A new partial differential equation for image inpainting

A considerable interest in the inpainting problem have attracted many researchers in applied mathematics community. In fact in the last decade, nonlinear high order partial dierential equations have payed a central role in high quality inpainting developments. In this paper, we propose a technique for inpainting that combines an anisotropic diusion process with an edge-corner enhancing shock ltering. This technique makes use of a partial differential equation that is based on a nonlinear structure tensor which increases the accuracy and robustness of the coupled diusion and shock ltering. A methodology of partition and adjustment is used to estimate the contrast parameters that control the strength of the diffusivity functions. We focus on restoring large missing regions in grey scale images containing complex geometries parts. Our model is extended to a three dimensional case, where numerical experimentations were carried out on lling brain multiple sclerosis lesions in medical images. The efficiency and the competitiveness of the proposed algorithm is numerically compared to other approaches on both synthetic and real images.

Algorithms for analysis of stability and dynamic characteristics of signal generators at the physical level in FANET networks

To ensure the reliability of the physical level of Flying Ad Hoc Networks (FANET), the article substantiates the relevance of the study of stability and dynamic processes of signal formation and processing paths in the terminal and intermediate network equipment. The limitations of the known methods of the theory of automatic control, which make it difficult to perform the analysis of essentially nonlinear high-order signal generators, are shown. To analyze the stability of such formations proposed algorithm based on the use of the Nyquist criterion and approximation of the characteristic polynomial of a device by continuous piecewise functions; to analyze the dynamic characteristics of the algorithm based on spectral method of the input signal approximation and the frequency characteristics of a device by continuous piecewise functions.

Remarks on the critical nonlinear high-order heat equation

The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.