3,529 research outputs found
Geometric Aspects of Frame Representations of Abelian Groups
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
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
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
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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