Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). T...Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). The main result in this paper says that if there exists a completely regular Hausdorff space X such that E is Riesz algebra isomorphic to C(X) then for every i ∈ I there exists a completely regular Hausdorff space X, such that B(ei) is Riesz algebra isomorphic to C(Xi). Under an additional condition the inverse holds.展开更多
The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean ...The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean Riesz space possessing a weak unit e and a maximal disjoint division{e i:i∈I} in which each e i is a proj ection element. Concerning the following statements:(1) There exists a completel y regular Hausdorff space X such that E is Riesz isomorphic to C(X);(2) For every i∈I there exi sts a completely regular Hausdorff space X i such that the band generated by e i is Riesz isomorphic to C(X i).It is shown that (1) implies (2),and find some conditions for the inverse bein g true are found.Furthermore,if each X i in (2) is a compact Ha usdorff space, a necessary and sufficient condition is established under which E can be represented as a C(X) for some compact Hausdorff space X.As corollaries, corresponding results for late rally complete Riesz spaces are obtained.展开更多
Projection welding is a variation of electric resistance welding with the dynamic changes of the flow paths for heat and electrical properties with changing temperature caused by the large plastic deformation collapse...Projection welding is a variation of electric resistance welding with the dynamic changes of the flow paths for heat and electrical properties with changing temperature caused by the large plastic deformation collapse of projection. As the joint type between the auto door hinge and the inner plate, projection welding may bring welding distortions and would affect the assembly quality of auto body. A comprehensive electric-thermal-mechanical numerical simulation was performed to quantitatively simulate the processes of projection welding by using a coupled finite element method. The mechanism of projection collapse and the formation process of nugget were discussed and good conclusions have been achieved comparing with the test results.展开更多
文摘Let E be an Archimedean Riesz algebra possessing a weak unit element e and a maximal disjoint system {e,: i∈I} in which e, is a projection element for each i. The principal band generated by eiis denoted by B(ei). The main result in this paper says that if there exists a completely regular Hausdorff space X such that E is Riesz algebra isomorphic to C(X) then for every i ∈ I there exists a completely regular Hausdorff space X, such that B(ei) is Riesz algebra isomorphic to C(Xi). Under an additional condition the inverse holds.
文摘The authors p oint out a problem in the article of Ref.(Xiong Hongyun,Rong Ximin.Maximal disjoint systems in Riesz space and representation.Acta Math Sinica ,1998,41(4):763-766.)and revise it.Let E be an Archimed ean Riesz space possessing a weak unit e and a maximal disjoint division{e i:i∈I} in which each e i is a proj ection element. Concerning the following statements:(1) There exists a completel y regular Hausdorff space X such that E is Riesz isomorphic to C(X);(2) For every i∈I there exi sts a completely regular Hausdorff space X i such that the band generated by e i is Riesz isomorphic to C(X i).It is shown that (1) implies (2),and find some conditions for the inverse bein g true are found.Furthermore,if each X i in (2) is a compact Ha usdorff space, a necessary and sufficient condition is established under which E can be represented as a C(X) for some compact Hausdorff space X.As corollaries, corresponding results for late rally complete Riesz spaces are obtained.
基金The National Natural Science Foundation of China(No.50575140)
文摘Projection welding is a variation of electric resistance welding with the dynamic changes of the flow paths for heat and electrical properties with changing temperature caused by the large plastic deformation collapse of projection. As the joint type between the auto door hinge and the inner plate, projection welding may bring welding distortions and would affect the assembly quality of auto body. A comprehensive electric-thermal-mechanical numerical simulation was performed to quantitatively simulate the processes of projection welding by using a coupled finite element method. The mechanism of projection collapse and the formation process of nugget were discussed and good conclusions have been achieved comparing with the test results.
