3,380 research outputs found

    Geometric Aspects of Frame Representations of Abelian Groups

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    We consider frames arising from the action of a unitary representation of a discrete countable abelian group. We show that the range of the analysis operator can be determined by computing which characters appear in the representation. This allows one to compare the ranges of two such frames, which is useful for determining similarity and also for multiplexing schemes. Our results then partially extend to Bessel sequences arising from the action of the group. We apply the results to sampling on bandlimited functions and to wavelet and Weyl-Heisenberg frames. This yields a sufficient condition for two sampling transforms to have orthogonal ranges, and two analysis operators for wavelet and Weyl-Heisenberg frames to have orthogonal ranges. The sufficient condition is easy to compute in terms of the periodization of the Fourier transform of the frame generators.Comment: 20 pages; contact author: Eric Webe

    Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver

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    The FEAST method for solving large sparse eigenproblems is equivalent to subspace iteration with an approximate spectral projector and implicit orthogonalization. This relation allows to characterize the convergence of this method in terms of the error of a certain rational approximant to an indicator function. We propose improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximants based on the work of Zolotarev. Numerical experiments demonstrate the possible computational savings especially for pencils whose eigenvalues are not well separated and when the dimension of the search space is only slightly larger than the number of wanted eigenvalues. The new approach improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.Comment: 22 pages, 8 figure

    Not Invisible: Asian Pacific Islander Juvenile Arrests in Alameda County

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    This report is based on data that were originally collected by the Alameda County Probation Department. The data reflect all juvenile arrest referrals to probation (i.e., official court referral) in the county of Alameda from 1991-2000 and are presented in two ways: number of arrests which are reports of events, not unduplicated individuals, and number of unique youths which are reports of unique youths for the given year. Many of the youths who were categorized in the race/ethnic field as "Other Asian" and "Other" can be classified into a specific race/ethnic group by examining the youth's last name. A database of common Asian Pacific Islander surnames and the race/ethnic group that coincides with that surname was developed for the purpose of this project

    婆婆的原宿 : 遊日本看銀髮市場

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    伴隨著人口不斷老化的趨勢,長者群組日益龐大,他們在不知不覺間改變著我們的社會。人口老化雖帶來種種挑戰,但也包含商機,有不少人正看準了這個新興市場,建立多姿多彩的銀髮經濟
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