18,703 research outputs found

    Some sharp inequalities involving Seiffert and other means and their concise proofs

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    In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square means of two positive real numbers aa and bb with a≠ba\ne b.Comment: 10 page

    Geometric convexity of the generalized sine and the generalized hyperbolic sine

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    In the paper, the authors prove that the generalized sine function sin⁑p,q(x)\sin_{p,q}(x) and the generalized hyperbolic sine function sinh⁑p,q(x)\sinh_{p,q}(x) are geometrically concave and geometrically convex, respectively. Consequently, the authors verify a conjecture posed in the paper "B. A. Bhayo and M. Vuorinen, On generalized trigonometric functions with two parameters, J. Approx. Theory 164 (2012), no.~10, 1415\nobreakdash--1426; Available online at \url{http://dx.doi.org/10.1016/j.jat.2012.06.003}".Comment: 5 page

    Cross-Modal Message Passing for Two-stream Fusion

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    Processing and fusing information among multi-modal is a very useful technique for achieving high performance in many computer vision problems. In order to tackle multi-modal information more effectively, we introduce a novel framework for multi-modal fusion: Cross-modal Message Passing (CMMP). Specifically, we propose a cross-modal message passing mechanism to fuse two-stream network for action recognition, which composes of an appearance modal network (RGB image) and a motion modal (optical flow image) network. The objectives of individual networks in this framework are two-fold: a standard classification objective and a competing objective. The classification object ensures that each modal network predicts the true action category while the competing objective encourages each modal network to outperform the other one. We quantitatively show that the proposed CMMP fuses the traditional two-stream network more effectively, and outperforms all existing two-stream fusion method on UCF-101 and HMDB-51 datasets.Comment: 2018 IEEE International Conference on Acoustics, Speech and Signal Processin
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