The existence of periodic solution for infinite dimensional Hamiltonian systems

In this paper, we will consider a kind of infinite dimensional Hamiltonian system(HS), by the method of saddle point reduction, topology degree and the index, we will get the existence of periodic solution for (HS)

Rank-frequency relation for Chinese characters

We show that the Zipf's law for Chinese characters perfectly holds for sufficiently short texts (few thousand different characters). The scenario of its validity is similar to the Zipf's law for words in short English texts. For long Chinese texts (or for mixtures of short Chinese texts), rank-frequency relations for Chinese characters display a two-layer, hierarchic structure that combines a Zipfian power-law regime for frequent characters (first layer) with an exponential-like regime for less frequent characters (second layer). For these two layers we provide different (though related) theoretical descriptions that include the range of low-frequency characters (hapax legomena). The comparative analysis of rank-frequency relations for Chinese characters versus English words illustrates the extent to which the characters play for Chinese writers the same role as the words for those writing within alphabetical systems.Comment: To appear in European Physical Journal B (EPJ B), 2014 (22 pages, 7 figures

The Least-core and Nucleolus of Path Cooperative Games

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity flows through a network. In these games, a coalition of edges or vertices is successful if it enables a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the CS-core, least-core and nucleolus of path cooperative games. Furthermore, we show that the least-core and nucleolus are polynomially solvable for path cooperative games defined on both directed and undirected network

Giant plexiform neurofibroma with hemorrhage in cranio-maxillofacial region as depicted on CT and MRI

Plexiform neurofibroma (PN) is a rare benign tumor and a special subtype of neurofibromatosis type 1 (NF1). Though the incidence is low, giant PN of the craniomaxillofacial region could result in severe hemifacial hypertrophy which is known as a typical manifestation of NF1 in young children. Here, we retrospectively reported a giant plexiform neurofibroma with hemorrhage in the cranio-maxillofacial region detected by CT and MRI. In addition, a brief review of the relevant literature is presented