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Abstract This paper studies the existence and uniqueness of solutions for a new kind of mixed fractional differential systems with slit-strips conditions, containing Caputo-type fractional derivatives. The first result on the existence and uniqueness is based on Banach’s fixed point theorem, and the second result on the existence and uniqueness of the solution is proved by using a Schaefer-type fixed point theorem. The applicability of our primary results is finally illustrated by some examples.

In this article, we consider the low Mach number limit of the compressible nematic liquid crystal flows in a 3D bounded domain. We establish the uniform estimates with respect to the Mach number for the strong solutions with large initial data in a short time interval. Consequently, we obtain the convergence of the compressible nematic liquid crystal system to the incompressible nematic liquid crystals system as the Mach number tends to zero.

Wavelet algorithms for high-resolution image reconstruction has been shown effectively, it relies on the decomposition of low/high frequency, and hard/soft thresholding arguments are often used to denoise for high frequency. In this paper, instead of using this kind of thresholding arguments, we apply the gradient based shrinkage thresholding optimization for high-frequency, in this way, we can keep the useful information in the original signal as much as possible, coupling the shrinkage thresholding optimization with the wavelet algorithm, we get an efficient reconstruction algorithm. Numerical results show we obtain a higher resolution, better peak signal-to-noise ratios and lower relative errors. [ABSTRACT FROM AUTHOR]

Image sharpening can highlight fine details in images but with a tendency of amplifying noise. This paper proposes a novel idea of incorporating an image sharpening operator into a framelet-based model for image deblurring. The proposed model is convex and hence it can be solved efficiently by the semi-proximal alternating direction method of multipliers (sPADMM) with guaranteed linear rate convergence, which covers the classical ADMM. The experimental results on different blurring kernels and Gaussian noise levels show that the proposed approach outperforms the state-of-the-art methods in terms of PSNR, SSIM, relative error, and visual quality. [ABSTRACT FROM AUTHOR]