10,316 research outputs found

    On construction of optimal mixed-level supersaturated designs

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    Supersaturated design (SSD) has received much recent interest because of its potential in factor screening experiments. In this paper, we provide equivalent conditions for two columns to be fully aliased and consequently propose methods for constructing E(fNOD)E(f_{\mathrm{NOD}})- and χ2\chi^2-optimal mixed-level SSDs without fully aliased columns, via equidistant designs and difference matrices. The methods can be easily performed and many new optimal mixed-level SSDs have been obtained. Furthermore, it is proved that the nonorthogonality between columns of the resulting design is well controlled by the source designs. A rather complete list of newly generated optimal mixed-level SSDs are tabulated for practical use.Comment: Published in at http://dx.doi.org/10.1214/11-AOS877 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Double Coronal Hard and Soft X-ray Source Observed by RHESSI: Evidence for Magnetic Reconnection and Particle Acceleration in Solar Flares

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    We present data analysis and interpretation of an M1.4-class flare observed with the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) on April 30, 2002. This event, with its footpoints occulted by the solar limb, exhibits a rarely observed, but theoretically expected, double-source structure in the corona. The two coronal sources, observed over the 6-30 keV range, appear at different altitudes and show energy-dependent structures with the higher-energy emission being closer together. Spectral analysis implies that the emission at higher energies in the inner region between the two sources is mainly nonthermal, while the emission at lower energies in the outer region is primarily thermal. The two sources are both visible for about 12 minutes and have similar light curves and power-law spectra above about 20 keV. These observations suggest that the magnetic reconnection site lies between the two sources. Bi-directional outflows of the released energy in the form of turbulence and/or particles from the reconnection site can be the source of the observed radiation. The spatially resolved thermal emission below about 15 keV, on the other hand, indicates that the lower source has a larger emission measure but a lower temperature than the upper source. This is likely the result of the differences in the magnetic field and plasma density of the two sources.Comment: Accepted by ApJ (12/06/2007), scheduled for the 03/20/2008 Vol. 676 No. 1 Issue, 13 pages, 9 figure

    Math and Data Exploration

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