Browsing by Author Wei, Tang
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We study the eigenvalues and eigenfunctions of one-dimensional weighted fractal Laplacians. These Laplacians are defined by self-similar measures with overlaps. We first prove the existence of eigenvalues and eigenfunctions. We then set up a framework for one-dimensional measures to discretize the equation defining the eigenvalues and eigenfunctions, and obtain numerical approximations of the eigenvalue and eigenfunction by using the finite element method. Finally, we show that the numerical eigenvalues and eigenfunctions converge to the actual ones and obtain the rate of convergence. |
Tactile perception plays a critical role in the interaction of humans and environment. It begins with the mechanical stimulation induced by friction and is processed in the somatosensory cortex. To quantify the tactile perceptions of textile fabrics, the mechanical properties of fabrics and the features extracted from the friction and vibration signals were correlated with the subjective sensation rated by questionnaires. Meanwhile, the technique of functional magnetic resonance imaging (fMRI) was used to identify the brain areas responsible for the tactile perception of textile fabrics. |
