Results 21 to 30 of about 1,153 (175)
LABELING OF N-DIMENSIONAL IMAGES WITH CHOOSABLE ADJACENCY OF THE PIXELS
Image Analysis and Stereology, 2011 The labeling of discretized image data is one of the most essential operations in digital image processing. The notions of an adjacency system of pixels and the complementarity of two such systems are crucial to guarantee consistency of any labeling ...
Kai Sandfort, Joachim Ohser
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A ternary relation for structuring the digital plane
ITM Web of Conferences, 2017 We discuss certain ternary relations, called plain, and show that each of them induces a connectedness on its underlying set. This connectedness allows for definitions of concepts of simple closed and Jordan curves.
Šlapal Josef
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A notion of continuity in discrete spaces and applications
Applied General Topology, 2013 We propose a notion of continuous path for locally finite metric spaces, taking inspiration from the recent development of A-theory for locally finite connected graphs.
Valerio Capraro
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Discrete Jordan Curve Theorem: A proof formalized in Coq with hypermaps [PDF]
, 2008 This paper presents a formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar subdivisions, formal specifications and proofs assisted by the Coq system. Fundamental properties are proven by
Dufourd, Jean-Francois
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Properties of а pseudo-harmonic function on closed domain
Pracì Mìžnarodnogo Geometričnogo Centru, 2015 Let f be a pseudo-harmonic function defined on $k-$connected oriented closed domain D whose boundary consists of closed Jordan curves. We remind that this class of functions coincides with continuous functions which have a finitely many critical points ...
Ірина Аркадіївна Юрчук
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Galois connections between sets of paths and closure operators in simple graphs
Open Mathematics, 2018 For every positive integer n,we introduce and discuss an isotone Galois connection between the sets of paths of lengths n in a simple graph and the closure operators on the (vertex set of the) graph.
Šlapal Josef
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Simple closed curves contained in ε-boundaries of planar sets
Applied General TopologyThe ε-boundary of a set A ⊆ R2 is the set { p ∈ R2 : ρ(p,A) = ε } , where ρ is the Euclidean distance. We prove that if A,B ⊆ R2 are nonempty, connected sets, A is bounded, and 0< ε < ρ(A,B), then the ε-boundary of A contains a simple closed curve (aka a
Mikhail Patrakeev, Aleksei Volkov
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, 2017 Title: The Jordan Curve Theorem Author: Jan Dudák Department: Department of Mathematical Analysis Supervisor: Mgr. Benjamin Vejnar, Ph.D., Department of Mathematical Analysis Abstract: The crucial part of this work is the proof of the Jordan curve ...
Dudák, Jan
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A nonstandard proof of the Jordan curve theorem [PDF]
Pacific Journal of Mathematics, 1971 In this paper a proof of the Jordan curve theorem will be presented. Some familiarity with the basic notions of nonstandard analysis is assumed. The rest of the paper is selfcontained except for some standard theorems about polygons. The theorem will be proved in what ought to be a natural way: by approximation by polygons.
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Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
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