Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively...Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain： （i） the necessary and sufficient conditions for S（A,b）≠Ф; （ii） the necessary conditions for IS（A,b）｜ = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S（A, b） if S（A, b）≠Ф.展开更多
Acyclic databases possess several desirable properties for their design and use. Adistributed algorithm is proposed for determining a minimal cover of an alpha-, beta-,gamma-, or Berge-acyclic database scheme over a s...Acyclic databases possess several desirable properties for their design and use. Adistributed algorithm is proposed for determining a minimal cover of an alpha-, beta-,gamma-, or Berge-acyclic database scheme over a set of attributes in a distributedenvironment.展开更多
Let B（G） denote the bipartite double cover of a non-bipartite graph G with v ≥ 2 vertices and s edges. We prove that G is a perfect 2-matching covered graph if and only if B（G） is a 1-extendable graph. Furthermor...Let B（G） denote the bipartite double cover of a non-bipartite graph G with v ≥ 2 vertices and s edges. We prove that G is a perfect 2-matching covered graph if and only if B（G） is a 1-extendable graph. Furthermore, we prove that B（G） is a minimally l-extendable graph if and only if G is a minimally perfect 2-matching covered graph and for each e = xy ∈ E（G）, there is an independent set S in G such that ｜ГG（S）｜ = ｜S｜ ＋ 1, x ∈ S and ｜ГG-xy（S）｜ = ｜S｜ Then, we construct a digraph D from B（G） or G and show that D is a strongly connected digraph if and only if G is a perfect 2-matching covered graph. So we design an algorithm in O（x√vε） time that determines whether G is a perfect 2-matching covered graph or not.展开更多
基金supported by the NNSF (10471035,10771056) of China
文摘Let （L, 〈, V, A） be a complete Heyting algebra. In this article, the linear system Ax = b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by V and A respectively, is studied. We obtain： （i） the necessary and sufficient conditions for S（A,b）≠Ф; （ii） the necessary conditions for IS（A,b）｜ = 1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S（A, b） if S（A, b）≠Ф.
文摘Acyclic databases possess several desirable properties for their design and use. Adistributed algorithm is proposed for determining a minimal cover of an alpha-, beta-,gamma-, or Berge-acyclic database scheme over a set of attributes in a distributedenvironment.
基金Acknowledgements The authors would like to thank the referees very much for their careful reading and their very instructive suggestions which improve this paper greatly. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11201158）.
文摘Let B（G） denote the bipartite double cover of a non-bipartite graph G with v ≥ 2 vertices and s edges. We prove that G is a perfect 2-matching covered graph if and only if B（G） is a 1-extendable graph. Furthermore, we prove that B（G） is a minimally l-extendable graph if and only if G is a minimally perfect 2-matching covered graph and for each e = xy ∈ E（G）, there is an independent set S in G such that ｜ГG（S）｜ = ｜S｜ ＋ 1, x ∈ S and ｜ГG-xy（S）｜ = ｜S｜ Then, we construct a digraph D from B（G） or G and show that D is a strongly connected digraph if and only if G is a perfect 2-matching covered graph. So we design an algorithm in O（x√vε） time that determines whether G is a perfect 2-matching covered graph or not.
