In this paper we introduce an obstacle thermistor system. The existence of weak solutions to the steady-state systems and capacity solutions to the time dependent systems are obtained by a penalized method under reasonable assumptions for the initial and boundary data. At the same time, we prove that there exists a uniform absorbing set for nonnegative initial data in L 2 (Ω). Finally for smooth initial data a global attractor to the system is obtained by a series of Campanato space arguments.

A modified algebraic multigrid (AMG) method for queueing networks is presented. The method keeps the singularity of queueing networks in the coarse grid by modifying the restriction operators. Numerical results demonstrate that this method is more efficient and robust than conventional AMG method.

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Music rhythm detection and tracking is an important part of the music comprehension system and visualization system. The music signal is subjected to a short-time Fourier transform to obtain the frequency spectrum. According to the perception characteristics of the human auditory system, the spectrum amplitude is logarithmically processed, and the endpoint intensity curve and the phase information of the peak value are output through half-wave rectification. The Pulse Code Modulation (PCM) characteristic value is extracted according to the autocorrelation characteristic of the endpoint intensity curve. This article proposes a rhythm detection algorithm based on multipath search and cluster analysis; that is, based on the clustering algorithm, it absorbs the idea of multipath tracking and proposes its own detection and tracking algorithm. It overcomes the weakness of the clustering algorithm that needs to use Musical Instrument Digital Interface (MIDI) auxiliary input to achieve the desired effect. This algorithm completely uses the PCM signal as the input, which is more robust than the clustering algorithm. The whole process is carried out in the time domain, and the amount of calculation is much smaller than the frequency domain calculation of multipath tracking, and the linear relationship with the rhythm of the music is much better than the filter bank algorithm. This algorithm can successfully detect the rhythm of the music with a strong sense of rhythm and can track the specific position of the rhythm point.