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
A comprehensive simulation was performed to better understand the impacts and effects of the additional technical noises on weak-light phase-locking for LISA. The result showed that the phase of the slave laser tracke...A comprehensive simulation was performed to better understand the impacts and effects of the additional technical noises on weak-light phase-locking for LISA. The result showed that the phase of the slave laser tracked well with the received transmitting light under different noise level, and the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed. This result was then confirmed by a benchtop experimental test. The required LISA noise floor was recovered from the simulation which proved the validity of the simulation program. In order to convert the noise function into real time data with random characteristics, an algorism based on Fourier transform was also invented.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.
基金supported by the Space Science Research Projects in Advance(Grant No.O930143XM1)the Scientific Equipment Development and Research Project(Grant No.Y231411YB1) of Chinese Academy of Sciences
文摘A comprehensive simulation was performed to better understand the impacts and effects of the additional technical noises on weak-light phase-locking for LISA. The result showed that the phase of the slave laser tracked well with the received transmitting light under different noise level, and the locking precision was limited by the phase readout noise when the laser frequency noise and clock jitter noise were removed. This result was then confirmed by a benchtop experimental test. The required LISA noise floor was recovered from the simulation which proved the validity of the simulation program. In order to convert the noise function into real time data with random characteristics, an algorism based on Fourier transform was also invented.
