A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for whic...A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.展开更多
Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeic...Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeichel.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10471139
文摘A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.
基金Supported partially by Project 02139 of Ministry of Education, China
文摘Let G be a hamiltonian, bipartite graph on 2n vertices, where n > 3. It isshown that if e(G) > n(n ― 1)/2 + 2 then G contains cycles of every possible even length. Thisimproves a result of Entringer and Schmeichel.
