Some characterizations of spheres and elliptic paraboloids II

We show some characterizations of hyperspheres in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$ with intrinsic and extrinsic properties such as the $n$-dimensional area of the sections cut off by hyperplanes, the $(n+1)$-dimensional volume of regions between parallel hyperplanes, and the $n$-dimensional surface area of regions between parallel hyperplanes. We also establish two characterizations of elliptic paraboloids in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$ with the $n$-dimensional area of the sections cut off by hyperplanes and the $(n+1)$-dimensional volume of regions between parallel hyperplanes. For further study, we suggest a few open problems.Comment: 10 page

A Fully Time-domain Neural Model for Subband-based Speech Synthesizer

This paper introduces a deep neural network model for subband-based speech synthesizer. The model benefits from the short bandwidth of the subband signals to reduce the complexity of the time-domain speech generator. We employed the multi-level wavelet analysis/synthesis to decompose/reconstruct the signal into subbands in time domain. Inspired from the WaveNet, a convolutional neural network (CNN) model predicts subband speech signals fully in time domain. Due to the short bandwidth of the subbands, a simple network architecture is enough to train the simple patterns of the subbands accurately. In the ground truth experiments with teacher-forcing, the subband synthesizer outperforms the fullband model significantly in terms of both subjective and objective measures. In addition, by conditioning the model on the phoneme sequence using a pronunciation dictionary, we have achieved the fully time-domain neural model for subband-based text-to-speech (TTS) synthesizer, which is nearly end-to-end. The generated speech of the subband TTS shows comparable quality as the fullband one with a slighter network architecture for each subband.Comment: 5 pages, 3 figur