scholarly journals On Ricci curvature of metric structures on g-manifolds

Author(s):  
Vladimir Rovenski ◽  
Robert Wolak
2018 ◽  
pp. 99-107
Author(s):  
V. V. Lavrov ◽  
R. S. Luchkin ◽  
O. I. Nemykin ◽  
M. E. Prokhorov ◽  
Yu. G. Ryndin ◽  
...  

Methods and algorithms for the complete processing of a post-detector low-contrast optical image (OI) of an unknown remote object obtained by ground-based optical means of observation under conditions of a complex background situation are considered. The purpose of processing is to separate and interpret at least with the help of the analyst, of the main constructive elements using the integrated indicators introduced in [6] and the characteristics of the analyzed OI, which are connected by the information, topological and metric structures of the OI. The stages of processing the OI include extracting the image-containing information object of the image portion (detection) and filtration of the OI, using recursive rank filtering. The final stages of processing include the segmentation of the OI and the allocation on it constructive elements using the apparatus of graph theory. An example of image processing of a Spot-5 spacecraft obtained in real conditions is given. It is shown that in this case at the detection stage it is possible to reduce the volume of information processed at subsequent stages by 8 times, in the filtration process to increase the compactness of the OI and to increase its connectivity in comparison with the post-detection OI. As a result of segmentation and allocation of constructive elements, three structural elements that can be interpreted as a spacecraft case and two remote panels can be identified with the analyst’s participation.


Author(s):  
Ulrich Kohlenbach

AbstractIn this note we show that proof-theoretic uniform boundedness or bounded collection principles which allow one to formalize certain instances of countable Heine–Borel compactness in proofs using abstract metric structures must be carefully distinguished from an unrestricted use of countable Heine–Borel compactness.


2012 ◽  
Vol 23 (04) ◽  
pp. 1250009 ◽  
Author(s):  
JEONGWOOK CHANG ◽  
JINHO LEE

We derive Harnack-type inequalities for non-negative solutions of the porous medium equation on a complete Riemannian manifold with non-negative Ricci curvature. Along with gradient estimates, reparametrization of a geodesic and time rescaling of a solution are key tools to get the results.


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