The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the ...The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the special cases including loopless nearly 2-regular maps and simple nearly 2-regular maps in terms of the above three parameters are derived.展开更多
In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of ...In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.展开更多
文摘The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the special cases including loopless nearly 2-regular maps and simple nearly 2-regular maps in terms of the above three parameters are derived.
基金This work is supported by National Natural Science Foundation of China under Grant nos, 10001013 and 10471047 and Natural Science Foundation of Guangdong Province of China under Grant no. 004020077.
文摘In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables （2D）. Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.
