Xiaoming Wang

Sigal Gottlieb, Florentina Tone, Cheng Wang et al.

We prove that a popular classical implicit-explicit scheme for the 2D incompressible Navier--Stokes equations that treats the viscous term implicitly while the nonlinear advection term explicitly is long time stable provided that the time step is sufficiently small in the case with periodic boundary conditions. The long time stability in the $L^2$ and $H^1$ norms further leads to the convergence of the global attractors and invariant measures of the scheme to those of the NSE itself at vanishing time step. Both semi-discrete in time and fully discrete schemes with either Galerkin Fourier spectral or collocation Fourier spectral methods are considered.

Xiaoming Wang, Zhiguo Gong

Robot calligraphy is an emerging exploration of artificial intelligence in the fields of art and education. Traditional calligraphy generation researches mainly focus on methods such as tool-based image processing, generative models, and style transfer. Unlike the English alphabet, the number of Chinese characters is tens of thousands, which leads to difficulties in the generation of a style consistent Chinese calligraphic font with over 6000 characters. Due to the lack of high-quality data sets, formal definitions of calligraphy knowledge, and scientific art evaluation methods, The results generated are frequently of low quality and falls short of professional-level requirements. To address the above problem, this paper proposes an automatic calligraphy generation model based on deep generative adversarial networks (deepGAN) that can generate style calligraphy fonts with professional standards. The key highlights of the proposed method include: (1) The datasets use a high-precision calligraphy synthesis method to ensure its high quality and sufficient quantity; (2) Professional calligraphers are invited to conduct a series of Turing tests to evaluate the gap between model generation results and human artistic level; (3) Experimental results indicate that the proposed model is the state-of-the-art among current calligraphy generation methods. The Turing tests and similarity evaluations validate the effectiveness of the proposed method.