scholarly journals Farthest points on most Alexandrov surfaces

2020 ◽  
Vol 20 (1) ◽  
pp. 139-148
Author(s):  
Joël Rouyer ◽  
Costin Vîlcu
Keyword(s):  
Distance Functions ◽  
Farthest Points ◽  
Baire Categories ◽  
Bounded Below

AbstractWe study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where most is used in the sense of Baire categories.

scholarly journals Nearest and farthest points in spaces of curvature bounded below

2010 ◽  
Vol 162 (7) ◽  
pp. 1364-1380 ◽  
Author(s):  
Rafa Espínola ◽  
Chong Li ◽  
Genaro López
Keyword(s):  
Farthest Points ◽  
Bounded Below

scholarly journals Moderate smoothness of most Alexandrov surfaces

2015 ◽  
Vol 26 (04) ◽  
pp. 1540004 ◽  
Author(s):  
Jin-ichi Itoh ◽  
Joël Rouyer ◽  
Costin Vîlcu
Keyword(s):  
Conical Points ◽  
Baire Categories ◽  
Bounded Below ◽  
Typical Point

We show that, in the sense of Baire categories, a typical Alexandrov surface with curvature bounded below by κ has no conical points. We use this result to prove that, on such a surface (unless it is flat), at a typical point, the lower and the upper Gaussian curvatures are equal to κ and ∞, respectively.

Assessing flood risk and detecting changes of salt water inflow in a coastal micro-tidal brackish marsh using GIS

2008 ◽  
Vol 37 (3) ◽  
Author(s):  
Jacek Urbański ◽  
Agata Ślimak
Keyword(s):  
Sea Level Rise ◽  
Sea Level ◽  
Flood Risk ◽  
Salt Water ◽  
Brackish Marsh ◽  
Distance Functions ◽  
Water Inflow ◽  
Small Range ◽  
Natural Environments ◽  
Baltic Coast

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.

Some results on farthest points

2016 ◽  
Vol 46 (1) ◽  
pp. 207-215
Author(s):  
F. Soleimany ◽  
M. Iranmanesh
Keyword(s):  
Farthest Points

Using clusterization principles for the selection of repair sections of main oil pipelines based on diagnostic data

2011 ◽  
Vol 8 (1) ◽  
pp. 201-210
Author(s):  
R.M. Bogdanov
Keyword(s):  
Cluster Analysis ◽  
Defect Density ◽  
Density Variation ◽  
Distance Functions ◽  
Oil Pipeline ◽  
Oil Pipelines ◽  
Classification Of Images ◽  
Main Oil Pipeline ◽  
Selection Of

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.

Some fixed point results for (β-ψ1-ψ2)-contractive conditions in ordered b-metric-like spaces

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4587-4612 ◽  
Author(s):  
S.K. Padhan ◽  
Rao Jagannadha ◽  
Hemant Nashine ◽  
R.P. Agarwal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Metric Spaces ◽  
Contractive Mapping ◽  
Existence Of Solution ◽  
Distance Functions ◽  
Point Boundary ◽  
Contractive Mappings ◽  
Altering Distance

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.

Minimal distributions in a stochastic partial ordering and bounds for Gaussian processes

1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Partial Ordering ◽  
Boundary Crossing ◽  
Conditional Probabilities ◽  
Life Distribution ◽  
Life Distributions ◽  
Bounded Below ◽  
Crossing Probabilities

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ W n be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let $W\in \mathcal {W}^{n}$ W ∈ W n and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in $W\in \mathcal {W}$ W ∈ W are considered.

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