In this paper, the authors discuss the upper bound for the genus of strong embeddings for 3-connected planar graphs on higher surfaces. It is shown that the problem of determining the upper bound for the strong embedd...In this paper, the authors discuss the upper bound for the genus of strong embeddings for 3-connected planar graphs on higher surfaces. It is shown that the problem of determining the upper bound for the strong embedding of 3-connected planar near-triangulations on higher non-orientable surfaces is NP-hard. As a corollary, a theorem of Richter, Seymour and Siran about the strong embedding of 3-connected planar graphs is generalized to orientable surface.展开更多
In this paper, it is shown that for every maximal planar graph G=(V,E) , a strong embedding on some non orientable surface with genus at most |V(G)|-22 is admitted such that the surface dual of G is also a...In this paper, it is shown that for every maximal planar graph G=(V,E) , a strong embedding on some non orientable surface with genus at most |V(G)|-22 is admitted such that the surface dual of G is also a planar graph. As a corollary, an interpolation theorem for strong embeddings of G on non orientable surfaces is obtained.展开更多
The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover. Conversely, i...The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover. Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.展开更多
Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under...Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes Gn(s,t) can be constructed such that sup a. s.,for S,T which together satisfy a certain condition.展开更多
We present an exact solution to the problem of electromagnetic scattering by nanosphere clusters embedded in a liquid crystal cell, based on the Mie theory. The dependence of the scattering property on the structure p...We present an exact solution to the problem of electromagnetic scattering by nanosphere clusters embedded in a liquid crystal cell, based on the Mie theory. The dependence of the scattering property on the structure parameters is investigated in detail. It is shown that strong transverse light currents at the optical frequency can be obtained from these complex structures. Furthermore, we find that sign reversal of the transverse light current can be realized by changing frequency and voltage. The physical origins of these phenomena have been analyzed.The transverse light current for subwavelength nanoscale dimensions is of practical significance. Thus, the application of these phenomena to optical devices is展开更多
文摘In this paper, the authors discuss the upper bound for the genus of strong embeddings for 3-connected planar graphs on higher surfaces. It is shown that the problem of determining the upper bound for the strong embedding of 3-connected planar near-triangulations on higher non-orientable surfaces is NP-hard. As a corollary, a theorem of Richter, Seymour and Siran about the strong embedding of 3-connected planar graphs is generalized to orientable surface.
文摘In this paper, it is shown that for every maximal planar graph G=(V,E) , a strong embedding on some non orientable surface with genus at most |V(G)|-22 is admitted such that the surface dual of G is also a planar graph. As a corollary, an interpolation theorem for strong embeddings of G on non orientable surfaces is obtained.
基金the National Natural Sciences Foundation of China (No.10271048).
文摘The strong embedding conjecture states that any 2-connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2-connected graph has a circuit double cover. Conversely, it is not true. But for a 3-regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.
文摘Let (X0,Y0), be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t) suggested by Campbell and Foldes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes Gn(s,t) can be constructed such that sup a. s.,for S,T which together satisfy a certain condition.
基金National Key R&D Program of China(2017YFA0303800)National Natural Science Foundation of China(NSFC)(11574031,61421001)
文摘We present an exact solution to the problem of electromagnetic scattering by nanosphere clusters embedded in a liquid crystal cell, based on the Mie theory. The dependence of the scattering property on the structure parameters is investigated in detail. It is shown that strong transverse light currents at the optical frequency can be obtained from these complex structures. Furthermore, we find that sign reversal of the transverse light current can be realized by changing frequency and voltage. The physical origins of these phenomena have been analyzed.The transverse light current for subwavelength nanoscale dimensions is of practical significance. Thus, the application of these phenomena to optical devices is
