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). Moreover, most morphodynamic flows cause the appearance of significant morphological changes for example the accumulation and deposition of sediments at crossroads and near all types of obstacles during torrential floods, these events constitute a serious

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. , and Ludmány , B. ( 2020 ). A new workflow for the automated measurement of shape descriptors of rocks . Budapest University of Technology and Economics, MTA-BME Morphodynamics Research Group . https://doi.org/10.5446/45980 , Last accessed : 20

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Pollack Periodica
Authors:
Daniel Buček
,
Martin Orfánus
,
Peter Dušička
, and
Peter Šulek

value represents an average of 10 repeated measurements in order to minimize the error due to temporal fluctuation in bed load rate [ 31 ]. Bedload data originating from this study provide extensive foundation for proper calibration of a morphodynamic

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A classical result of Dowker (Bull. Amer. Math. Soc. 50: 120-122, 1944) states that for any plane convex body 𝐾, the areas of the maximum (resp. minimum) area convex 𝑛-gons inscribed (resp. circumscribed) in 𝐾 is a concave (resp. convex) sequence. It is known that this theorem remains true if we replace area by perimeter, or convex 𝑛-gons by disk-𝑛-gons, obtained as the intersection of 𝑛 closed Euclidean unit disks. It has been proved recently that if 𝐶 is the unit disk of a normed plane, then the same properties hold for the area of 𝐶-𝑛-gons circumscribed about a 𝐶-convex disk 𝐾 and for the perimeters of 𝐶-𝑛-gons inscribed or circumscribed about a 𝐶-convex disk 𝐾, but for a typical origin-symmetric convex disk 𝐶 with respect to Hausdorff distance, there is a 𝐶-convex disk 𝐾 such that the sequence of the areas of the maximum area 𝐶-𝑛-gons inscribed in 𝐾 is not concave. The aim of this paper is to investigate this question if we replace the topology induced by Hausdorff distance with a topology induced by the surface area measure of the boundary of 𝐶.

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Hujter and Lángi defined the k-fold Borsuk number of a set S in Euclidean n-space of diameter d > 0 as the smallest cardinality of a family F of subsets of S, of diameters strictly less than d, such that every point of S belongs to at least k members of F.

We investigate whether a k-fold Borsuk covering of a set S in a finite dimensional real normed space can be extended to a completion of S. Furthermore, we determine the k-fold Borsuk number of sets in not angled normed planes, and give a partial characterization for sets in angled planes.

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Abstract

While three-dimensional measurement technology is spreading fast, its meaningful application to sedimentary geology still lacks content. Classical shape descriptors (such as axis ratios, circularity of projection) were not inherently three-dimensional, because no such technology existed. Recently a new class of three-dimensional descriptors, collectively referred to as mechanical descriptors, has been introduced and applied for a broad range of sedimentary particles. First-order mechanical descriptors (registered for each pebble as a pair {S, U} of integers), refer to the respective numbers of stable and unstable static equilibria and can be reliably detected by hand experiments. However, they have limited ability of distinction, as the majority of coastal pebbles fall into primary class { S , U } = { 2 , 2 } . Higher-order mechanical descriptors offer a more refined distinction. However, for the extraction of these descriptors (registered as graphs for each pebble), hand measurements are not an option and even computer-based extraction from 3D scans offers a formidable challenge. Here we not only describe and implement an algorithm to perform this task, but also apply it to a collection of 271 pebbles with various lithologies, illustrating that the application of higher-order descriptors is a viable option for geologists. We also show that the so-far uncharted connection between the two known secondary descriptors, the so-called Morse–Smale graph and the Reeb-graph, can be established via a third order descriptor which we call the master graph.

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] Villaret C. , Kopmann R. , Wyncoll D. , Riehme J. , Merkel U. M. , Naumann U. First-order uncertainty analysis using Algorithmic Differentiation of morphodynamic models , Computers & Geosciences , Vol. 90

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Hreško, J. and M. Boltižiar. 2001. The influence of the morphodynamic processes to landscape structure in the high mountains (Tatra Mts.). Ekológia (Bratislava) 20,Supplement 3: 141–149. Boltižiar M

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France by Paul Guillaume in 1937. 25 The following list stems from my musicological work, and focuses on the stages of theoretical evolution as determined by musical practice. Circa 1968: the emergence of morphodynamics, morphogenesis, catastrophe

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