• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.725-743
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• 2017

We prove that there exist foliations whose leaves are the maximal integral null manifolds immersed as submanifolds of indefinite locally conformal cosymplectic manifolds. Necessary and sufficient conditions for such leaves to be screen conformal, as well as possessing integrable distributions are given. Using Newton transformations, we show that any compact ascreen null leaf with a symmetric Ricci tensor admits a totally geodesic screen distribution. Supporting examples are also obtained.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.149-157
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• 2015

We show that $C^1$-generically, the shadowable chain component of a $C^1$-vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.

• 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.9 no.2
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• pp.261-264
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• 1994

Throughout this paper, all rings are assumed to be commutative with identity. By a local ring (R, m), we mean a Noetherian ring R which has the unique maximal ideal m. By dim(R) we always mean the Krull dimension of R. Let I be an ideal in a ring R and t an indeterminate over R. Then the Rees algebra R[It] is defined to be(omitted)

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.45-52
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• 2013

We show that a nontrivial transitive set is $C^1$-stably limit shadowable if and only if the transitive set is hyperbolic.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.147-152
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• 1998

In this paper, we shall investigate the admittance of a fixed point free deformation(FPFD) on the locally nilpotent spaces when ${\pi}_1(X)$ is infinite. More precisely, for $X{\in}(S_{{\ast}{LN}})$ with ${\pi}_1(X)$ infinite, we prove the admittance of a FPFD where ${\pi}_1(X)$ has the maximal condition on normal subgroups, or ${\pi}_1(X)$ satisfies either the max-${\infty}$ or min-${\infty}$ for non-nilpotent subgroups where $S_{{\ast}{LN}}$ denotes the category of the locally nilpotent spaces and base point preserving continuous maps.

• Journal of the Korean Data and Information Science Society
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• v.14 no.3
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• pp.707-714
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• 2003

Because of complex aliasing, nonregular designs have traditionally been used for screening only main effects. However, complex aliasing actually may allow some interactions entertained and estimated without making additional runs. According to hierarchical principle, the minimum aberration has been used as an important criterion for selecting regular fractional factorial designs. The criterion is not applicable to nonregular designs. In this paper, we give a criterion for choosing fractional factorial designs based on the fan theory. The criterion is focused on the partial ordering given by set inclusion on estimable sets which is called leaves.

• Journal of Communications and Networks
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• v.16 no.6
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• pp.667-676
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• 2014

Connectivity is a crucial quality of service measure in wireless sensor networks. However, the network is always at risk of being split into several disconnected components owing to the sensor failures caused by various factors. To handle the connectivity problem, this paper introduces an in-advance mechanism to prevent network partitioning in the initial deployment phase. The approach is implemented in a distributed manner, and every node only needs to know local information of its 1-hop neighbors, which makes the approach scalable to large networks. The goal of the proposed mechanism is twofold. First, critical nodes are locally detected by the critical node detection (CND) algorithm based on the concept of maximal simplicial complex, and backups are arranged to tolerate their failures. Second, under a greedy rule, topological holes within the maximal simplicial complex as another potential risk to the network connectivity are patched step by step. Finally, we demonstrate the effectiveness of the proposed algorithm through simulation experiments.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.103-108
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• 2015

In this paper we prove that $C^1$-generically, if a diffeomorphism f on a closed $C^{\infty}$ manifold M satisfies weak specification on a locally maximal set ${\Lambda}{\subset}M$ then ${\Lambda}$ is hyperbolic for f. As a corollary we obtain that $C^1$-generically, every diffeomorphism with weak specification is Anosov.