Geodesic acoustic mode (GAM) and low-frequency zonal flow (LFZF) are both observed through Langmuir probe arrays during electron cyclotron resonance heating (ECRH) on the HL-2A tokamak edge. The radial distributions of the amplitude and peak frequency of GAM in floating potential fluctuations are investigated through rake probe arrays under different ECRH powers. It is observed that the GAM frequency would decrease and the intensity of carbon line emission would increase as the ECRH power exceeds a certain threshold. The analyses suggest that the impurity ions may play an important role in the GAM frequency at the edge region. It is also found that during the ECRH phase besides the mean flow, both GAM and LFZF are strengthened. The total fluctuation power and the fraction of that power associated with zonal flows both increase with the ECRH power, consistent with a predator–prey model. The auto- and cross-bicoherence analyses show the coupling between GAM and its second harmonic during the ECRH phase. Moreover, the results also suggest that the couplings between GAM and the components with multiple GAM frequency are strengthened. These couplings may be important for GAM saturation during the ECRH phase.

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In this paper, we investigate a scheduling problem with optional job rejection in a proportionate flow shop setting, where the job processing times are machine independent. A solution to our problem is characterized by (i) partitioning the set of jobs into a set of accepted jobs and a set of rejected jobs, and (ii) scheduling the accepted jobs in a proportionate flow shop setting. The aim is to find a solution to minimize the sum of total weighted late work of the accepted jobs and total rejection cost of the rejected jobs. When all jobs share a common due date, we show that the single-machine case is [Formula: see text]-hard by reduction from the Subset Sum problem. When the operations of all jobs have equal processing times, we solve the case in [Formula: see text] time by reducing it into a linear assignment problem. For the general problem, we first provide a pseudo-polynomial-time algorithm via the dynamic programming method, then we convert it into a fully polynomial time approximation scheme. As a byproduct, we also resolve an open question in the literature.