相关论文: Convexity and Freezing Sets in Digital Topology
We continue the study of freezing sets for digital images introduced in [4, 2, 3]. We prove methods for obtaining freezing sets for digital images (X, c_i) for X \subset Z^2 and i \in {1, 2}. We give examples to show how these methods can…
Freezing sets and cold sets have been introduced as part of the theory of fixed points in digital topology. In this paper, we introduce a generalization of these notions, the limiting set, and examine properties of limiting sets.
Cold sets and freezing sets belong to the theory of (approximate) fixed points for continuous self-maps on digital images. We study some properties of cold sets for digital images in the digital plane, and we examine some relationships…
Cone and suspension constructions have been introduced in digital topology, modeled on those of classical topology. For digital cones and suspensions, and for some related digital images, we find (m, n)-limiting sets; especially (0,…
We use results of [6] to enlarge our knowledge of the approximate fixed point property (AFPP) for digital images in $\mathbb{Z}^2$. In particular, we study conditions under which the union of two convex digital disks has the AFPP.
We develop new tools for the construction of fixed point sets in digital topology. We define excludable points and show that these may be excluded from all freezing sets. We show that articulation points are excludable. We also present…
We show how to obtain freezing sets for digital images in $\mathbb{Z}^n$ for arbitrary $n$, using the $c_1$ and $c_n$ adjacencies.
We study how the properties of irreducibility and rigidity in digital images interact with Cartesian products, wedges, and cold and freezing sets.
We examine the relationship between convexity and the approximate fixed point property (AFPP) for digital images in Z^2.
In this article, we investigate some properties of the coincidence point set of digitally continuous maps. Following the Rosenfeld graphical model which seems more combinatorial than topological, we expect to achieve results that might not…
We present some complexity results concerning the problems of covering a graph with $p$ convex sets and of partitioning a graph into $p$ convex sets. The following convexities are considered: digital convexity, monophonic convexity,…
Digital topological methods are often used on computing the topological complexity of digital images. We give new results on the relation between reducibility and digital contractibility in order to determine the topological complexity of a…
Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…
With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as…
We define LCL decompositions of the plane and investigate the advantages of using such decompositions in the context of digital topology. We show that discretization schemes based on such decompositions associate, to each LCL tiling of the…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
Digital topology has its own working conditions and sometimes differs from the normal topology. In the area of topological robotics, we have important counterexamples in this study to emphasize this red line between a digital image and a…
We give exact and approximation algorithms for two-center problems when the input is a set $\mathcal{D}$ of disks in the plane. We first study the problem of finding two smallest congruent disks such that each disk in $\mathcal{D}$…
Theories of rough sets and soft sets are powerful mathematical tools for modelling various types of vagueness. Hybrid model combining a rough set with a soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In this…
In this paper, we study a particular conservative standard map in complex dimension 2. In this example, Siegel disks can be visualized and analyzed numerically as to the smoothness of their boundaries. We formulate and numerically support…