• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1161-1178
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• 2018

In this paper, we consider the Cauchy problem for a class of nonlinear sixth-order wave equation. The global existence and the finite time blow-up for the problem are proved by the potential well method at both low and critical initial energy levels. Furthermore, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level by introducing a new stable set.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.37-50
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• 2014

Using variational methods, we prove some results on the nonexistence and multiplicity of weak solutions for a class of semilinear elliptic systems of two equations involving Grushin type operators with sign-changing nonlinearities. We also shows that the similar results can be obtained for systems of m equations, where m is arbitrary.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.351-360
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• 2005

This paper finds a new class of generalized convex function which satisfies the following properties: It's level set is $\eta$-convex set; Every feasible Kuhn-Tucker point is a global minimum; If Slater's constraint qualification holds, then every minimum point is Kuhn-Tucker point; Weak duality and strong duality hold between primal problem and it's Mond-Weir dual problem.

• Proceedings of the Korean Information Science Society Conference
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• 2001.10a
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• pp.481-483
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• 2001

클래스의 응집도를 측정하기 위한 여러 연구들이 제안되었지만, 이런 연구들은 데이터 상호작용에 의해 응집도를 측정하므로 메소들간에 데이터 상호작용이 없지만 객체의 또 다른 속성들을인 데이터들이 함께속하는 경우를 고려하지 못하고 있다. 따라서 본 연구에서는 데이터 상호작용이 없는 경우를 고려하고, 또한 클래스 내의 멤버들과 멤버들간의 연결을 모두 고려하여 응집도를 측정할 수 있는 새로운 응집도 척도를인 강 클래스 응집도(Strong Class Cohesion: SCC)와 약 클래스 응집도(Weak Class Cohesion: WCC)를 제안하였다. 또한 기존 척도들과의 비교평가를 통해서 WCC와 SCC가 향상된 측정을 제시함을 보여 주었다.

• Communications of the Korean Mathematical Society
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• v.34 no.4
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• pp.1365-1388
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• 2019

In this paper we consider a class of nonlinear nonlocal parabolic equations involving p-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1529-1560
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• 2019

We are concerned with the following elliptic equations: $$(-{\Delta})^s_pu+V (x){\mid}u{\mid}^{p-2}u={\lambda}g(x,u){\text{ in }}{\mathbb{R}}^N$$, where $(-{\Delta})_p^s$ is the fractional p-Laplacian operator with 0 < s < 1 < p < $+{\infty}$, sp < N, the potential function $V:{\mathbb{R}}^N{\rightarrow}(0,{\infty})$ is a continuous potential function, and $g:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ satisfies a $Carath{\acute{e}}odory$ condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter ${\lambda}$ for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.

• Language and Information
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• v.12 no.2
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• pp.77-93
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• 2008

This paper examines a condition that licenses distributivity. Choe (1987) and Link (1998) have proposed an indefiniteness condition on distributivity. However, detecting counter-examples, Zimmermann (2002) has argued for a non-specificity condition. This paper primarily revises the indefiniteness/non-specificity condition. Observing that the systematic class of the exceptions belongs to weak definites proposed by Poesio (1994), I claim that the property that constrains distributivity is non-strong-definiteness. Based on Landman (2000), I further explain the non-strong-definiteness condition and argue that the condition does not need to be imposed on the grammar independently. The new condition naturally accounts for Spector's (2003) scopal asymmetry. Even more, defining donkey pronouns as weak definites, I cope with various properties of donkey sentences.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.48 no.1
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• pp.44-50
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• 2011

We propose a multi-class AdaBoost algorithm for en efficient classification of multi-class data in this paper. Traditional AdaBoost algorithm is basically a binary classifier and it has limitations when applied to multi-class data problems even though multi-class versions are available. In order to overcome the problems on the AdaBoost algorithm for multi-class classification problems, we devise an AdaBoost architecture with a training algorithm that utilizes multi-class classifiers for its weak classifiers instead of series of binary classifiers. Experiments on a image classification problem using collected Caltech Image Database are preformed. The results show that the proposed AdaBoost architecture can reduce its training time while maintaining its classification accuracy competitive when compared to Adaboost.M2.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.67-80
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• 2002

We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.465-475
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• 2016

We establish necessary and sufficient optimality conditions for a class of generalized nondifferentiable fractional optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.