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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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Newcomb M Chandrasena RE Lansakara-P DS Kim HY Lippard SJ Beauvais LG Murray LJ Izzo V Hollenberg PF Coon MJ 《The Journal of organic chemistry》2007,72(4):1121-1127
Norcarane, bicyclo[4.1.0]heptane, has been widely used as a mechanistic probe in studies of oxidations catalyzed by several iron-containing enzymes. We report here that, in addition to oxygenated products, norcarane is also oxidized by iron-containing enzymes in desaturase reactions that give 2-norcarene and 3-norcarene. Furthermore, secondary products from further oxidation reactions of the norcarenes are produced in yields that are comparable to those of the minor products from oxidation of the norcarane. We studied oxidations catalyzed by a representative spectrum of iron-containing enzymes including four cytochrome P450 enzymes, CYP2B1, CYPDelta2B4, CYPDelta2E1, and CYPDelta2E1 T303A, and three diiron enzymes, soluble methane monooxygenase (sMMO) from Methylococcus capsulatus (Bath), toluene monooxygenase (ToMO) from Pseudomonas stutzeri OX1, and phenol hydroxylase (PH) from Pseudomonas stutzeri OX1. 2-Norcarene and 3-norcarene and their oxidation products were found in all reaction mixtures, accounting for up to half of the oxidation products in some cases. In total, more than 20 oxidation products were identified from the enzyme-catalyzed reactions of norcarane. The putative radical-derived product from the oxidation of norcarane, 3-hydroxymethylcyclohexene (21), and the putative cation-derived product from the oxidation of norcarane, cyclohept-3-enol (22), coelute with other oxidation products on low-polarity GC columns. The yields of product 21 found in this study are smaller than those previously reported for the same or similar enzymes in studies where the products from norcarene oxidations were ignored, and therefore, the limiting values for lifetimes of radical intermediates produced in the enzyme-catalyzed oxidation reactions are shorter than those previously reported. 相似文献
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