For a wide class of radial weights we calculate the essential norm of a weighted composition operator uCϕ on the weighted Banach spaces of analytic functions in terms of the analytic function u : D → C and the nth power of the analytic selfmap ϕ of the open unit disc D.We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general radial weights.Mathematics Subject Classification (2010). Primary 47B33, 47B38.

The present qubit technology, in particular in Josephson qubits, allows an unprecedented control of discrete energy levels. This motivates a new study of the old pump-probe problem, where a discrete quantum system is driven by a strong drive and simultaneously probed by a weaker one. The strong drive is included by the Floquet method and the resulting quasienergy states are then studied with the probe. We study a qubit where the harmonic drive has a significant longitudinal component relative to the static equilibrium state of the qubit. Both analytical and numerical methods are used to solve the problem. We present calculations with realistic parameters and compare the results with recent experimental results. A short introduction to the Floquet method and the probe absorption is given.

No abstract

The reliability of non-destructive evaluation depends on multitude of different factors. Consequently, it is difficult to assess the performance of the system. The only practical way to overcome this complexity and asses inspection reliability is using practical trials. In practical trials the inspection is performed on a known, flawed sample and reliability is judged by comparing the acquired inspection result with known state of the sample. However, confirming (and demonstrating), that the practical trials and, in particular, the used flaws are representative to postulated inspection case is, at present, challenging.In this paper, the open literature is reviewed and compiled to the extent necessary for providing a starting point for confirming and demonstrating representativeness of flaws used in the practical trials. The available information on essential flaw parameters for various NDE techniques is reviewed. The used measurement methods for each parameter is discussed and the available in-service data summarized. Finally, a simple procedure is proposed for confirming and demonstrating the representativeness of used flaws.

No abstract