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For l, an -triangulation F of a planar domain is such that,for every T F, there holds 1 RT/2rT , where RT (resp. rT)denotes the radius of the circumscribed (resp. inscribed) circleof the triangle T. When T is varying in F the centre of itsinscribed circle is varying in a compact interior to T and itsorthogonal projections on the sides are varying in compact intervalsinterior to these sides. Precise results are given about thesizes of these compacts and are used for the computation oferror constants in the problem of Hermite interpolation by Powell-Sabinquadratic finite elements, bringing to the fore their dependenceon the parameter . 相似文献
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Kittiwachana S Ferreira DL Fido LA Thompson DR Escott RE Brereton RG 《Journal of chromatography. A》2008,1213(2):130-144
A continuous process was studied over 83.32 h using on-line high-performance liquid chromatography, involving the acquisition of 252 chromatograms. A method for analysis of these data using multivariate statistical process control on peak tables, in real-time, is described. The normal operating condition (NOC) region of the process was identified using evolving principal components analysis to be between 5.77 and 8.13 h. 19 out of the 37 peaks detected throughout the process were found in the NOC region, the remainder representing undesirable contaminants found elsewhere in the process. A major challenge is to develop the peak table as the process evolves, which is dynamically updated as new peaks are detected after the NOC region: this approach involving an "unlocked" peak table is contrasted to an approach using a "locked" peak table where only peaks detected during the NOC region are included in the model. In addition, results are compared to those obtained using baseline corrected and aligned chromatograms, using a NOC region of 5.85-8.33h. D- and Q-charts were obtained. It is shown that the "unlocked" peak table detects out of control samples best and provides good diagnostic insight into problems with the process. 相似文献