The notion of $k$-frames was recently introduced by Gu avruc ta in Hilbert  spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system ...

A vacuum ultraviolet absorption spectroscopy system for a wide measurement range of atomic number densities is developed. Dual-tube inductively coupled plasma was used as a light source. The probe beam profile was optimized for the target number density range by changing the mass flow rate of the inner and outer tubes. This system was verified using cold xenon gas. As a result, the measurement ...

We analyse the conditions for producing atomic number states in a one-dimensional optical box using the Bethe ansatz method. This approach provides a general framework, enabling the study of number state production over a wide range of realistic experimental parameters. (Some figures in this article are in colour only in the electronic version)

We propose a novel unsupervised learning framework to model activities and interactions in crowded and complicated scenes. Under our framework, hierarchical Bayesian models are used to connect three elements in visual surveillance: low-level visual features, simple “atomic” activities, and interactions. Atomic activities are modeled as distributions over low-level visual features, and multiagen...