Driver fatigue problem is one of the important factors of traffic accidents. Recent years, many research had investigated that using EEG signals can effectively detect driver's drowsiness level. However, real-time monitoring system is required to apply these fatigue level detection techniques in the practical application, especially in the real-road driving. Therefore, it required less channels, portable and wireless, real time monitoring and processing techniques for developing the real-time monitoring system. In this study, we develop a single channel wireless EEG device which can real-time detect driver's fatigue level on the mobile device such as smart phone or tablet. The developed device is investigated to obtain a better and precise understanding of brain activities of mental fatigue under driving, which is of great benefit for devolvement of detection of driving fatigue system. This system consists of a Bluetooth enabled one channel EEG, a regression model, and smartphone, which was a platform recording and transforming the raw EEG data to useful driving status. In the experiment, this was a sustained-attention driving task to implement in a virtual-reality (VR) driving simulator. To training model and develop the system, we were performed for 15 subjects to study Electroencephalography (EEG) brain dynamics by using a mobile and wireless EEG device. Based on the outstanding training results, the leave-one-subject-out cross validation test obtained 90% fatigue detection accuracy. These results indicate that the combination of a smartphone and wireless EEG device constitutes an effective and easy wearable solution for detecting and preventing driver fatigue in real driving environments.
Using a forward-backward induction method, we proved that n 1+β is a lower bound of the series n i=1 1 1+a i , where a i is a positive integer greater than 1, and β is the geometric mean from a 1 to a n . We also proved that n 1+γ is an upper bound of the series, where γ is the harmonic mean from a 1 to a n .
Let ϕ be an Orlicz function that has a complementary function ϕ * and let ϕ be an Orlicz sequence space. We prove two results in this paper. Result 1: ϕ⊗F X, the Fremlin projective tensor product of ϕ with a Banach lattice X, has the Radon-Nikodym property if and only if both ϕ and X have the Radon-Nikodym property. Result 2: ϕ⊗iX , the Wittstock injective tensor product of ϕ with a Banach lattice X, has the Radon-Nikodym property if and only if both ϕ and X have the Radon-Nikodym property and each positive continuous linear operator from hϕ * to X is compact.
While studying Cvetkovski's book "Inequalities: Theorems, Techniques and Selected Problems", we noticed a pattern from several three variable cyclic inequalities with sums of fractions. Using mathematical induction and AM-GM inequality, we proved our assertion of this pattern. We also used rearrangement inequality, Chebyshev's sum inequality and a weighted Hölder's inequality to generalize our results to the case when the exponents in these fractions are positive real numbers.
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