Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace ...Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace of mixed signed Selmer group of the elliptic curve are pseudoisomorphic.As a corollary,we show that the η-eigenspace is trivial if and only if the ■-eigenspace is trivial.Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a "reflected" eigenspace.展开更多
Let G =（V, E） be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f： VUE→{-1,1}such that ∑y∈Nm（x）U{x}f（y） ≥1 for every element x ∈ V U E, where Nm （x...Let G =（V, E） be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f： VUE→{-1,1}such that ∑y∈Nm（x）U{x}f（y） ≥1 for every element x ∈ V U E, where Nm （x） is the set of elements of V U E adjacent or incident to x. The weight of f isw（f）∑x∈VUEf（x）.The signed mixed domination problem is to find a minimum-weight signed mixed dominating function of a graph. In this paper we study the computational complexity of signed mixed domination problem. We prove that the signed mixed domination problem is NP-complete for bipartite graphs, chordal graphs, even for planar bipartite graphs.展开更多
基金The second author is supported by National Natural Science Foundation of China(Grant Nos.11550110172 and 11771164)。
文摘Let p be an odd prime number,and let E be an elliptic curve defined over a number field which has good reduction at every prime above p.Under suitable assumptions,we prove that the η-eigenspace and the ■-eigenspace of mixed signed Selmer group of the elliptic curve are pseudoisomorphic.As a corollary,we show that the η-eigenspace is trivial if and only if the ■-eigenspace is trivial.Our results can be thought as a reflection principle which relates an Iwasawa module in a given eigenspace with another Iwasawa module in a "reflected" eigenspace.
基金Supported by the Natural Science Foundation of Jiangsu Province(Grant No.BK20151117)the Key Scientific Research Foundation of Higher Education Institutions of Henan Province(Grant No.15B110009)
文摘Let G =（V, E） be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f： VUE→{-1,1}such that ∑y∈Nm（x）U{x}f（y） ≥1 for every element x ∈ V U E, where Nm （x） is the set of elements of V U E adjacent or incident to x. The weight of f isw（f）∑x∈VUEf（x）.The signed mixed domination problem is to find a minimum-weight signed mixed dominating function of a graph. In this paper we study the computational complexity of signed mixed domination problem. We prove that the signed mixed domination problem is NP-complete for bipartite graphs, chordal graphs, even for planar bipartite graphs.
