• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.283-287
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• 2007

An extension of the contraction mapping theorem is provided in a Banach space setting to approximate fixed points of operator equations. Our approach is justified by numerical examples where our results apply whereas the classical contraction mapping principle cannot.

• 대한수학회보
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• 제38권1호
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• pp.175-182
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• 2001

In this paper we prove the existence and uniqueness of a mild solution of a functional differential equation with nonlocal condition using the semigroup theory and the Banach fixed point principle.

• 대한수학회보
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• 제54권3호
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• pp.715-729
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• 2017

In this paper, we investigate the existence and multiplicity of solutions for systems driven by two non-local integrodifferential operators with homogeneous Dirichlet boundary conditions. The main tools are the Saddle point theorem, Ekeland's variational principle and the Mountain pass theorem.

• 한국수학사학회지
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• 제14권2호
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• pp.77-92
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• 2001

P. Dirac's contribution to the advent of the modern quantum mechanics is undeniable. His main research guideline is the principle of mathematical beauty. What is this principle on the earth\ulcorner Are there distinctive features between pure mathematician's mind and theoretical physicist' mind about the mathematical beauty\ulcorner These problems will be analyzed with respect to Dirac's case which can reflect a historical interrelationship between science and philosophy.

• 대한수학회논문집
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• 제20권2호
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• pp.381-393
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• 2005

We consider a type of large deviation principle obtained by Freidlin and Wentzell for the solution of Stochastic differential equations in a conuclear space. We are using exponential tail estimates and exit probability of a Ito process. The nuclear structure of the state space is also used.

• 대한수학회논문집
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• 제34권2호
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• pp.495-506
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• 2019

Motivated by Bloch's principle, we prove a value distribution result for meromorphic functions which is related to Hayman's alternative in certain sense.

• East Asian mathematical journal
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• 제40권1호
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• pp.37-50
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• 2024

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

• 한국수학교육학회지시리즈A:수학교육
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• 제55권2호
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• pp.193-208
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• 2016

This study analyzes the likelihood principle and elicits an educational implication. As a result of analysis, this study shows that Frequentist and Bayesian interpret the principle differently by assigning different role to that principle from each other. While frequentist regards the principle as 'the principle forming a basis for statistical inference using the likelihood ratio' through considering the likelihood as a direct tool for statistical inference, Bayesian looks upon the principle as 'the principle providing a basis for statistical inference using the posterior probability' by looking at the likelihood as a means for updating. Despite this distinction between two methods of statistical inference, two statistics schools get clues to compromise in a regard of using frequency prior probability. According to this result, this study suggests the statistics education that is a help to building of students' critical eye by their comparing inferences based on likelihood and posterior probability in the learning and teaching of updating process from frequency prior probability to posterior probability.

• 산업기술연구
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• 제28권B호
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• pp.193-198
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• 2008

When the existing polder levee was constructed, the river's numerical analysis decided the bank raise by applying the planned flood stage or by using the result from the sectional 1st dimensional numerical analysis. But, it was presented that there is a limitation in the 1st dimensional value analysis when the structure like the polder levee obstructs the special shaped running water flow. Therefore, in order to verify the numerical value applicability when the polder levee is constructed, this report compared each other through the 1st and 2nd dimensional numerical analysis and the mathematical principle model laboratory. In case of the polder levee construction through the numerical analysis and the mathematical principle model laboratory, it was decided that there was no big problem in the 1st dimensional numerical analysis applied design, considering the uncertainty of mathematical principle analysis though the first dimensional numerical analysis was calculated a little bigger than the second. But, after construction, it was found that the water level deviation of the 1st, 2nd occurred biggest at the place where the flow was divided into two. Also, as a result of comparing the 1st, 2nd dimensional numerical analysis with the mathematical principle model laboratory, it was confirmed that the 1st numerical analysis applied design decreased the modal safety largely, as the left side water level was calculated smaller more than 0.5m in case of the 1st dimensional numerical analysis.

• 대한수학회보
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• 제59권4호
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• pp.961-977
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• 2022

In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.