The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup...The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup if and only if it can be expressed by WBR（T, 0）, namely, the weakly Bruck-Reilly extensions of a monoid T. This result not only extends and amplifies the structure theorem of bisimple inverse ω-semigroups given by N. R. Reilly, but also generalizes the structure theorem of ,-bisimple type A ω-semigroups given by U. Asibong-Ibe in 1985.展开更多
In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some ...In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some important properties of （-）-Green＇s relations and super E（S）-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the （-）-Green＇s relations, and the semi-spined product of semigroups.展开更多
In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and ...In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.展开更多
文摘The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup if and only if it can be expressed by WBR（T, 0）, namely, the weakly Bruck-Reilly extensions of a monoid T. This result not only extends and amplifies the structure theorem of bisimple inverse ω-semigroups given by N. R. Reilly, but also generalizes the structure theorem of ,-bisimple type A ω-semigroups given by U. Asibong-Ibe in 1985.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10871161, 10926031）, Natural Science Foundation Project of CQ CSTC2009BB2291, the Young Science and Technology Fund of Xi＇an University of Architecture and Technology （Grant No. QN0829）
文摘In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some important properties of （-）-Green＇s relations and super E（S）-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the （-）-Green＇s relations, and the semi-spined product of semigroups.
文摘In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.
