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The harmonic index of a graph G is defined as the sum of weights 2 d(u)+d(v) of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G, respectively. In this paper, we give a sharp lower bound on the harmonic index of trees with a perfect matching in terms of the number of vertices. A sharp lower bound on the harmonic index of(More)
An efficient rhodium-catalyzed method for direct C-H functionalization at the C4 position of unprotected indoles has been developed. The utility of this method is demonstrated by the concise total syntheses of agroclavine and elymoclavine in a divergent manner. These syntheses feature a Pd-catalyzed asymmetric allylic alkylation reaction to assemble the(More)
This study is to develop a hybrid technology of plasma and catalysis for odor control. Reactive species were generated from the three types of plasma discharge, such as pulsed corona discharge, dielectric barrier discharge (DBD) and hybrid discharge (pulsed corona discharge and DBD plasma occurring together), driven by a self-made pulsed high voltage power(More)
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