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Francesco Bigolin 《Journal of Mathematical Analysis and Applications》2010,366(2):561-108
In the present paper we will characterize the continuous distributional solutions of Burgers' equation as those which induce intrinsic regular graphs in the first Heisenberg group H1≡R3, endowed with a left-invariant metric d∞ equivalent to its Carnot-Carathéodory metric. We will also extend the characterization to higher Heisenberg groups Hn≡R2n+1. 相似文献
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In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph Γ is n‐HC‐extendable if it contains a path of length n and if every such path is contained in some Hamilton cycle of Γ. Similarly, Γ is weakly n‐HP‐extendable if it contains a path of length n and if every such path is contained in some Hamilton path of Γ. Moreover, Γ is strongly n‐HP‐extendable if it contains a path of length n and if for every such path P there is a Hamilton path of Γ starting with P. These concepts are then studied for the class of connected Cayley graphs on abelian groups. It is proved that every connected Cayley graph on an abelian group of order at least three is 2‐HC‐extendable and a complete classification of 3‐HC‐extendable connected Cayley graphs of abelian groups is obtained. Moreover, it is proved that every connected Cayley graph on an abelian group of order at least five is weakly 4‐HP‐extendable. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory 相似文献