scholarly journals Distance functions with dense singular sets

Author(s):  
Mario Santilli
2008 ◽  
Vol 37 (3) ◽  
Author(s):  
Jacek Urbański ◽  
Agata Ślimak

Assessing flood risk and detecting changes of salt water inflow in a coastal micro-tidal brackish marsh using GISIn order to assess changes in salt water inflow and potential flood risks due to sea level rise in a micro-tidal Beka brackish marsh on the Polish Baltic Coast GIS was used. Such wetlands are important elements of coastal zone natural environments. Creating a geodatabase within a GIS system makes it possible to carry out broad analyses of complex systems, such as coastal wetlands. The results indicate that a 40 cm sea-level rise would considerably increase the frequency of flooding in the investigated area, in part because of the small range of the annual sea level oscillations there. A map of the index of changes in saltwater inflow, created with the help of cost-weighted distance (functions), shows that changes which have occurred along the shore, consisting of filling in the drainage channel outlets, have likely had a significant impact on the vegetation of the area.


2011 ◽  
Vol 8 (1) ◽  
pp. 201-210
Author(s):  
R.M. Bogdanov

The problem of determining the repair sections of the main oil pipeline is solved, basing on the classification of images using distance functions and the clustering principle, The criteria characterizing the cluster are determined by certain given values, based on a comparison with which the defect is assigned to a given cluster, procedures for the redistribution of defects in cluster zones are provided, and the cluster zones parameters are being changed. Calculations are demonstrating the range of defect density variation depending on pipeline sections and the universal capabilities of linear objects configuration with arbitrary density, provided by cluster analysis.


Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4587-4612 ◽  
Author(s):  
S.K. Padhan ◽  
Rao Jagannadha ◽  
Hemant Nashine ◽  
R.P. Agarwal

This paper extends and generalizes results of Mukheimer [(?,?,?)-contractive mappings in ordered partial b-metric spaces, J. Nonlinear Sci. Appl. 7(2014), 168-179]. A new concept of (?-?1-?2)-contractive mapping using two altering distance functions in ordered b-metric-like space is introduced and basic fixed point results have been studied. Useful examples are illustrated to justify the applicability and effectiveness of the results presented herein. As an application, the existence of solution of fourth-order two-point boundary value problems is discussed and rationalized by a numerical example.


Author(s):  
Ahmad Afuni

AbstractWe establish new local regularity results for the harmonic map and Yang–Mills heat flows on Riemannian manifolds of dimension greater than 2 and 4, respectively, obtaining criteria for the smooth local extensibility of these flows. As a corollary, we obtain new characterisations of singularity formation and use this to obtain a local estimate on the Hausdorff measure of the singular sets of these flows at the first singular time. Finally, we show that smooth blow-ups at rapidly forming singularities of these flows are necessarily nontrivial and admit a positive lower bound on their heat ball energies. These results crucially depend on some local monotonicity formulæ for these flows recently established by Ecker (Calc Var Partial Differ Equ 23(1):67–81, 2005) and the Afuni (Calc Var 555(1):1–14, 2016; Adv Calc Var 12(2):135–156, 2019).


2021 ◽  
Vol 9 (1) ◽  
pp. 53-64
Author(s):  
Vitali Kapovitch ◽  
Alexander Lytchak

Abstract We discuss folklore statements about distance functions in manifolds with two-sided bounded curvature. The topics include regularity, subsets of positive reach and the cut locus.


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