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Abstract The inertial measurement unit (IMU) and magnetic, angular rate, and gravity (MARG) sensor orientation and position are widely used in the medical, robotics, and other fields. In general, the orientations can be defined by the integration of angular velocity data, and the positions are also computed from the double integration of acceleration data. However, the acceleration and angular velocity data are often inaccurate due to measurement errors which arise when the sensor moves quickly. Therefore, the orientations and positions significantly differ from the actual values. To address these issues, several techniques are proposed for the accurate measurement of IMU and MARG sensor orientations and positions. The proposed optimization method is applied to raw sensor data to compute faithful orientations by stabilizing and accelerating the convergence of the optimization process. Furthermore, a deep neural network based on 1D convolutional neural network (CNN) layers is proposed to predict the desired velocity from raw acceleration data. The method is validated qualitatively and quantitatively with an optical motion capture (mocap) system. The experimental results show that the proposed method significantly improves orientation and position estimations compared to those of other approaches.

Three-dimensional mesh post-processing is an important task because low-precision hardware and a poor capture environment will inevitably lead to unordered point clouds with unwanted noise and holes that should be suitably corrected while preserving the original shapes and details. Although many 3D mesh data-processing approaches have been proposed over several decades, the resulting 3D mesh often has artifacts that must be removed and loses important original details that should otherwise be maintained. To address these issues, we propose a novel 3D mesh completion and denoising system with a deep learning framework that reconstructs a high-quality mesh structure from input mesh data with several holes and various types of noise. We build upon SpiralNet by using a variational deep autoencoder with anisotropic filters that apply different convolutional filters to each vertex of the 3D mesh. Experimental results show that the proposed method enhances the reconstruction quality and achieves better accuracy compared to previous neural network systems.

We prove Amann type three solutions theorem for one dimensional p-Laplacian problems with a singular weight function. To prove this theorem, we define a strong upper and lower solutions and compute the Leray-Schauder degree on a newly established weighted solution space. As an application, we consider the combustion model and show the existence of three positive radial solutions on an exterior domain.

This article explores the Korean application of "mind-transmission" (K. chŏnsim, C. chuanxin) episodes to the intra-Sŏn (C. Chan) polemics. Korean Sŏn masters, unlike Chinese counterparts, sought for the religious meaning of the existence of multiple transmission episodes that circulated in East Asia from the Sŏn polemical perspective. In particular, Kagun and Paekp'a used the term "samch' ŏ chŏnsim" to promote their own visions of Sŏn within the situation in which different visions of Sŏn competed for dominance. [ABSTRACT FROM AUTHOR]