteroscedastic time series model of multiplicative form Xt=σtZtX_t=\sigma_tZ_t, where the unobservable volatility σt\sigma_t is a parametric function of (Xt−1,...,Xt−p,σt−1,...,σt−q)(X_{t-1},...,X_{t-p},\sigma_{t-1},... ,\sigma_{t-q}) for some p,q≥0p,q\ge0, and (Zt)(Z_t) is standardized i.i.d. noise. We assume that these models are solutions to stochastic recurrence equations which satisfy a contraction (random Lipschitz coefficient) property. These assumptions are satisfied for the popular GARCH, asymmetric GARCH and exponential GARCH processes. Exploiting the contraction property, we give conditions for the existence and uniqueness of a strictly stationary solution (Xt)(X_t) to the stochastic recurrence equation and establish consistency and asymptotic normality of the QMLE. We also discuss the problem of invertibility of such time series models.Comment: Published at http://dx.doi.org/10.1214/009053606000000803 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Frequency response of electrochemical cells

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    Impedance concepts can be applied to the analysis of battery electrodes, yielding information about the structure of the electrode and the processes occurring in the electrode. Structural parameters such as the specific area (surface area per gram of electrode) can be estimated. Electrode variables such as surface overpotential, ohmic losses, and diffusion limitations may be studied. Nickel and cadmium electrodes were studied by measuring the ac impedance as a function of frequency, and the specific areas that were determined were well within the range of specific areas determined from BET measurements. Impedance spectra were measured for the nickel and cadmium electrodes, and for a 20 A-hr NiCd battery as functions of the state of charge. More work is needed to determine the feasibility of using frequency response as a nondestructive testing technique for batteries

    Characterization of Line-Consistent Signed Graphs

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    The line graph of a graph with signed edges carries vertex signs. A vertex-signed graph is consistent if every circle (cycle, circuit) has positive vertex-sign product. Acharya, Acharya, and Sinha recently characterized line-consistent signed graphs, i.e., edge-signed graphs whose line graphs, with the naturally induced vertex signature, are consistent. Their proof applies Hoede's relatively difficult characterization of consistent vertex-signed graphs. We give a simple proof that does not depend on Hoede's theorem as well as a structural description of line-consistent signed graphs.Comment: 5 pages. V2 defines sign of a walk and corrects statement of Theorem 4 ("is balanced and" was missing); also minor copyeditin
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