This paper studies the frames corresponding to oversampled filter banks (FBs). For this class of FB frames, we present a state-space parameterization of perfect reconstruction FB frames and explicit and numerically efficient formulas to compute the tightest frame bounds, to obtain the dual FB frame, and to construct a tight (paraunitary) FB frame from a given untight (nonparaunitary) FB frame. The derivation uses well-developed techniques from modern control theory, which results in the unified formulas for generic infinite-impulse-response (IIR) and finite-impulse-response (FIR) FBs. These formulas involve only algebraic manipulations of real matrices and can be computed efficiently, reliably, and exactly without the approximation required in the existing methods for generic FBs. The results provide a unified framework for frame-theory-based analysis and systematic design of oversampled filter banks.

The rapid drop of frequency under the disturbance is a major threat to the safe and stable operation of a microgrid (MG) system. Emergency load shedding is the main measure to prevent continuous frequency drop and power outage. The existing load shedding strategies have poor adaptability to deal with the problem of MG load shedding under different disturbance situations, and it is difficult to ensure the safe and stable operation of an MG in different operating environments. To address this problem, this paper proposes a data-driven load shedding strategy. First, considering the importance of the load and the frequency recovery time of the system, a load shedding contribution indicator is designed that takes into account the load frequency adjustment effect and the load shedding priority. This contribution indicator is introduced as a load shedding criterion into the reward value function of dueling deep Q learning. Second, considering the suddenness and uncertainty of emergency load shedding, a MG emergency load shedding strategy (ELSS) based on dueling deep Q-learning is proposed. On this basis, the dueling deep Q learning algorithm is used to obtain the load shedding decision with the maximum cumulative reward. Finally, taking the MG load shedding cases in two different scenarios as examples, a simulation study is carried out on a modified IEEE-25 bus MG. The simulation results show that, compared with the model-driven implicit enumeration strategy (IES), the proposed ELSS has superiority in maintaining stable power supply for important loads and reducing load shedding decision-making time and frequency fluctuations.

Phase change mechanisms during femtosecond laser pulse train ablation of nickel thin filmsCopper microdroplets were deposited onto a quartz substrate by the laser-induced forward transfer ͑LIFT͒ using laser pulses of 148 fs at a center wavelength of 775 nm. The droplets with 2 -3 m diameters were transferred at a laser pulse energy slightly above the threshold at which the copper film could be removed completely. The droplet formation was a result of the blow-off of a molten film from the quartz substrate by a compressive stress of plasma when the free surface was melted and was different from the microdroplet formation by the LIFT technique using nanosecond laser pulse.

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