The Chaotic Motion of a Rigid Body Rotating About a Fixed Point

El-Sabaa, F. M.; El-Tarazi, M. N.

doi:10.1007/978-1-4684-5997-5_53

Cited by 2 publications

(4 citation statements)

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“…)) has at least the elements 9, 10 because there are at least three points in C 2, 4 8 ⊂ C n,8 k ∨ C n,4 k that satisfies the condition (1) of ( 13) and (C 3f), we conclude that F(Con 8 (C 2,9 8 ∨ C 2,7 8 )) is not perfect.…”

Section: Examplementioning

confidence: 81%

“…For instance, we obtain the following [12,13]: (3,2,18), (3,3,26); (4,1,8), (4, 2, 32), (4,3,64), (4,4,80); and…”

Section: Preliminariesmentioning

confidence: 99%

“…Let DTC(k) be the category consisting of the set of digital images (X, k), denoted by Ob(DTC(k)), and the set of k-continuous maps of (X, k), denoted by Mor(DTC(k)) (for more details see Section 2). Motivated by the study of homotopy fixed point sets in Reference [1], we are recently interested in the set of cardinal numbers of fixed point sets of all k-continuous maps of a digital image (X, k) [2,3] because this topic can be used in studying some "motions of a rigid body with a fixed point" [4,5] from the viewpoint of digital geometry. To be specific, given a digital image (X, k) in Ob(DTC(k)), a paper [2] explored some features of (k-homotopy) fixed point sets related to this issue in a DTC(k) setting.…”

Section: Introductionmentioning

confidence: 99%

“…(Q5) Given a simple k-path (P, k) with a length d, what conditions make F(Con k (W ∨ P)) perfect? (Q6) How can we formulate F(Con k (W ∨ t-times C n, 4 k ∨ • • • ∨ C n,4 k ))? (Q7) Is F(Con k (X)) a digital k-homotopy invariant?…”

Section: Introductionmentioning

confidence: 99%

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Fixed Point Sets of k-Continuous Self-Maps of m-Iterated Digital Wedges

Han

2020

Mathematics

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Let Ckn,l be a simple closed k-curves with l elements in Zn and W:=Ckn,l∨⋯∨Ckn,l︷m-times be an m-iterated digital wedges of Ckn,l, and F(Conk(W)) be an alignment of fixed point sets of W. Then, the aim of the paper is devoted to investigating various properties of F(Conk(W)). Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of Ckn,l, denoted by F(Conk(Ckn,l)), where l(≥7) is an odd natural number and k≠2n. Secondly, given a digital image (X,k) with X♯=n, we find a certain condition that supports n−1,n−2∈F(Conk(X)). Thirdly, after finding some features of F(Conk(W)), we develop a method of making F(Conk(W)) perfect according to the (even or odd) number l of Ckn,l. Finally, we prove that the perfectness of F(Conk(W)) is equivalent to that of F(Conk(Ckn,l)). This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k-connected digital images (X,k) such that X♯≥2.

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Section: Examplementioning

confidence: 81%

“…For instance, we obtain the following [12,13]: (3,2,18), (3,3,26); (4,1,8), (4, 2, 32), (4,3,64), (4,4,80); and…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fixed Point Sets of k-Continuous Self-Maps of m-Iterated Digital Wedges

Han

2020

Mathematics

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Fixed Point Sets of Digital Curves and Digital Surfaces

Han¹

2020

Mathematics

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Given a digital image (or digital object) (X,k), we address some unsolved problems related to the study of fixed point sets of k-continuous self-maps of (X,k) from the viewpoints of digital curve and digital surface theory. Consider two simple closed k-curves with li elements in Zn, i∈{1,2},l1⪈l2≥4. After initially formulating an alignment of fixed point sets of a digital wedge of these curves, we prove that perfectness of it depends on the numbers li,i∈{1,2}, instead of the k-adjacency. Furthermore, given digital k-surfaces, we also study an alignment of fixed point sets of digital k-surfaces and digital wedges of them. Finally, given a digital image which is not perfect, we explore a certain condition that makes it perfect. In this paper, each digital image (X,k) is assumed to be k-connected and X♯≥2 unless stated otherwise.

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The Chaotic Motion of a Rigid Body Rotating About a Fixed Point

Cited by 2 publications

References 3 publications

Fixed Point Sets of k-Continuous Self-Maps of m-Iterated Digital Wedges

Fixed Point Sets of k-Continuous Self-Maps of m-Iterated Digital Wedges

Fixed Point Sets of Digital Curves and Digital Surfaces

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