Browsing by Author "Zweck, John"

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    Compactification problems in the theory of characteristic currents associated with a singular connection
    (1993) Zweck, John; Harvey, F. Reese
    A compactification of the Chern-Weil theory for bundle maps developed by Harvey and Lawson is described. For each smooth section $\nu$ of the compactification $\IP(\underline{\doubc}\oplus F)\to X$ of a rank n complex vector bundle $F\to X$ with connection, and for each Ad-invariant polynomial $\phi$ on ${\bf gl}\sb{n},$ there are associated current formulae generalizing those of Harvey and Lawson. These are of the form $$\eqalign{\phi(\Omega\sb{\it F}) &+\rm \nu\sp*(Res\sb\infty(\phi))\ Div\sb\infty(\nu) - \phi(\Omega\sb0)\ -\cr&\qquad\rm Res\sb0(\phi)\ Div\sb0(\nu) = {\it dT}\quad on\ {\it X},\cr}$$where Div$\sb0(\nu)$ and Div$\sb\infty(\nu)$ are integrally flat currents supported on the zero and pole sets of $\nu,$ where Res$\sb0(\phi)$ and Res$\sb\infty(\phi)$ are smooth residue forms which can be calculated in terms of the curvature $\Omega\sb{F}$ of F, where T is a canonical transgression form with coefficients in $L\sbsp{\rm loc}{1},$ and where $\phi(\Omega\sb0)$ is an $L\sbsp{\rm loc}{1}$ form canonically defined in terms of a singular connection naturally associated to $\nu.$ These results hold for $C\sp\infty$-meromorphic sections $\nu$ which are atomic. The notion of an atomic section of a vector bundle was first introduced and studied by Harvey and Semmes. The formulae obtained include a generalization of the Poincare-Lelong formula to $C\sp\infty$-meromorphic sections of a bundle of arbitrary rank. Analogous results hold for real vector bundles and for quaternionic line bundles.
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    Influence of Tuning Fork Resonance Properties on Quartz-Enhanced Photoacoustic Spectroscopy Performance
    (MDPI, 2019) Zheng, Huadan; Lin, Haoyang; Dong, Lei; Liu, Yihua; Patimisco, Pietro; Zweck, John; Mozumder, Ali; Sampaolo, Angelo; Spagnolo, Vincenzo; Huang, Bincheng; Tang, Jieyuan; Dong, Linpeng; Zhu, Wenguo; Yu, Jianhui; Chen, Zhe; Tittel, Frank K.
    A detailed investigation of the influence of quartz tuning forks (QTFs) resonance properties on the performance of quartz-enhanced photoacoustic spectroscopy (QEPAS) exploiting QTFs as acousto-electric transducers is reported. The performance of two commercial QTFs with the same resonance frequency (32.7 KHz) but different geometries and two custom QTFs with lower resonance frequencies (2.9 KHz and 7.2 KHz) were compared and discussed. The results demonstrated that the fundamental resonance frequency as well as the quality factor and the electrical resistance were strongly inter-dependent on the QTF prongs geometry. Even if the resonance frequency was reduced, the quality factor must be kept as high as possible and the electrical resistance as low as possible in order to guarantee high QEPAS performance.