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Remarks on the Belitskii-Lyubich and discrete Markus-Yamabe conjectures

Sart Frédéric

Journal of Applied Analysis

2023

Vol. 29, nr 1

99--103

In this paperwe prove the Belitskii-Lyubich conjecture for triangular and gradientmappings. These results resemble those obtained for the discrete Markus-Yamabe conjecture. However, the proofs are quite different,which sheds new light on the subject.We complete the picture by showing that the general versions of the two conjectures can be turned into theorems at little cost, simply by relaxing their spectral condition.

Application of high-density bathymetric data for visualization of MSIS sonar data

Wawrzyniak N., Bodus-Olkowska I., Stateczny A.

Zeszyty Naukowe / Akademia Morska w Szczecinie

2013

nr 35 (107)

154--160

Mechanically scanned imaging sonars (MSIS) are mainly used for detection of small objects or aiding in underwater navigation in limited area. Obtained images are detailed and, especially for not experienced user, they may give an impression of a photography. However, the acoustic method of acquisition of sonar data must be taken into account, as understanding observed scene is essential to properly interpret the data. To aid the process of image interpretation the reference data may be used. In this paper the application of bathymetric data to MSIS sonar images is proposed. To match high resolution of MSIS images the density of bathymetric data must exceed the requirements of S-44 IHO norm. For this research a swath bathymetric system based on phase interferometry of acoustic signal was used to obtain such data in shallow waters. The article covers the motivation of usage of such data in comparison to other existing bathymetric systems. The proposed method uses acquired data to create additional channel in sonar image emphasizing sea-bed gradient in relation to sonar head position and distinguish invisible / shadowed areas. Proposed method is based on directional derivative of a sea-bed. Method presented in this article is a part of bigger research on enhancing interpretative potential of stationary sonar images [1].