摘要： The St. Benedict ion trapping system, which aims to measure the β−ν angular correlation parameter in superallowed-mixed mirror transitions, is under construction at the University of Notre Dame. These measurements will provide much-needed data to improve the accuracy of the Vud element of the CKM matrix. One of the major components of this system is the radio frequency quadrupole cooler-buncher, which is necessary to create low-emittance ion bunches for injection into the measurement Paul trap. The off-line commissioning of the cooler-buncher, using a potassium ion source, determined that the device could produce cooled ion bunches characterized by a 50-ns full-width-half-maximum time width. The commissioning results also determined the trapping efficiency to be 93(1)% and the trapping half-life to be 20.0(5) s.

关键词： Probabilistic normed space   Set-valued functions   Kuratowski convergence   alpha beta-statistical convergence   Graph convergence   Pointwise convergence   Semi-continuity   Equi-continuity  

摘要： The notions of graphical and pointwise limits of a sequence of set-valued functions defined from one metric space into another were studied by Aubin and Frankowska. In this study, by using the concept of alpha beta-density of subsets of natural numbers, we introduce the notions of St(gamma)(alpha beta)-graphical and St(gamma)(alpha beta)-pointwise limits of a sequence of set-valued functions defined from one probabilistic normed space into another. Subsequently, the article introduces the notions of St(gamma)(alpha beta)-graph and St(gamma)(alpha beta)-pointwise convergence of these sequences. Moreover, we look at the correspondence between these convergences and establish some associated theorems.