In this paper, we propose a new set of orthogonal basis functions in the arbitrarytriangular domain. At first, we generalize the 1-D Sturm-Liouville equation tothe arbitrary triangular domain on a barycentric coordina...In this paper, we propose a new set of orthogonal basis functions in the arbitrarytriangular domain. At first, we generalize the 1-D Sturm-Liouville equation tothe arbitrary triangular domain on a barycentric coordinate, and derive a set ofcomplete orthogonal basis functions on this domain. Secondly, we analyze thesymmetry and periodicity property of these functions and classify them into fourclasses. At last, we show some of the visualization results of these basis functions.展开更多
A near-triangular embedding is an embedded graph into some surface whose all but one facial walks are 3-gons. In this paper we show that if a graph G is a triangulation of an orientable surface Sh, then G has a near-t...A near-triangular embedding is an embedded graph into some surface whose all but one facial walks are 3-gons. In this paper we show that if a graph G is a triangulation of an orientable surface Sh, then G has a near-triangular embedding into Sk for k=h, h＋1,...1,[β（G）/2], where β（G） is the Betti number of G.展开更多
文摘In this paper, we propose a new set of orthogonal basis functions in the arbitrarytriangular domain. At first, we generalize the 1-D Sturm-Liouville equation tothe arbitrary triangular domain on a barycentric coordinate, and derive a set ofcomplete orthogonal basis functions on this domain. Secondly, we analyze thesymmetry and periodicity property of these functions and classify them into fourclasses. At last, we show some of the visualization results of these basis functions.
基金the National Natural Science Foundation of China (19831080)Shanghai City Fundation of Selected Academic Research (04JC14031)
文摘A near-triangular embedding is an embedded graph into some surface whose all but one facial walks are 3-gons. In this paper we show that if a graph G is a triangulation of an orientable surface Sh, then G has a near-triangular embedding into Sk for k=h, h＋1,...1,[β（G）/2], where β（G） is the Betti number of G.
