An orientation of a graph G with even number of vertices is Pfaffian if every even cycle C such that G-V(C) has a perfect matching has an odd number of edges directed in either direction of the cycle. The significance...An orientation of a graph G with even number of vertices is Pfaffian if every even cycle C such that G-V(C) has a perfect matching has an odd number of edges directed in either direction of the cycle. The significance of Pfaffian orientations stems from the fact that if a graph G has one, then the number of perfect matchings of G can be computed in polynomial time. There is a classical result of Kasteleyn that every planar graph has a Pfaffian orientation. Little proved an elegant characterization of bipartite graphs that admit a Pfaffian orientation. Robertson, Seymour and Thomas (1999) gave a polynomial-time recognition algorithm to test whether a bipartite graph is Pfaffian by a structural description of bipartite graphs. In this paper, we consider the Pfaffian property of graphs embedding on the orientable surface with genus one (i.e., the torus). Some sufficient conditions for Pfaffian graphs on the torus are obtained. Furthermore, we show that all quadrilateral tilings on the torus are Pfaffian if and only if they are not bipartite graphs.展开更多
A new kind of single-polarization photonic crystal fiber(PCF) is proposed.Two kinds of multi-component glasses and the air are selected as working materials.Through using the full vector finite element method(FEM) and...A new kind of single-polarization photonic crystal fiber(PCF) is proposed.Two kinds of multi-component glasses and the air are selected as working materials.Through using the full vector finite element method(FEM) and the perfectly matched layers(PML),the polarization-maintaining characteristic and the confinement loss of the fiber are analyzed,respectively.In addition,the single-polarization region of the fiber around 1.55 ìm is discussed.Numerical simulations show that the fiber maintains single-polarization operation within the wavelength range of 1.421-1.696μm.The birefringence can reach 6.988×10-3,and the confinement loss is as low as 0.012 dB/m when 7 layers of ring holes are arranged in the cladding at λ=1.55μm.展开更多
基金National Natural Science Foundation of China (Grant Nos. 10831001 and 11171279)the Scientific Research Foundation of Zhangzhou Normal University (Grant No. SX1002)
文摘An orientation of a graph G with even number of vertices is Pfaffian if every even cycle C such that G-V(C) has a perfect matching has an odd number of edges directed in either direction of the cycle. The significance of Pfaffian orientations stems from the fact that if a graph G has one, then the number of perfect matchings of G can be computed in polynomial time. There is a classical result of Kasteleyn that every planar graph has a Pfaffian orientation. Little proved an elegant characterization of bipartite graphs that admit a Pfaffian orientation. Robertson, Seymour and Thomas (1999) gave a polynomial-time recognition algorithm to test whether a bipartite graph is Pfaffian by a structural description of bipartite graphs. In this paper, we consider the Pfaffian property of graphs embedding on the orientable surface with genus one (i.e., the torus). Some sufficient conditions for Pfaffian graphs on the torus are obtained. Furthermore, we show that all quadrilateral tilings on the torus are Pfaffian if and only if they are not bipartite graphs.
基金supported by the Basic Research Foundation of Harbin Engineering Universitythe Special Foundation for Harbin Young Scientists (No. 2008RFQXG031)
文摘A new kind of single-polarization photonic crystal fiber(PCF) is proposed.Two kinds of multi-component glasses and the air are selected as working materials.Through using the full vector finite element method(FEM) and the perfectly matched layers(PML),the polarization-maintaining characteristic and the confinement loss of the fiber are analyzed,respectively.In addition,the single-polarization region of the fiber around 1.55 ìm is discussed.Numerical simulations show that the fiber maintains single-polarization operation within the wavelength range of 1.421-1.696μm.The birefringence can reach 6.988×10-3,and the confinement loss is as low as 0.012 dB/m when 7 layers of ring holes are arranged in the cladding at λ=1.55μm.
