• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.41-56
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• 2007

A 3-partite 2-digraph is an orientation of a 3-partite multi-graph that is without loops and contains at most two edges between any pair of vertices from distinct parts. Let D(X, Y, Z) be a 3-partite 2-digraph with ${\mid}X{\mid}=l,\;{\mid}Y{\mid}=m,\;{\mid}Z{\mid}=n$. For any vertex v in D(X, Y, Z), let $d^+_{\nu}\;and\;d^-_{\nu}$ denote the outdegree and indegree respectively of v. Define $p_x=2(m+n)+d^+_x-d^-_x,\;q_y=2(l+n)+d^+_y-d^-_y\;and\;r_z=2(l+m)+d^+_z-d^-_z$ as the marks (or 2-scores) of x in X, y in Y and z in Z respectively. In this paper, we characterize the marks of 3-partite 2-digraphs and give a constructive and existence criterion for sequences of non-negative integers in non-decreasing order to be the mark sequences of some 3-partite 2-digraph.

• Journal of the Korean Magnetics Society
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• v.16 no.1
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• pp.88-91
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• 2006

We present a method describing the quantum entanglement. We knows the criterion which can determine entanglement in a bipartite system. It is difficult in mixed states. Even though the entanglement criterion for multipartite systems is difficult, we offer a criterion for multiqubits and discuss entanglement of the mixed state.

• The KIPS Transactions:PartD
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• v.10D no.2
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• pp.261-266
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• 2003

A protein, which is a linear polymer of amino acids, is one of the most important bio-molecules composing biological structures and regulating bio-chemical reactions. Since the characteristics and functions of proteins are determined by their amino acid sequences in principle, protein sequence determination is the starting point of protein function study. This paper proposes a protein sequence prediction method based on data mining techniques, which can overcome the limitation of previous bio-chemical sequencing methods. After applying multiple proteases to acquire overlapped protein fragments, we can identify candidate fragment sequences by comparing fragment mass values with peptide databases. We propose a method to construct multi-partite graph and search maximal paths to determine the protein sequence by assembling proper candidate sequences. In addition, experimental results based on the SWISS-PROT database showing the validity of the proposed method is presented.