• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.901-906
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• 2013

In this paper, we show that if a nontrivial transitive set is $C^1$-stably measure expansive, then it admits a dominated splitting.

• Geomechanics and Engineering
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• v.8 no.5
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• pp.687-706
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• 2015

Methods commonly used to evaluate the improvement of lime-treated expansive soil include swelling characteristics and unconfined compressive strength. In the field, lime-treated expansive soils are in compacted unsaturated state. Soil water characteristic curves (SWCCs) represent a key parameter to interpret and describe the behavior of unsaturated expansive soil. This paper investigates the use of SWCC as a technique to evaluate improvements acquired by expansive soil after lime treatment. Three different lime contents were considered 2%, 4% and 6% by dry weight of clay. Series of tests were performed to determine the SWCC for the different lime content under curing periods of 7 and 28 day. Correlations between key features of the soil water characteristic curves of lime treated expansive soils and basic engineering behavior such as swelling characteristics and unconfined compression strength were established. Test results revealed that initial slope ($S_1$), saturated water content ($w_{sat}$), and air entry value (AEV) play an important role in reflecting improvement in engineering behavior achieved by lime treatment.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1131-1142
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• 2018

A notion of measure expansivity for homeomorphisms was introduced by Morales recently as a generalization of expansivity, and he obtained many interesting dynamic results of measure expansive homeomorphisms in [8]. In this paper, we introduce a concept of weak measure expansivity for homeomorphisms which is really weaker than that of measure expansivity, and show that a diffeomorphism f on a compact smooth manifold is $C^1$-stably weak measure expansive if and only if it is ${\Omega}$-stable. Moreover we show that $C^1$-generically, if f is weak measure expansive, then f satisfies both Axiom A and the no cycle condition.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.377-384
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• 2015

It is well known that the entropy map is upper semi-continuous for expansive homeomorphisms on a compact metric space. Recently, Morales [3] introduced the notion of measure expansiveness which is general than that of expansiveness. In this paper, we prove that the entropy map is upper semi-continuous for measure expansive homeomorphisms.

• Proceedings of the Korea Concrete Institute Conference
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• 1999.10a
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• pp.585-588
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• 1999

This study is performed to verify the effect of CSA expansive additives for concrete by material properties test and 4 point-bendig test of RC slabs. The result shows that the variations of compress strength, bending strength, and modulus of elasticity of expansive concrete are the same as those of plain concrete. And the crack load of RC slabs with expansive concrete are increased in comparision with that of plain concrete, but the ultimate strength of RC slabs with expansive concrete is decreased.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1329-1334
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• 2019

We define the concept of a generator for a ${\mathbb{Z}}^k$-action T and show that T is expansive if and only it has a generator. Further, we prove several properties of a ${\mathbb{Z}}^k$-action including that the least upper bound of the set of expansive constants is not an expansive constant.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.259-269
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• 2021

We shall study the following. Let 𝜙 be an expansive flow on a compact TVS-cone metric space (X, d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space [?].

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.987-998
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• 2023

It is shown that every continuum-wise expansive C¹ generic vector field X on a compact connected smooth manifold M satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a C¹ generic vector field X on a compact connected smooth manifold M is hyperbolic. Moreover, every continuum-wise expansive C¹ generic divergence-free vector field X on a compact connected smooth manifold M is Anosov.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.345-349
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• 2014

We show that $C^1$-generically, a differentiable map is positively measure expansive if and only if it is expanding.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.151-155
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• 2016

In this paper, we show that if a continuum-wise expansive homeomorphism on a compact connected metric space is shadowing then it is topologically stable. This generalizes the main result of [4].