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In this paper, we characterize, for 1≤$p$<∞, the multiple ($p$, 1)-summing multilinear operators on the product of$C(K)$spaces in terms of their representing polymeasures. As consequences, we obtain a new characterization of ($p$, 1)-summing linear operators on$C(K)$in terms of their representing measures and a new multilinear characterization of$L$_{∞}spaces. We also solve a problem stated by M.S. Ramanujan and E. Schock, improve a result of H. P. Rosenthal and S. J. Szarek, and give new results about polymeasures.

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Nowadays, China has become the country with the largest aging population. The increasing proportion of the elders inspires the development of related industries. Falling is extremely dangerous for the elders. Thus, it is of vital importance to detect it and send an SOS signal immediately when an elder falls. Existing methods in fall detection include vision based, wearable sensor-based, ambinent device-based techniques. However, there are drawbacks in these existing methods. The video detection cannot guarantee the privacy of the elderly. Monitoring the changing of the environment requires high cost and its accuracy may be degraded by similar phenomena like strenuous exercise or a heavy object dropping down. The wearable sensors need to be worn all the time which is uncomfortable. In this paper, widely deployed Wi-Fi system is used for detecting a fall. It has little influence on the daily life of the elderly and can make up the drawbacks of the methods above. Because human movements would affect wifi signal propagation, we could detect human behaviors, like falling, through wifi. We firstly extract Channel State Information(CSI) from the original wifi signals collected. After performing noise and dimensionality reduction via Principal Component Analysis (PCA), the characteristic data of the Wi-Fi signal is obtained. Then, the detection model is trained using Recurrent Neural Networks (RNN) based on the PyTorch deep learning. Finally, fall detection is achieved automatically based on the trained model. For further improvement of its function, a strategy based on Random State Reset (RSR) and RNN is brought up in this paper, called RSR-RNN. Related experiments have been conducted to verify the feasibility of the method developed in this paper. Six types of fall scenarios are designed according to the data collected under different situations. The results of the experiments show that the RNN model can detect a fall effectively at an accuracy of 84.67%. The average accuracy of detection is further increased to 85.83% using RSR-RNN, which indicates that this strategy is effective. Keywords:

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