• Journal of Information Technology Applications and Management
• /
• v.18 no.4
• /
• pp.41-53
• /
• 2011

Trust prediction between users in social network based on the trust propagation assumes properties of transitivity and composability of trust propagation. But it has been hard to find studies which test on how those properties have been operated in real social network. This study aims to validate if the longer the distance of trust paths and the less the numbers of trust paths, the higher prediction error occurs using two real social network data set. As a result, the longer the distance of trust paths, we can find higher prediction error when predicting level of trust between source and target users. But we can not find decreasing trend of prediction error though the possible number of trust paths between source and target users increases.

• Kyungpook Mathematical Journal
• /
• v.62 no.2
• /
• pp.213-227
• /
• 2022

We discuss the relation between units and nilpotents of a ring, concentrating on the transitivity of units on nilpotents under regular group actions. We first prove that for a ring R, if U(R) is right transitive on N(R), then Köthe's conjecture holds for R, where U(R) and N(R) are the group of all units and the set of all nilpotents in R, respectively. A ring is called right UN-transitive if it satisfies this transitivity, as a generalization, a ring is called unilpotent-IFP if aU(R) ⊆ N(R) for all a ∈ N(R). We study the structures of right UN-transitive and unilpotent-IFP rings in relation to radicals, NI rings, unit-IFP rings, matrix rings and polynomial rings.

• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.3
• /
• pp.341-355
• /
• 2017

This paper is devoted to some dynamical properties such as transitivity, mixing and specification of two discrete dynamical systems (X, f) and ($2^X$, ${\bar{f}}$) on compact metric spaces.

• Communications of the Korean Mathematical Society
• /
• v.25 no.1
• /
• pp.97-104
• /
• 2010

The article is devoted to exhibit some general properties of strong chain recurrent set and strong chain transitive components for a continuous map f on a compact metric space X. We investigate the relation between the weak shadowing property and strong chain transitivity. It is shown that a continuous map f from a compact metric space X onto itself with the average shadowing property is strong chain transitive.

• Journal of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.837-851
• /
• 2014

We consider ${\omega}$-chaos as defined by S. H. Li in 1993. We show that c-dense ${\omega}$-scrambled sets are present in every transitive system with two-sided limit shadowing property (TSLmSP) and that every transitive map on topological graph has a dense Mycielski ${\omega}$-scrambled set. As a preliminary step, we provide a characterization of dynamical properties of maps with TSLmSP.

• Communications of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.1249-1258
• /
• 2022

In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

• Communications of the Korean Mathematical Society
• /
• v.24 no.3
• /
• pp.361-366
• /
• 2009

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2004.10a
• /
• pp.351-354
• /
• 2004

Using the idea of generalized intuitionistic fuzzy set, we study the notion of generalized intuitionistic fuzzy matrices as a generalization of fuzzy matrices, We show that some properties of a square generalized intuitionistic fuzzy matrix such as reflexivity, transitivity and circularity are carried over to the adjoint generalized intuitionistic fuzzy matrix.

• Journal of the Korean Mathematical Society
• /
• v.58 no.4
• /
• pp.977-1000
• /
• 2021

Consider the high dimensional torus 𝕋ⁿ and the set 𝜺 of its endomorphisms. We construct a map in 𝜺 that is robustly transitive if 𝜺 is endowed with the C² topology but is not robustly transitive if 𝜺 is endowed with the C¹ topology.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.247-262
• /
• 2024

In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space X, a syndetically transitive semiflow (T, X, 𝜋) having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a T₃ space X, a transitive, nonminimal semiflow (T, X, 𝜋) having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.