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In this paper, Gd-promoted Co3O4 catalysts were prepared via a facile coprecipitation method for low-temperature catalytic N2O decomposition. Due to the addition of Gd, the crystallite size of Co3O4 in the Gd0.06Co catalyst surprisingly decreased to 4.9 nm, which is much smaller than most additive-modified Co3O4 catalysts. This huge change in the catalyst’s textural structure endows the Gd0.06Co catalyst with a large specific surface area, plentiful active sites, and a weak Co–O bond. Hence, Gd0.06Co exhibited superior activity for catalyzing 2000 ppmv N2O decomposition, and the temperature for the complete catalytic elimination of N2O was as low as 350 °C. Meanwhile, compared with pure Co3O4, E a decreased from 77.4 to 46.8 kJ·mol–1 and TOF of the reaction increased from 1.16 × 10–3 s–1 to 5.13 × 10–3 s–1 at 300 °C. Moreover, Gd0.06Co displayed a quite stable catalytic performance in the presence of 100 ppmv NO, 5 vol % O2, and 2 vol % H2O.

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The notion of ε-kernel was introduced by Agarwal et al. (J. ACM 51:606-635, 2004) to set up a unified framework for computing various extent measures of a point set P approximately. Roughly speaking, a subset Q ⊆ P is an ε-kernel of P if for every slab W containing Q, the expanded slab (1 + ε)W contains P . They illustrated the significance of ε-kernel by showing that it yields approximation algorithms for a wide range of geometric optimization problems.We present a simpler and more practical algorithm for computing the ε-kernel of a set P of points in R d . We demonstrate the practicality of our algorithm by showing its empirical performance on various inputs. We then describe an incremental algorithm for fitting various shapes and use the ideas of our algorithm for computing ε-kernels to analyze the performance of this algorithm. We illustrate the versatility and practicality of this technique by implementing approximation algorithms for minimum enclosing cylinder, minimum-volume bounding box, and minimum-width annulus. 379 Finally, we show that ε-kernels can be effectively used to expedite the algorithms for maintaining extents of moving points.

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