Friction stir welding （FSW） of 6061 aluminium alloy butt joint was carried out at each rotation speed of 600, 800, 1000, 1200 r/min for two different travel speeds, 80 and 100 mm/min, at a constant probe depth of 1....Friction stir welding （FSW） of 6061 aluminium alloy butt joint was carried out at each rotation speed of 600, 800, 1000, 1200 r/min for two different travel speeds, 80 and 100 mm/min, at a constant probe depth of 1.85 mm. The calculated energy input based on the FSW parameters studied shows that the ultimate tensile strength （UTS） of the butt joint is obtained within a certain range of energy input of 297 kJ to 354 kJ out of total range of energy input studied from 196 kJ to 405 kJ. The fatigue behaviors of high-strength and low-strength joints performed at different stress ratios, i.e., 0.5, 0.3, 0.1, -0.3, -0.5, indicate that the fatigue behaviors of both the welds are sensitive to the microstructural features, such as stir zone （SZ）, thermo mechanically affected zone （TMAZ） and heat affected zone （HAZ）. The observed fatigue strengths were discussed in terms of the microstructure, crack path behavior and fracture surface.展开更多
A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices＇ coloring sets are not identical and the difference of the elements colored by any...A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices＇ coloring sets are not identical and the difference of the elements colored by any two colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs Pn VPn, Cn VCn and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing equitable total are the same for join graphs Pn V Pn and Cn ∨ Cn.展开更多
Hypergraphs are the most general structures in discrete mathematics. Acyclic hypergraphs have been proved very useful in relational databases. New systems of axioms for paths, connectivity and cycles of hypergraphs ar...Hypergraphs are the most general structures in discrete mathematics. Acyclic hypergraphs have been proved very useful in relational databases. New systems of axioms for paths, connectivity and cycles of hypergraphs are constructed. The systems suit the structure properties of relational databases. The concepts of pseudo cycles and essential cycles of hypergraphs are introduced. They are relative to each other. Whether a family of cycles of a hypergraph is dependent or independent is defined. An enumeration formula for the maximum number of independent essential cycles of a hypergraph is given.展开更多
文摘Friction stir welding （FSW） of 6061 aluminium alloy butt joint was carried out at each rotation speed of 600, 800, 1000, 1200 r/min for two different travel speeds, 80 and 100 mm/min, at a constant probe depth of 1.85 mm. The calculated energy input based on the FSW parameters studied shows that the ultimate tensile strength （UTS） of the butt joint is obtained within a certain range of energy input of 297 kJ to 354 kJ out of total range of energy input studied from 196 kJ to 405 kJ. The fatigue behaviors of high-strength and low-strength joints performed at different stress ratios, i.e., 0.5, 0.3, 0.1, -0.3, -0.5, indicate that the fatigue behaviors of both the welds are sensitive to the microstructural features, such as stir zone （SZ）, thermo mechanically affected zone （TMAZ） and heat affected zone （HAZ）. The observed fatigue strengths were discussed in terms of the microstructure, crack path behavior and fracture surface.
基金the Xianyang Normal University Foundation for Basic Research(No.06XSYK266)Com~2 MaCKOSEP(R11-1999-054)
文摘A vertex distinguishing equitable total coloring of graph G is a proper total coloring of graph G such that any two distinct vertices＇ coloring sets are not identical and the difference of the elements colored by any two colors is not more than 1. In this paper we shall give vertex distinguishing equitable total chromatic number of join graphs Pn VPn, Cn VCn and prove that they satisfy conjecture 3, namely, the chromatic numbers of vertex distinguishing total and vertex distinguishing equitable total are the same for join graphs Pn V Pn and Cn ∨ Cn.
基金partially supported by the Fundamental Research Funds for the Central Universities,Nankai Universitypartially supported by NSFC(Nos.12161141006,12111540249)+2 种基金the Natural Science Foundation of Tianjin(No.20JCJQJC00090)the Fundamental Research Funds for the Central Universities,Nankai Universitypartially supported by grant DFF-7014-00037B of Independent Research Fund Denmark。
文摘Hypergraphs are the most general structures in discrete mathematics. Acyclic hypergraphs have been proved very useful in relational databases. New systems of axioms for paths, connectivity and cycles of hypergraphs are constructed. The systems suit the structure properties of relational databases. The concepts of pseudo cycles and essential cycles of hypergraphs are introduced. They are relative to each other. Whether a family of cycles of a hypergraph is dependent or independent is defined. An enumeration formula for the maximum number of independent essential cycles of a hypergraph is given.
