• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.263-270
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• 2012

We prove that a locally maximal chain transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is shadowable.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.613-619
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• 2012

In this paper, we prove that locally maximal transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit weak shadowable.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.389-394
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• 2016

Let $f:M{\rightarrow}M$ be a diffeomorphism on a closed $C^{\infty}\;d({\geq}2)$ dimensional manifold M. For $C^1$-generic f, if a diffeomorphism f satisfies the local star condition on a transitive set, then it is hyperbolic.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.285-291
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• 2011

In this paper, we show that if a transitive set ${\Lambda}$ is $C^1$-stably expansive, then ${\Lambda}$ admits a dominated splitting.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.1
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• pp.80-87
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• 1989

Many Traditional Algebraic Analyses of preference and choice for a finite set of alternatives have been based on binary choices. They have assumed that the binary preference information given by a decision maker is transitive. However, there is considerable evidence that many relations that might occur as preference relations cannot be presented as transitive relations. To construct transitive binary comparisons from intransitive ones, we suggest the notion of superior set, which helps us to understand the structure of intransitive binary comparisons. We also provide a heuristic method to construct transitive binary comparisons. And some merits merits of the suggested method over the existing methods are also discussed.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.6
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• pp.3316-3332
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• 2019

In a transitive signature scheme, a signer wants to authenticate edges in a dynamically growing and transitively closed graph. Using transitive signature schemes it is possible to authenticate an edge (i, k), if the signer has already authenticated two edges (i, j) and (j, k). That is, it is possible to make a signature on (i, k) using two signatures on (i, j) and (j, k). We propose the first transitive signature schemes for undirected graphs from lattices. Our first scheme is provably secure in the random oracle model and our second scheme is provably secure in the standard model.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.31 no.3
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• pp.509-516
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• 2021

The transitive signature scheme is a technique that can be very useful when authenticating edges in a graph that is transitively closed. In other words, when there is an authentication value for an edge (i, j) and an authentication value for an edge (j, k), the authentication value for the edge (i, k) can also be calculated immediately without any separate authentication procedure through a transitive signature. In this paper, we propose the first identity-based transitive signature scheme. Our scheme is based on the lattice problem.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.657-661
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• 2016

Let $f:X{\rightarrow}X$ be a continuous surjection of a compact metric space and let ($X_f,{\tilde{f}}$) be the inverse limit of a continuous surjection f on X. We show that for a continuous surjective map f, if f has the asymptotic average, the average shadowing, the ergodic shadowing property then ${\tilde{f}}$ is topologically transitive.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1169-1183
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• 2015

We describe generalized Cayley graphs of rectangular groups, so that we obtain (1) an equivalent condition for two Cayley graphs of a rectangular group to be isomorphic to each other, (2) a necessary and sufficient condition for a generalized Cayley graph of a rectangular group to be (strong) connected, (3) a necessary and sufficient condition for the colour-preserving automorphism group of such a graph to be vertex-transitive, and (4) a sufficient condition for the automorphism group of such a graph to be vertex-transitive.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2029-2041
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• 2017

The main aim of this article is to study symmetric (v, k, ${\lambda}$) designs admitting a flag-transitive and point-primitive automorphism group G whose socle is PSU(3, q). We indeed show that such designs must be complete.