• 한국콘텐츠학회논문지
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• 제5권5호
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• pp.140-144
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• 2005

본 논문에서는 퍼지측도가 공(空) 가법성을 갖는 경우 준노름퍼지 보적분의 거의모든점에서의 수렴정리가 성립함을 보였다.

• 대한수학회논문집
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• 제37권2호
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• pp.415-421
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• 2022

This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the M_α-integral using the M_α-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform M_α-strong Lusin condition was imposed.

• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

• 경영과학
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• 제15권2호
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• pp.153-159
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• 1998

Clustering or classification is a very fundamental task that may occur almost everywhere for the purpose of grouping. Optimal clustering is an example of very complicated combinatorial optimization problem and it is hard to develop a generally applicable optimal algorithm. In this paper we propose a general-purpose algorithm for the optimal clustering based on SA(simulated annealing). Among various iterative global optimization techniques imitating natural phenomena that have been proposed and utilized successfully for various combinatorial optimization problem, simulated annealing has its superiority because of its convergence property and simplicity. We first present a version of accelerated simulated annealing(ASA) and then we apply ASA to develop an efficient clustering algorithm. Application examples are also given.

• 대한수학회지
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• 제60권5호
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• pp.1057-1072
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• 2023

Let 𝜑 : ℝⁿ × [0, ∞) → [0, ∞) be a growth function and H^𝜑(ℝⁿ) the Musielak-Orlicz Hardy space defined via the non-tangential grand maximal function. A general summability method, the so-called 𝜃-summability is considered for multi-dimensional Fourier transforms in H^𝜑(ℝⁿ). Precisely, with some assumptions on 𝜃, the authors first prove that the maximal operator of the 𝜃-means is bounded from H^𝜑(ℝⁿ) to L^𝜑(ℝⁿ). As consequences, some norm and almost everywhere convergence results of the 𝜃-means, which generalizes the well-known Lebesgue's theorem, are then obtained. Finally, the corresponding conclusions of some specific summability methods, such as Bochner-Riesz, Weierstrass and Picard-Bessel summations, are also presented.