• Korean Journal of Mathematics
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• v.17 no.3
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• pp.237-244
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• 2009

In this paper, we define property ($C_k$) and show that Property ($C_k$) implies property ($C_{k+1}$). The converse does not hold. Moreover, we prove that property ($C_k$) implies the Banach-Saks property.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.505-511
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• 2015

In this paper, we investigate relationships among property ($k-{\beta}$), weak property (${\beta}_k$), k-nearly uniformly convexity and property ($A_k$).

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1345-1356
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• 2017

For a given number field K, we show that the ranks of elliptic curves over K are uniformly finitely bounded if and only if the weak Mordell-Weil property holds in all (some) ultrapowers $^*K$ of K. We introduce the nonstandard weak Mordell-Weil property for $^*K$ considering each Mordell-Weil group as $^*{\mathbb{Z}}$-module, where $^*{\mathbb{Z}}$ is an ultrapower of ${\mathbb{Z}}$, and we show that the nonstandard weak Mordell-Weil property is equivalent to the weak Mordell-Weil property in $^*K$. In a saturated nonstandard number field, there is a nonstandard ring of integers $^*{\mathbb{Z}}$, which is definable. We can consider definable abelian groups as $^*{\mathbb{Z}}$-modules so that the nonstandard weak Mordell-Weil property is well-defined, and we conclude that the nonstandard weak Mordell-Weil property and the weak Mordell-Weil property are equivalent. We have valuations induced from prime numbers in nonstandard rational number fields, and using these valuations, we identify two nonstandard rational numbers.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.135-140
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• 2006

The paper by Paik (1985) introduced a structural property of the designs which was related to the concordance matrix $NN^{t}$ of the design. This special property was termed Property-C. The designs which have Property-C need not calculation of the generalize inverse of C matrix for solution of reduced normal equation. Paik also mentioned that some block designs belong to Property-C. This paper show the Extended Group Divisible designs defined by Hinkelmann (1964) are included in Property-C.

• Journal of the Chungcheong Mathematical Society
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• v.15 no.1
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• pp.61-73
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• 2002

We consider the inverse shadowing property of a dynamical system which is an "inverse" form of the shadowing property of the system. In particular, we show that every Morse-Smale system f on a compact smooth manifold has the inverse shadowing property with respect to the class $\mathcal{T}_h(f)$ of continuous methods generated by homeomorphisms, but the system f does not have the inverse\mathrm{T} shadowing property with respect to the class $\mathcal{T}_c(f)$ of continuous methods.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.581-588
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• 2016

Komuro [3] proved that geometric Lorentz attractor does not satisfy the shadowing property. In this paper we study the condition under which geometric Lorenz attractor has the orbital shadowing property that is weaker than the shadowing property.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.53-63
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• 2000

The inverse shadowing property of a dynamical system is an "inverse" form of the shadowing property of the system. Recently, Kloeden and Ombach proved that if an expansive system on a compact manifold has the shadowing property then it has the inverse shadowing property. In this paper, we study topological stability of the inverse shadowing dynamical systems. In particular, we show that if an expansive system on a compact manifold has the inverse shadowing property then it is topologically stable, and so it has the shadowing property.

• Journal of Korean Institute of Industrial Engineers
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• v.41 no.6
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• pp.559-571
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• 2015

To strengthen competences, most of firms have co-operated with external partners. This increases the possibility of unexpected conflicts between firms due to the intellectual property litigation. A suitable intellectual property strategy for firms has to be developed to settle this issue. This study aims to analyze an utilization of intellectual property strategy in firms, and tries to suggest a concept of IP roadmap to support intellectual property strategy planning aligned with technology planning process. For the purposes, we derive five types of intellectual property strategy of firms using Korea Innovation Survey. Then, we explore significant affecting factors using a decision-tree and conduct in-depth analysis for them. Lastly, we suggest a concept of IP roadmap, which can be a supporting tool for developing intellectual property strategy in firms, based on analysis results.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1519-1525
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• 2010

In this paper, we define property ($D_k$) and get the following strict implications. $$(UC){\Rightarrow}(D_2){\Rightarrow}(D_3){\Rightarrow}{\cdots}{\Rightarrow}(D_{\infty}){\Rightarrow}(BS)$$.

• Journal of Information Processing Systems
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• v.13 no.5
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• pp.1103-1125
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• 2017

This paper aims to extract an ObjectProperty-UsageMethod relation, in particular the HerbalMedicinalProperty-UsageMethod relation of the herb-plant object, as a semantic relation between two related sets, a herbal-medicinal-property concept set and a usage-method concept set from several web documents. This HerbalMedicinalProperty-UsageMethod relation benefits people by providing an alternative treatment/solution knowledge to health problems. The research includes three main problems: how to determine EDU (where EDU is an elementary discourse unit or a simple sentence/clause) with a medicinal-property/usage-method concept; how to determine the usage-method boundary; and how to determine the HerbalMedicinalProperty-UsageMethod relation between the two related sets. We propose using N-Word-Co on the verb phrase with the medicinal-property/usage-method concept to solve the first and second problems where the N-Word-Co size is determined by the learning of maximum entropy, support vector machine, and naïve Bayes. We also apply naïve Bayes to solve the third problem of determining the HerbalMedicinalProperty-UsageMethod relation with N-Word-Co elements as features. The research results can provide high precision in the HerbalMedicinalProperty-UsageMethod relation extraction.